Every machine in every lab falls into one of three categories. The category tells you who has to be standing there before you switch it on.
Three categories, one question
Three categories, one question
Every piece of equipment in the lab is Category 1, 2 or 3. The
category answers one question: who has to be present before you switch it on?
Permission from an instructor is required in every case. What changes between categories is
when that permission can be given, and who has to be in the room while the machine is running.
Category 1
Permission may be given in advance. Work alone once you have it.
Category 2
Permission at the time of use. A peer must be present throughout.
Category 3
Permission at the time of use. A peer and an instructor must be present throughout.
Power down safely — turn off and disconnect the equipment from its power source.
Report issues immediately — notify the instructor of any broken or malfunctioning equipment.
Return and organize — put all equipment and tools back in their designated locations.
Restore to shutdown state — return the equipment to its original, safe configuration.
Clean thoroughly — remove all dust, chips, liquids and debris from the equipment and the work area.
The habit behind the last two is 5S — the same discipline,
named and made routine.
Safety/Universal Rules
Personal Protective Equipment
What you wear, and when. Eye protection is mandatory in the lab spaces at all times; the rest depends on the task.
Personal Protective Equipment
Personal Protective Equipment
Five topics. One of them — eye protection — applies the moment you walk
in. The rest are set by what you are doing.
Eyes
Always, in the lab spaces. No exceptions.
Hearing
Prolonged exposure to loud equipment.
Feet
Closed-toe shoes, always.
Respiratory
Any grinding or sanding; hazardous dust or fumes.
Clothing & hair
Always, near anything that rotates.
Eye protection; Watch out
Eye protection
Safety glasses are MANDATORY in the lab spaces at all times.
If you wear prescription glasses
Side shields that attach to your existing frames.
Oversized safety glasses that fit over corrective glasses.
Prescription safety glasses are also acceptable.
Lens requirements
Safety glasses must be clear or yellow tinted only.
Dark or shaded safety glasses are not acceptable for indoor lab use.
Must meet ANSI Z87.1 safety standards.
Hearing protection; Watch out
Hearing protection
Industry standard: shop tools nearly always require hearing protection in
professional settings. In a teaching lab the exposure is typically shorter than in production
work, but the protection still matters.
When to use it
Required for prolonged exposure to loud equipment — grinders, sanders, planers and similar.
The rule of thumb: if you have to raise your voice to be heard by someone at arm’s
length, it is loud enough to need protection. You do not need a meter, and most shop
tools fail this test the moment they start.
The numbers behind it
OSHA measures noise as an average across the working day, in A-weighted decibels
(dBA). Two figures matter:
85 dBA
The action level, averaged over 8 hours — the point at which a workplace must run a hearing conservation programme.
90 dBA
The permissible exposure limit, averaged over 8 hours.
Above 90 dBA the allowed time drops fast — every extra 5 dBA halves it:
90 dBA
8 hours
95 dBA
4 hours
100 dBA
2 hours
105 dBA
1 hour
110 dBA
30 minutes
115 dBA
15 minutes or less
Impact noise should not exceed 140 dB peak — a single hammer blow or
nail gun can reach it, and that damage is immediate rather than cumulative.
These are OSHA workplace limits (29 CFR 1910.95). NIOSH recommends a stricter
85 dBA limit that halves the allowed time every 3 dBA rather than every 5. Hearing loss
from noise does not come back, so treat these as ceilings, not targets.
Two types available
Earplugs
Small foam plugs inserted into the ear canal. Disposable or reusable. Available on request from the instructor.
Ear muffs
Over-ear cups covering the whole ear. Reusable and adjustable. Often preferred for intermittent use.
Both types significantly reduce harmful noise levels.
Foot protection
Foot protection
Minimum requirement: closed-toe shoes are MANDATORY — no sandals, no flip-flops, no open-toe footwear.
Recommended upgrades
Slip-resistant soles, for traction on surfaces that may be slippery.
Puncture-resistant soles, against sharp metal debris.
Steel-toe or composite-toe protection — recommended, not required.
Avoid
Canvas shoes or thin-soled footwear.
High heels or unstable footwear.
Anything that does not fully enclose your feet.
You will be standing for most of the lab period — choose something
supportive and comfortable.
Respiratory protection; Stop
Respiratory protection
MANDATORY when using any grinder or sander, and when working with materials
that produce hazardous dust.
Grinding galvanized material is PROHIBITED. Zinc fumes from galvanized steel
are toxic when heated.
Health hazards
Metal dust and particles cause respiratory irritation and long-term lung damage.
Wood dust can cause allergic reactions.
Dust and fumes are not the same problem, and they do not take the
same protection. The next section is the one that decides which you need.
Respiratory protection — what to wear; Stop; Watch out
Respiratory protection — what to wear
A dust mask does nothing against fumes or vapours. An N95 is a
particle filter. It does not stop gases, welding or brazing fume, solvent vapour, or
anything else you can smell. Wearing one while you can smell the air is not protection.
For dust — grinding, sanding, sawing
N95 mask
Filters 95% of airborne particles. The minimum for dusty work.
Half- or full-face respirator
Fitted with a particulate filter, for heavy or extended dust.
For fumes and vapours
You need an approved respirator with the right chemical cartridge, not a
dust mask. Ask the instructor which cartridge before you start.
A respirator only works if it seals. A loose mask, or a beard along the
seal, defeats it.
If there is no correct cartridge available, the job does not happen until
there is.
If you can smell fumes or taste particles, your protection is inadequate.
Stop work immediately and upgrade it — or stop the job.
Loose clothing and accessories catch in rotating machinery. That is how this
causes serious injury or death — it is not a dress code.
Prohibited
Loose-fitting clothing, or garments with dangling features — drawstrings, ties and similar.
Long sleeves, hoodies or jackets near rotating equipment.
ALL jewelry, except silicone wedding rings.
Neckties, scarves and lanyards.
Hair, and what to wear instead
Hair, and what to wear instead
Hair
Long hair must be secured back and kept away from equipment.
Use hair ties, clips or caps to prevent entanglement.
Recommended
Cotton or fire-retardant materials — preferred, not required.
Close-fitting, short-sleeved shirts.
Pants without excessive loose material.
Safety/Universal Rules
Lifting and Carrying
Team lifting above 40 lbs, and the technique that keeps you in control of the load. What usually defeats a lift is the size of the thing, not its weight.
Lifting Rules; Watch out
Lifting Rules
Get a second person for anything over 40 lbs. A gym weight plate is
45 lbs and nobody lifts one in pairs. Size — not weight — is what makes shop
materials hard to carry.
Forty pounds of aluminum bar is about four inches square and two feet long: you can hold it
against your chest, see over it, and set it down where you meant to. A twenty-foot piece of tube
can weigh less than that and still put half its length out in front of you, and a sheet of
plywood fills your arms and hides the floor you are walking on. Same weight, different job.
OSHA sets no weight limit — no standard says how much a person may
lift, only that a workplace be kept free of recognized hazards. The number everyone borrows
comes from NIOSH, the federal institute that researches workplace injury:
51 lbs with two hands under ideal conditions, cut for every way a real
lift is worse. Hold that same load at arm's length instead of against you and it rates about
20 lbs. Turning a quarter circle as you lift takes off another 30%, and
nothing good to grab takes off 10% more. A load much wider than your body is outside what the equation covers
at all — used there, it underestimates the hazard.
Team lifting is required for
Anything over 40 lbs.
Items lighter than 40 lbs but awkward in shape, size or balance.
Any object that feels unstable or is difficult to grip.
The 40 lb line is as much about dropping it as about your back.
A load you cannot fully control is a hazard to your feet, the floor, the workpiece and anyone
walking past — well before it is a hazard to your spine.
If you cannot hold it against your body and keep your back straight, it is too heavy
for you to lift alone — whatever the number says. Weight still wins in the end;
that point just sits somewhere different for every person and every shape.
Proper lifting technique; Checklist
Proper lifting technique
Plan the lift — clear your path and know where you are going.
Get close to the object before lifting.
Squat down using your leg muscles; keep your back straight.
Grip firmly with both hands; avoid awkward hand positions.
Lift smoothly using your legs, not your back.
Keep the load close to your body throughout the lift.
Setting it down
Use the same technique in reverse — squat down, do not bend over.
Place objects gently. Do not drop them.
Safety/Universal Rules
Electrical Safety
Why 50 V is a workplace control threshold, why 5 V can still burn you, the inspection required before every use, cords on the floor, and what to do when someone is shocked.
Electrical Sources
Electrical Sources
What hurts you at 5 V is not what hurts you at 240 V; one is a burn hazard
while the other is a shock hazard.
5 V / 12 V
The power supply on the bench, batteries, and the battery
pack out of a cordless drill. Lower shock risk, not a magic cutoff. Not below the
burn threshold.
120 V
Wall outlets. Dangerous — can cause serious injury or
death.
240 V / 480 V
Industrial equipment. Extremely dangerous — often
fatal.
Voltage tells you whether a circuit can push current through you. It does
not tell you what that circuit can do to a ring, a dropped tool or a shorted cell.
Those are two different hazards with two different thresholds. The next two sections are
about how each hazard changes.
Electrical — Shock Hazard; Stop
Electrical — Shock Hazard
There is no magic voltage at which shock suddenly becomes possible. A shock can be
painful without being life-threatening, and its severity depends on current, path, duration, and
your body’s resistance. Higher voltage can drive more current through the body, so the risk of
serious injury rises with it. In U.S. workplace rules, 50 volts is a common
control threshold: at or above it, live parts must be guarded and work near exposed live parts
requires specific controls.
OSHA requires live parts to be de-energized before you work on or near them — and then
says that “live parts that operate at less than 50 volts to ground need not be
deenergized if there will be no increased exposure to electrical burns or to explosion due to
electric arcs” (29 CFR 1910.333(a)(1)). Read that second
half again; the rest of this page hangs on it.
At or above the line, live parts must be guarded against accidental contact.
The rule is written for “electric equipment operating at 50 volts or more”
(29 CFR 1910.303(g)(2)(i)).
That number applies to DC as well as AC. The standard does not distinguish
between them, and OSHA has stated it “considers all voltages of 50 volts or above to be
hazardous” (interpretation letter, 4 September 2015).
NFPA 70E draws the same line. Below 50 V you may work live only where the
capacity of the source and any overcurrent protection have been considered and found
not to add burn or arc exposure (2024 edition, 110.2(B) Exception No. 5).
Supporting detail: Addendum 1 — “It’s not the voltage that gets you, it’s the current”.
Supporting detail: Addendum 2 — The international standards are not one number.
In this lab, use 50 V — AC or DC. It is the number OSHA enforces,
it is the most conservative of the figures above, and it assumes nothing about your skin being
dry or your hands being clean. If a circuit is at or above 50 V, it is not something you
work on live.
Electrical — Burn Hazard; Stop
Electrical — Burn Hazard
Below 50 V, the primary concern often shifts from shock to
short-circuit current. This is the half of the page people get wrong, because the
voltage people assume is harmless is the one nobody is careful with.
Look at what the exemption above is actually conditioned on. Not shock — burns
and arcs. NFPA 70E names the same condition as the capacity of the source.
Both standards are telling you that once you are under that workplace control threshold, the
question changes from how many volts to how many amps can this thing deliver into
a dead short.
Where the current comes from
A bench supply set to 5 V will deliver its full rated current into a
short without complaint. That is what the current limit is for — and if you have wound the
limit up to get a motor turning, you have wound the protection off.
A lithium cell or pack has almost no internal resistance. Shorted, a single
cell can dump tens of amps within milliseconds. A pack does considerably worse.
A lead-acid battery is rated in hundreds of cold-cranking amps — and
that is a 30-second load test, not a ceiling. A dead short pulls far more.
None of these can push meaningful current through your body at 12 V. All of them can push
hundreds of amps through a piece of metal — and metal carrying current it was never sized
for gets hot, fast.
Metal jewelry is the classic way this happens
ALL jewelry is already PROHIBITED here — see
clothing and jewelry. That rule was written for rotating machinery. It earns its keep a
second time on the bench, and OSHA writes it a second time for exactly this reason: conductive
jewelry “may not be worn if they might contact exposed energized parts”
(29 CFR 1910.333(c)(8)) — a rule that states no voltage
floor. The same sentence gives the way out: such articles may be worn if they are
“rendered nonconductive by covering, wrapping, or other insulating means.”
A ring or a metal watch band bridging a low-voltage source is a near-zero-resistance path
across something that can supply hundreds of amps. The ring becomes the heating element. This is
documented injury, not a story: a mechanic’s gold ring touched the positive terminal of a
12 V car battery while the wrench in his hand bridged the ring and the
negative terminal, and the result was a deep circumferential burn around the base of the finger
that needed a skin graft. A review of nine ring burns at one burn center found the same pattern:
the small size of the burn hides how bad it is, because a burn that wraps a
finger is far more likely to need grafting and to leave lasting loss of function than a burn of
the same area anywhere else.
You can drop a wrench. You cannot drop a ring.
The silicone wedding ring that the PPE rule allows is also the right answer
electrically: silicone does not conduct, so it cannot become the short.
A shorted lithium cell does not just get warm
An external short is one of the recognized triggers for thermal runaway
— the cell generates heat faster than it can shed it, and the outcome is
“extremely high temperatures, violent cell venting, smoke and fire” (UL Research
Institutes). Once it has started, disconnecting it does not stop it. The cell is
now its own energy source.
NEVER leave loose cells or packs where metal can bridge the terminals
— a drawer with tools in it, a pocket with keys in it, a bin with offcuts in it. Federal
transport rules require lithium cells and batteries to be packed so their terminals cannot short
(49 CFR 173.185). The reason that rule exists is the reason to do the same
thing on your own bench.
A cell that has been shorted, dropped, crushed, punctured or has swollen is out of
service. Tell the instructor. Do not put it back on charge to find out. See
Fire Safety.
The sentence to take away: low voltage does not mean low energy.
Voltage helps determine whether a circuit can shock you. Current decides whether it can burn
you — and current is set by what the source can deliver and what is in the path,
not by the number printed on the front of the supply.
Electrical Conductors; Stop; Watch out; Checklist
Electrical Conductors
Inspect every cord, every time, before it goes into the receptacle.
Never run your hand along a cord while it is plugged in; that is a dangerous way to find fraying.
It takes about five seconds, and it is the one check that catches most of this page before it
happens rather than after.
With the cord unplugged, run it through your hand end to end. Look for frayed,
cracked, cut or exposed insulation, and for flat spots where something has been driven
over it.
Check the plug: blades all present, straight, tight in the body, not
discolored or pitted. Check the ground pin is still there — a missing
ground pin means the cord is out of service, not that you have found a workaround.
Check where the cord enters the plug and enters the tool. That is where
flexing breaks conductors, and it is where the damage hides.
Inspect extension cords for cuts, crushing and wear, and check the receptacle end for
scorching or melted plastic.
Damage like this means the cord is finished, not that it needs watching.
If you find damage, stop, unplug it, and notify the instructor. Not
“just for this one cut”. Tag it or hand it over, so the next person does not find it
the hard way.
Tape is not a repair. OSHA allows electrical tape over superficial scuffs in
the outer jacket, and has stated just as plainly that “tape repairs of the jacket may not
be used to bring a worn or frayed flexible cord into compliance” (interpretation letter,
16 December 1998). If conductors or their insulation are showing, the cord is done.
Connections and plugs
Always disconnect power before performing any maintenance or adjustment.
NEVER yank or pull a cord — grasp the plug, not the cord. Pulling by
the cord wrecks the strain relief where you cannot see it, and it is how a plug ends up
half out of the receptacle with the blades exposed.
Push a plug fully home, and look at it. A plug that will not seat is a
fault to report, not a fit problem to force.
Keep electrical connections away from water and wet surfaces. Wet skin has on the order of
1,000 ohms of resistance where dry skin has 100,000 ohms or
more, so water moves you roughly a hundredfold closer to the current every rule on this
page is trying to keep out of you.
Be aware of overhead wiring when you are handling long stock, moving a
ladder or lifting.
A partly unplugged appliance is a short waiting for something to land on it
The hazard is the gap, and it is there before anything lands in it.
Exposed blades sit at full line voltage with nothing between them but air. Anything
conductive that falls across them completes the circuit straight across the supply — and
in a shop, the thing that falls is a metal chip. What follows is not a shock.
It is a dead short: a bang, a hard flash, and enough heat at the contact point to weld and
pit the blades. It will very likely trip the breaker and it can wreck the outlet or whatever
is plugged into it. The breaker protects the wiring, not your face, and it does not act until
after the flash.
Plugs are all the way in or all the way out. Nothing in between, and nothing
left in between.
Chips travel further than you expect and they conduct — see
Metal Chips and Swarf. That is the direct line between the housekeeping rules and this one.
Cords on the floor — the one most likely to get you; Stop; Checklist
Cords on the floor — the one most likely to get you
Nothing else on this page is as likely to actually injure someone as a cord
lying across a walkway. It is not a shock hazard at all. It is a trip hazard
— and a trip in a shop is not a trip onto carpet. You land on concrete, or into a machine, or on something sharp.
The regulation treats this as a floor problem rather than an electrical one:
“walking-working surfaces are maintained free of hazards such as sharp or protruding
objects, loose boards, corrosion, leaks, spills, snow, and ice”
(29 CFR 1910.22(a)(3)), and passageways and work areas are kept “in a
clean, orderly, and sanitary condition” (29 CFR 1910.22(a)(1)). A cord
across an aisle is an obstruction in an aisle.
A trip in a shop is not a trip onto carpet. You land where the machines are.The correct route is longer and costs nothing. That is the whole argument.
What to do, in order of preference
Do not cross the walkway. Move the work to the outlet, or use a different
outlet. This is almost always available, and it is almost never the first thing anyone tries.
Route along the wall or the bench line rather than across open floor. Take
the long way around the edge of the room.
Go overhead where a drop or a reel is provided. That is what they are
for.
If it genuinely must cross, cover or anchor it. OSHA’s own guidance is
to “ensure that temporary electrical cords that cross aisles are taped or anchored to the
floor”. A cord ramp or cord cover does the same job better and protects the cord as well
as the person.
Use the shortest cord that reaches. Slack on the floor is the hazard, and a
coiled surplus in a walkway is the same hazard in a tighter package.
Unplug it and put it away when you are done, in the same movement as
shutting the tool down. The cord left out after the job is finished is the one nobody is
expecting.
PROHIBITED — running a flexible cord through a doorway, a window, or a hole in
a wall, ceiling or floor, and attaching it to building surfaces. Those are named
prohibitions in the electrical standard (29 CFR 1910.305(g)(1)(iv)),
along with using flexible cord as a substitute for the fixed wiring of a building. Flexible cord
is temporary by definition. A cord treated as permanent gets pinched, crushed and forgotten.
NEVER walk past a cord lying across a walkway and leave it because it is not
yours. If you can see it, you can move it or say something. The person who trips over it will
not have seen it.
Read from the cord’s side, the rule is the same: portable equipment must be
handled so it is not damaged, and every cord set must be inspected before use on any shift for
cuts, crushing and a pinched jacket (29 CFR 1910.334(a)). A cord that gets
walked on is a cord that fails the inspection above. This section and that one are the same
problem twice.
Keeping walkways clear is the Set in Order and Shine part of
5S. The safety case and the lean case are the same case.
If someone is shocked; Stop; Watch out
If someone is shocked
Do NOT touch them directly. If current is still flowing they are part of the
circuit, and grabbing them puts you in it as well.
Kill the power first — the machine switch, the disconnect, the
breaker, or pull the plug.
If you cannot kill it, use a dry, non-conductive object to separate them
from the source, and stand on something dry while you do it.
A small mark is not evidence of a small injury. Electrical and electrothermal
burns run deep with very little to see on the surface, and a burn that wraps a finger can cost
the use of it. Any shock, and any electrical burn, gets reported and gets looked at
— however fine the person says they are.
Safety/Universal Rules
Chemicals and Safety Data Sheets
Every chemical and liquid in the shop has a Safety Data Sheet. Read it before you use the material, not after.
What is a Safety Data Sheet (SDS)?
What is a Safety Data Sheet (SDS)?
A Safety Data Sheet is the manufacturer's written answer to
what their product can do to you, what to wear, and what to do when it goes wrong.
There are sixteen sections, always in the same order. You do not need to read a SDS front to
back but you should read the following three sections before you use a product.
Section 2
Hazard(s) identification. What the chemical can do
to you, in the manufacturer's own words — a signal word, the hazard statements, the
red-bordered pictograms.
Section 4
First-aid measures. On skin, in eyes, breathed in,
swallowed.
Section 8
Exposure controls / personal protection. Gloves,
eye protection, ventilation — the PPE answer for that specific chemical, rather
than the general one.
None of this is a local rule. OSHA requires a sheet for every hazardous chemical, and requires
the sixteen sections and the order they come in — 29 CFR 1910.1200(g).
Supporting detail: Addendum 3 — All sixteen sections, and the four OSHA does not enforce.
Supporting detail: Addendum 4 — Signal words, pictograms and H-numbers — how Section 2 is written.
Where is SDS binder located?
Where is SDS binder located?
All Safety Data Sheets are organized in a designated binder for easy reference.
Review before use — check the sheet for any unfamiliar chemical or liquid.
Ask the instructor if you cannot locate the sheet for a material.
The binder is one way of satisfying the rule underneath it.
1910.1200(g)(8) requires an employer to keep the sheets "readily accessible
during each work shift to employees when they are in their work area(s)", and allows
electronic copies in place of paper "as long as no barriers to immediate employee access in
each workplace are created by such options." Binder or screen, the test is the same: the
sheet is something you can reach now, not something you have to go and ask for.
Your responsibility: know the hazards of any chemical you are using, and
follow the proper handling procedures.
Supporting detail: Addendum 5 — Telling a current sheet from an old one.
Material Storage and incompatible materials
Material Storage and incompatible materials
Flammable liquids must be stored in an approved flammables cabinet when not in use.
NEVER store incompatible chemicals together.
All containers must be properly labeled.
“Incompatible” is not a judgement call, and answering it needs no
chemistry. It is written on the sheet, by name, in two places:
Section 10
Stability and reactivity. One of its required
entries is "incompatible materials" — what this chemical must not contact.
Beside it sit "conditions to avoid" and "hazardous decomposition products",
which is what the two of them would make.
Section 7
Handling and storage. Required to give
"conditions for safe storage, including any incompatibilities" — the same
question answered for the shelf rather than for the reaction.
So the test before two things share a cabinet: open both sheets and read Section 10 on
each. The entry may name a specific substance or a whole class of them — oxidizers,
strong acids. If either sheet names the other material, they do not go together. Read both,
because the pair may only be called out on one of them.
Supporting detail: Addendum 6 — What makes a flammables cabinet “approved”, and how to spot one.
Safety/Universal Rules
Machine Hazards and Housekeeping
The two ways a machine injures you - it catches hold and pulls you in, or it closes on you - plus the environment around it and the habits that keep both off you.
Rotating machinery; Stop; Watch out
Rotating machinery
Rotating machinery injures you by catching hold of something and pulling
it in. It does not have to catch your hand. It catches a sleeve, a glove, a lanyard or a
strand of hair, and your hand goes wherever that goes.
Gears, pulleys and belts, chains and sprockets are extremely dangerous.
Where a rotating part meets another surface there is a wedge that closes to nothing — an
in-running nip point, the place the machine feeds things into itself. It is
where the belt runs onto the pulley, where the chain runs onto the sprocket, where the gear
teeth mesh.
The contact and the injury happen in different places. You touch the belt out
in the open, where it looks like a moving strap; the belt carries you to the pulley, where there
is no gap at all. That distance is why staying clear of the nip point is not enough on its own
— anything the machine can grip is a handle it uses to bring you there.
Gloves. Gloves or rags are for handling sharp objects such as cutters, and
only once the machine is shut down. NEVER wear gloves at a running
machine — a glove catches where bare skin would pull free, and takes your hand
with it. See chips and gloves.
It does not take teeth, and it does not take speed. A plain smooth shaft turning
slowly will still wind hair or cloth onto itself, and once it has a turn or two it does not let
go.
Contact happens where the belt is open. The injury happens where it closes.
Supporting detail: Addendum 7 — The word for this, and where it comes from.
The rotating parts that have no cover
Belts, gears and chains belong behind covers. The working end of a machine does
not. The spindle — the driven shaft the motor turns — the
chuck that grips the tool or the work, and the stock (the raw
material) held in it all turn out in the open. Nothing is between you and them, because you have to
reach them to do the job.
So everything above about what gets caught applies here with nothing in the way — and it
applies to every machine that turns, not only the loud ones. A drill press is
quiet, it is slow, and it looks like the harmless one. It is still an open chuck spinning, and it
will wind hair, a sleeve or a glove onto itself like anything else. Slow is how long it
takes, not whether it happens.
The sleeve tore before the arm did. That is the shirt’s doing, not the machine’s.
The lathe is where this goes furthest, and the reason is what a lathe is. Most
machines hold the work still and move a cutter across it; a lathe does the opposite and
turns the work. What is spinning in the open is then not a bit the width of a
pencil — it is the whole part, as long and as heavy as that part happens to be. That is why
the fatality reports for lathes describe something other than a hand injury: a person wound onto
their own workpiece.
Wound on, cloth is a rope. Each revolution takes up another turn, and bracing changes nothing.
The question, before anything is switched on: what is turning, and what of mine can
reach it? A sleeve, a glove, loose hair and a strip of abrasive cloth held against the
work have each pulled somebody into a machine. Every one of them is easier to deal with before
the spindle is turning than after.
None of this is a ranking. The mechanism is the same on every machine that turns,
and the one that can catch you is whichever one you are standing at.
Supporting detail: Addendum 8 — What the investigations actually describe.
Moving machinery and pinch points; Watch out
Moving machinery and pinch points
Moving machinery injures you without ever catching hold of you.
Two surfaces close on each other with you in between. Nothing pulls you anywhere — you run
out of room.
What makes a pinch point
A pinch point is a gap that is closing: two parts, at least one of them
moving, with space between them that is on its way to nothing. That is the whole of it, and it is
why pinch points are hard to spot. There are no teeth, no edge and often no noise. A wide gap and
a narrow gap look the same until the last inch, and the gap does not care what is in it.
Two kinds of movement, and both make one:
Back and forth, up and down
A press ram, a drill head coming down, a saw guide
being lowered, a clamp closing. You are caught between the part that moves and the part that
does not.
Straight along
A table, a carriage or a saddle travelling. It closes the gap
against whatever waits at the end of its travel — a stop, a column, the machine’s
own frame, or the hand resting there.
Where they hide
Between the work and whatever holds it. A vise jaw, a clamp, a fixture: the
hand steadying the workpiece is inside the gap that is closing on the workpiece.
At the end of a table’s travel. Wind it far enough and the space
between the table and the frame goes to zero, with whatever was resting there in between.
Under anything that comes down. A head, a ram, a guard, a guide.
On hinges. Covers, doors and lids close on their own frames — at the
free edge, where a hand is holding them, and again right at the hinge, where the gap closes over
almost no distance at all.
A pinch point needs no power, no speed and no noise. A vise turned by hand
multiplies what you put into the handle many times over, and it closes slowly and quietly enough
that nothing warns you. Switching a machine off removes the part that would have closed the gap
for you. It does not remove the gap.
The question to ask
Before moving anything — a handwheel, a lever, a clamp, a guard —
what closes, and what is in the way? Follow the moving part to the end of its
travel and find what it meets there. Then look at where your hands are, and where they will still
be once you are watching the cut instead of watching your hands.
A pinch point is a gap on its way to zero. It looks safe for most of the trip.
Supporting detail: Addendum 9 — Why belts and chains count as rotating, not pinching.
Guards stay on, and taking one off is not your call; Stop
Guards stay on, and taking one off is not your call
A guard is the thing standing between you and everything the two sections above
describe. It is not an accessory, and it is not in your way — it is doing the one job
nothing else on the machine does.
No one removes a guard in this lab. A machine that needs a guard off is the
instructor’s to deal with, out of class.
That is the whole rule, and it is deliberately not a judgement call. You do not have to decide
whether this particular setup is the exception, whether the cut is short enough, or whether you
will be careful. If the guard is in the way, the answer is to stop and say so — not to
work out whether you can manage without it.
It also means a machine you find with a guard already missing is not ready to use.
Say something. You have not done anything wrong by finding it that way, and the person who uses it
after you has no way of knowing.
Supporting detail: Addendum 10 — Why the rule has no exceptions in it.
Lockout/Tagout — before anyone works on a machine; Stop
Lockout/Tagout — before anyone works on a machine
Everything on a machine that turns or travels does so because something is
powering it. Lockout/Tagout is how that power is taken away and kept away while somebody
works on the machine.
NEVER work on equipment with rotating or moving parts without first
disconnecting power.
Lockout/Tagout procedures must be followed for maintenance.
The two words
Lockout
A lock on the device that isolates the energy — the disconnect,
the breaker, the valve — so it physically cannot be switched back on.
Tagout
A tag on that same device saying who put it there and why, so nobody
removes it wondering.
Off is not disconnected, and disconnected is not still
Off is not disconnected. A machine’s own on/off switch is a control.
Someone can press it back on, and either way the machine is still connected to its supply. The
disconnect is the thing that gets locked.
Disconnected is not still. A spindle coasts. A raised head or ram drops. A
spring, a charged capacitor or air still in a line will all move something after the power is
gone. Energy already inside the machine is part of what the procedure has to deal with.
Supporting detail: Addendum 11 — What the standard actually covers.
The environment around the machine
The environment around the machine
Slip hazards
Clean dust, metal chips, water and coolant off the floor immediately.
Lighting
Ensure lighting is adequate before operating any machine.
Walkways
Keep aisles and emergency exits unobstructed.
Operating habits
Operating habits
The chuck key never leaves your hand. It is not released until it is out of
the chuck. There is no moment where the key is in the chuck and not in your grip — not to
reach for something, not to answer someone, not for a second.
Stop machines completely before taking measurements or making adjustments.
Secure all workpieces before operation — use clamps, vises or fixtures.
Never leave tools on or near operating machinery.
Supporting detail: Addendum 12 — Why the chuck key rule is worded as a grip and not as a reminder.
When to fight a fire and when to leave, and how to use an extinguisher.
Decide before you reach for anything; Stop; Checklist
Decide before you reach for anything
An extinguisher is for a small fire you caught early.
Fight it only if all four are true
The fire is small and contained — a bin, a rag, a puddle. Not spreading.
You know what is burning, and you have the right extinguisher for it.
You have a clear exit behind you and the fire is not between you and it.
Someone else has already raised the alarm.
Otherwise: get out. Pull the alarm, leave, call 911 from
outside, and tell the instructor and the fire crew what was burning.
If you try and it does not go out in the first few seconds, stop and leave.
A hand extinguisher lasts roughly 10–20 seconds. That is your whole attempt.
Using an extinguisher — PASS
Using an extinguisher — PASS
Remember the acronym: P–A–S–S.
When it looks out, back away watching the fire, exit behind
you. Do not assume it is over — a knocked-down fire can reignite.
Fire classes, and what puts them out
Fire classes, and what puts them out
Fires are classed by what is burning. An extinguisher is rated
for the classes it can handle, and using the wrong one ranges from useless to dangerous.
Most extinguishers on a wall are ABC dry chemical — one
unit covering the first three classes. Check the label; the classes it is rated for are printed
on it.
Metal fires, and what it takes to start one; Stop; Watch out
Metal fires, and what it takes to start one
Metal burns only when it is divided finely enough, and then only when several
conditions line up at once. Ordinary aluminum chips and swarf will not do this,
and neither will the quantities of fine material a lab space like this one generates. Solid stock
does not burn at all. The cases below are the ones that are genuinely different.
The form matters more than the metal
Magnesium is the real Class D case. Thin sections, chips and turnings
ignite readily and burn with intense heat and a brilliant white light, and dull tools alone can
produce enough heat during machining to start it.
Titanium turnings can ignite, and titanium fines and grinding dust are
worse — fine enough that a static discharge is a credible ignition source.
Aluminum fines — the dust off sanding, grinding, buffing and
polishing — are a genuine hazard, but only through the specific mechanisms below.
Aluminum chips and swarf are hard to ignite. Aluminum carries heat away
from a hot spot fast, it wears a tough oxide skin that holds together while the metal
underneath melts, and a chip has little surface area for its mass. Put a torch to a pile of
chips and they melt.
Solid stock does not burn. A block of aluminum is not fuel.
Magnesium and titanium are not common in student labs. A senior project
might bring one in. If you are about to cut, grind or sand either one, ask
first — every time.
Size is the usual line — shape is the exception
The line in the standard is about half a millimeter, measured across a
particle’s smallest dimension — which different editions write as
500 microns or as 420 microns (fine enough to pass a 40-mesh sieve), not two separate
limits. Below it, metal dust can carry an explosion. Above it, generally it cannot — and
generally is the word the standard uses, not never.
Flakes are the exception, and buffing and polishing make flakes. A flake is
wide but thin, so it is too big for the sieve and still burns like dust. Treat anything off a
buffing or polishing wheel as fines however big it looks. Machining chips are genuinely coarse
— that is the difference between a chip tray and a dust collector.
The ways fine metal actually ignites
A suspended dust cloud meeting an ignition source. Fines sitting in a tray
are not the hazard. Fines thrown into the air, at the right concentration, reaching a flame, a
torch, a spark or a static discharge, are — burning travels from one particle to the next
with extreme speed. It is why you never blow fine dust around, and why you do not raise a cloud
of it cleaning up.
Fines heavily mixed with rust or grinding scale. Aluminum plus iron
oxide — rust, or the scale off steel grinding — is a thermite reaction: the
aluminum strips the oxygen off the iron, so the mixture burns without needing air from outside.
That is what makes it a metal fire rather than an ordinary one, and why water and an ABC
extinguisher do nothing to it. It takes a real mixture to go — something near
three parts iron oxide to one part aluminum by weight, and an ignition source
far hotter than a spark. That is a rust-caked pile, not a trace. See Metal Chips and Swarf for how far
apart that threshold and the recycling one actually sit.
Wet fines. Aluminum fines in contact with water slowly give off hydrogen.
That is a reason not to seal damp fines into a closed container, and part of the reason water is
the wrong thing to put on a metal fire.
If fine metal does ignite
Do not fight it. Most general-purpose shops have no Class D
extinguisher — assume you do not have one unless somebody has shown you
where it is. Pull the alarm, get out, call 911, and tell the fire crew
it is a metal fire. That changes how they fight it, and they need to know
before they arrive with a hose.
PROHIBITED — the ABC extinguisher off the wall. “Dry
powder” (Class D) and “dry chemical” (ABC) are not the same thing. An ABC
unit throws an incompatible agent at pressure: it scatters burning fines and spreads the
fire.
NEVER put water on a metal fire. The stream throws burning material, can
raise an explosive dust cloud, and reacts with the metal to release hydrogen.
Alarm, evacuate, report.
Supporting detail: Addendum 13 — Why dry sand is on the list, and why it is probably not on yours.
What that means day to day
Do not let fine dust accumulate. Empty trays, vacuums and collectors rather than letting
them fill — see Machine Hazards and Housekeeping for housekeeping.
Chips and fines are disposed of differently, and the difference matters — see
Metal Chips and Swarf.
Let hot chips and debris cool before they go anywhere near a bin of paper or rag.
Ask before you machine an unfamiliar metal. If you do not know what it is,
that is the answer: ask.
Hot work and the things that start fires
Hot work and the things that start fires
Grinding throws sparks a surprising distance. Clear rag, sawdust, solvent
and packaging out of the area before you start, not after it smolders.
Oily rags — it depends entirely on which oil.Drying oils — linseed, tung, oil-based stains, varnishes and finishes
— cure by reacting with oxygen, and that reaction gives off heat. Bunched in a pile the
rags hold the heat in, and the pile can reach ignition on its own with nothing to light it.
Those rags NEVER go in a pile: spread them flat to dry, drop them in water, or
use the designated container.
Petroleum oils do not do that. Way oil, cutting fluid, hydraulic oil and
ordinary shop oil do not cure by oxidation, so a rag wiped with them will not self-heat and will
not spontaneously combust. It is still combustible — a spark or a hot
chip will light it like any oily cloth — so keep it away from hot work and out of a bin of
paper or sawdust. If you do not know which oil is on the rag, treat it as a drying
oil.
Chips come off hot, razor sharp and fast. How to handle them, how to clean them up, and the rules on compressed air.
Four reasons a chip is dangerous
Four reasons a chip is dangerous
A chip is not scrap until it has cooled and stopped moving. Straight off the
tool it is every one of these at once.
Hot
Where an aluminum chip forms, the cut runs roughly
250–650 °C (500–1200 °F), depending on the alloy
and the speed. Chips do not look it.
Sharp
The leading edge of a chip is always razor sharp. It is
a freshly cut edge and it will open a hand.
Strong
A long continuous chip is a steel ribbon. If it wraps a sleeve or a
limb it can pull you into the machine.
Slippery
Chips on the floor roll underfoot. This is one of the most common
ways people get hurt without the machine touching them.
Never clear chips with your hands; Stop
Never clear chips with your hands
Do not reach into a machine to clear chips while it is running, and do not
pick up a long stringy chip by hand at any time. Stop the spindle, then deal with it.
Gloves
Gloves may only be used for cleanup after the machine is shut
down.
Never wear gloves at a running machine. A glove catches where bare skin
would pull free, and takes your hand with it — see Machine Hazards and Housekeeping.
Brush
A brush may be used while the machine is in operation — your hands stay
outside the machine. If clearing the chip means reaching in, stop the spindle first.
On a CNC machine, take particular care: the tool can move without warning, and the
enclosure invites you to reach further in than you should.
Compressed air — there are limits on this; Watch out; Checklist
Compressed air — there are limits on this
Compressed air is convenient and it is the option people reach for first. It is also
regulated, because a chip in a moving air stream is a projectile and air
forced against skin can be driven into the body.
The rule
OSHA permits compressed air for cleaning only where it is
reduced to less than 30 psi, and only then with
effective chip guarding and personal protective equipment
(29 CFR 1910.242(b)). All three conditions, together — not the
pressure alone.
Chip guarding is anything that stops a chip reaching eyes or unbroken skin: a
protective cone nozzle covers the operator, and a screen or barrier is what covers everyone
else.
In practice
The 30 psi is measured at the nozzle, dead-ended — blocked by the
work or a hand — and is met by a limited air nozzle or a regulator, not by the supply
pressure upstream of it.
Eye protection, every time. Everyone nearby too — you do not get to decide the
range.
Never at skin, yours or anyone else’s.
Never toward another person, and check who is behind the machine first.
Never into an enclosed space.
If air would just relocate the mess into the air or across the shop, use a brush or the
vacuum instead.
Cleaning up; Stop; Checklist
Cleaning up
Use cleaning equipment or gloves to handle chips for disposal — the sharp edge does
not dull because the machine stopped.
Clear the machine so only the residue in the bottom tray remains.
Sweep the floor, and mop if the floor is wet with coolant.
If cleaning equipment such as a vacuum gets wet, open it up and let it dry
before it is put away.
Chips and fines do not go in the same place
Chips and swarf go in the recycling container. That container is for
chips only.
Fines go in the trash. Dust from sanding, grinding, buffing and polishing,
and what comes out of a dust collector — never the recycling container.
Why — two reasons, and the second one is the safety reason
The recycler pays for clean aluminum. A clean load gets the aluminum price;
mix another metal in and the whole load drops to a much cheaper one. Fines pick iron up —
off a shared belt or wheel, off steel work at the next bench — so fines do not go in.
Compare how often each container actually leaves the building. A chip
recycling container fills slowly and can stand most of a semester between pickups; the trash
goes out daily. Fines belong in the stream that leaves, not the one that stands in the corner
for months quietly collecting more of them. Anything whose problem is accumulation does
not go in the container designed to accumulate.
Two thresholds, same observation. “There is iron in the
fines” is a real problem for the recycling price and not a fire problem — and the
reason both are true at once is that the two thresholds are orders of magnitude apart. The price
threshold is a trace: a few steel chips are enough to drop the whole load to the
cheaper price. A thermite reaction needs iron oxide — rust or grinding
scale, not bright steel — at something near
three parts oxide to one part aluminum by weight, plus an ignition source far
hotter than a spark. That is most of the pile, not a trace. Most rules in a shop have a number
behind them; knowing which number you are being measured against, and how far you
actually are from it, is the difference between following a rule and understanding it.
Fine dust burns; chips do not. Aluminum chips and swarf are hard to ignite.
The fire hazard is fines — and then only when a cloud of them is thrown
into the air and meets an ignition source, or when a great deal of rust or steel grinding scale
is mixed into them. Do not let fine dust accumulate, and do not raise a cloud of it
cleaning up.
If fine metal debris does ignite, do not fight it. The ABC extinguisher on
the wall is the wrong tool and will scatter it. Alarm, evacuate, and tell the fire crew it is a
metal fire. See Fire Safety.
Safety/Universal Rules
Lab Conduct and Emergencies
What is never acceptable in a lab, what alertness actually requires, and what to do when something goes wrong.
Prohibited behavior; Stop
Prohibited behavior
NEVER operate equipment under the influence of drugs, alcohol, or medication that causes drowsiness.
NO horseplay, pranks or roughhousing in any lab area.
Do not distract others who are operating equipment.
No unauthorized experiments or modifications to equipment.
Staying alert
Staying alert
Stay focused — maintain concentration while operating equipment.
Take breaks when tired or distracted.
Ask questions if you are unsure about any procedure.
Report unsafe conditions immediately to the instructor.
Emergency procedures; Checklist
Emergency procedures
Know the location of emergency stops, fire extinguishers, first aid kits and exits.
Call 911 for serious injuries or fires.
Notify the instructor immediately of any incident, injury, or near-miss.
Do not move a seriously injured person unless they are in immediate danger.
For electrical shock specifically, the first action is different — see
If someone is shocked.
Workspace responsibility
Workspace responsibility
Clean as you go — do not wait until the end.
Report equipment problems before they become safety hazards.
Lab Conduct and Emergencies
Lean and Quality/Lean and Organization
5S Workplace Organization
The five-step workplace organization method. It is a lean manufacturing practice, and it is also why a tidy shop is a safer one.
Why 5S sits in a safety module
Why 5S sits in a safety module
5S is a lean manufacturing method for organizing a workplace. It
earns its place here because most of what it asks for is also what keeps people from getting hurt.
A cluttered bench hides a hazard. An unlabeled container is an unknown chemical. A floor with
chips on it is a slip. Every one of those is a 5S failure before it is an incident — which is
why the shutdown steps in After operating any equipment are 5S in
everything but name.
This page is the basics. 5S will get its own expanded treatment later.
Sort — Seiri
Sort — Seiri
Separate necessary items from unnecessary ones.
Remove or relocate items that do not belong in the work area.
Keep only what you need for the task in front of you.
Set in Order — Seiton
Set in Order — Seiton
Organize and label the remaining items clearly, for easy identification.
A place for everything, and everything in its place.
Create logical, efficient storage systems.
Shine — Seiso
Shine — Seiso
Clean work areas to maintain high hygiene standards.
Reduce accident risk through cleanliness and organization.
Inspect while cleaning — that is how problems get found early.
Get the project and material approved before printing
Get the project and material approved before printing
In our labs, a DET faculty member must approve a 3D-printing project before it starts. A project assigned by DET faculty needs no separate project approval, but must stay within its own guidelines and all RPC rules.
For approval, explain what the item is, where its design came from, how it will be made, the material amount and source, and its intended use; supply the digital file through the instructor's designated channel.
No personal material without prior approval.
No weapons, weapon-like items, weapon components, ammunition, dangerous materials or drug paraphernalia.
No commercial use. Class projects take priority over personal projects.
Slice for the selected printer, then check it in person; Checklist
Slice for the selected printer, then check it in person
In PrusaSlicer, arrange and orient the model. Select the printer and filament, and set supports, infill and brim as needed. Slice, review the preview, material use and estimated time, then export the .gcode or .bgcode file.
Use the lab's private job-identification instructions to name the file. In Prusa Connect, select a printer matching the type used when slicing.
Check that printer's queue before uploading the file. In our labs, talk with the uploader before deleting a named job you think is no longer needed.
Upload the file to the selected printer's dashboard, or use the guide's Send to Connect workflow from PrusaSlicer.
Before choosing Set Ready and Print Now, go to the machine and check:
The build plate is clear.
The loaded filament type matches the sliced file.
There is enough filament for the job.
If you are unsure the machine is ready, choose Add to print queue and check it before setting it ready later.
Hot surfaces and moving parts remain hazards during remote printing
Hot surfaces and moving parts remain hazards during remote printing
The nozzle and heated bed can burn, including after motion stops. Let them cool before handling the finished print or build plate. Keep hands and tools out of the printer's moving area; use Machine Hazards and Housekeeping for the general movement and isolation rules. See Prusa's hot-part precautions for further reading, not permission to service lab equipment.
The lab guide uses Prusa Connect or its app to monitor progress. A remote status display does not replace the physical readiness check. Set Ready can release the next queued job, so use it only after checking the machine and clearing the work area.
When your print is finished and safe to handle, remove it, check the plate and material again, and set the printer ready for the next job. Remove scrap and purged filament, return tools and leave the work area tidy.
Report jams and faults; do not repair the printer yourself
Report jams and faults; do not repair the printer yourself
In our labs, report jams, malfunctions and other technical problems to DET faculty. Do not try to fix equipment yourself. Stop a failing print using the controls covered in your training, and do not set a faulty printer ready for another job.
The student guide permits resetting an offline printer only when it is not currently in use. If you cannot establish that, or if a fault remains, report it rather than repeatedly resetting. Use Lab Conduct and Emergencies for an injury or emergency.
Engineering Graphics and CAD/Reading Drawings
The Alphabet of Lines
Read line patterns, weights, and endpoints to distinguish part edges from centers, dimensions, cuts, and alternate positions.
Read the pattern before deciding what the line means
Read the pattern before deciding what the line means
Every line on an engineering drawing has a job. Some describe the part;
others tell you how to measure it, where to look, or how a view was made. Treating every
line as a physical edge gives you the wrong part.
Use three clues together: pattern (solid or dashed), weight
(thick or thin), and context (arrows, letters, numbers, and nearby features).
A thin solid line alone could be a dimension, an extension, a leader, or section hatching.
Patterns are enlarged for recognition. These samples are not a specification for plotted line widths or dash lengths.
Visible and hidden lines describe edges; center lines locate axes
Visible and hidden lines describe edges; center lines locate axes
Visible / object
A relatively thick, continuous line shows an edge or outline
you can see from this viewing direction.
Hidden
A thin series of short, evenly spaced dashes shows an edge concealed
by material. A hole may appear as a visible circle in one view and two hidden lines in another.
Center
A thin long-short pattern locates a center, axis, or symmetry reference.
The center line through a cylinder is not a seam in the cylinder.
Phantom
A thin long-short-short pattern can show an alternate position,
repeated detail, or a nearby part used as a reference. An open position of a lever does not
mean there are two levers.
Read all views together. A line's visibility depends on where you are looking
from. The same edge can be solid in one view and dashed in another.
Arrows, notes, and hatching tell you what to do with a view
Arrows, notes, and hatching tell you what to do with a view
Read the endpoints and surrounding information as well as the line pattern.
Dimension
A thin line with arrowheads identifies the extent of a measurement.
Read the associated value; do not measure the picture on your screen.
Extension
A thin line carries a feature's location out to a dimension line.
A small gap usually separates it from the part outline.
Leader
A thin line connects a note to the feature it describes, usually with
an arrow at an edge or a dot on a surface. Follow it to its endpoint.
Cutting plane
A prominent line marks an imaginary cut used to expose the
interior. Read its arrows for the viewing direction and its letters to find the matching
section, such as A–A. The line pattern can vary; arrows and identification matter.
Section / hatch
Thin parallel strokes inside a section view identify material
crossed by the imaginary cut. They are not grooves machined into the part.
Break
A short freehand break or a long thin line with zigzags marks an omitted
portion of a view. The actual part is not necessarily broken; a long uniform member can be
shortened on paper while its dimension gives the full length.
When lines coincide, do not invent a second feature; Practice
When lines coincide, do not invent a second feature
Where a visible edge and a hidden edge project to exactly the same place, read the visible
line. Where a hidden edge and a center line coincide, read the hidden line; the center line
may still be identifiable where it extends beyond the edge.
A crossing is different from an overlap. Two lines crossing on the sheet do not prove that
two physical edges meet in space. Check another view before deciding.
Supporting detail: Addendum 14 — Why context matters more than one dash.
Connect a part's width, height, and depth across aligned views, then unfold the six faces of an imaginary glass box.
Each view looks straight at the part from one direction
Each view looks straight at the part from one direction
A pictorial helps you recognize a part. A multiview drawing helps you describe
its shape without the apparent shrinkage of perspective. In orthographic projection, the
lines of sight are parallel and perpendicular to the viewing plane.
Choose a front direction and keep the part fixed. Look straight from the front, from above,
and from the right. Do not turn the part independently to make each view look convenient.
Front and rear
Show width and height; depth points toward or away from you.
Top and bottom
Show width and depth; height points toward or away from you.
Right and left
Show depth and height; width points toward or away from you.
A face parallel to its viewing plane shows its true shape at the drawing's scale. A face
tilted to that plane is foreshortened; a face viewed exactly edge-on becomes a line.
The glass box unfolds into six related views
The glass box unfolds into six related views
Imagine the part inside a transparent box. For third-angle projection, trace
what you see onto the box face between you and the part. Each face receives one principal view:
front, rear, top, bottom, left, and right.
Keep the front face fixed. Hinge the top upward, bottom downward, and side faces outward.
The rear can unfold beyond a side face; this net places it beyond the right.
The names identify the direction you look from. A right-side view means you stood
at the part's right, even if a different projection convention puts that view elsewhere on
the sheet. Compare First-Angle and Third-Angle Projection.
Predict a view, then compare it with the same block part; Interactive
Predict a view, then compare it with the same block part
Choose a part and a viewing direction in the explorer. Before revealing the view, predict
its outline and any step edges. Switch the layout convention and notice what moves on the
sheet. The part and the named views stay the same.
Static example: the tall strip is on the left of the front view and extends
through the full depth. The top view gives its width; the right view gives its height.
These are simple solids with constant depth. Construction guides are teaching
aids. The explorer includes the step edges visible or hidden from each selected direction;
it is not a dimensioned manufacturing drawing.
Use alignment to follow one feature through the drawing; Checklist
Use alignment to follow one feature through the drawing
Identify the front view and confirm the projection convention.
Track the same left-to-right position between front and top: they share width.
Track the same elevation between front and side: they share height.
Compare front-to-back positions between top and side: they share depth.
Explain each solid or dashed edge using the shape seen in another view.
At the same scale, a feature cannot be one width in the front view and a different width
in the top view. A 45° miter construction can transfer depth between top and side while
sketching; that construction line is not an edge of the part.
Supporting detail: Addendum 15 — Why one view can hide an entire change in shape.
Match the pictorial to its front, top, and right views; Practice
Match the pictorial to its front, top, and right views
Identify each numbered candidate using the viewing directions on the pictorial. These
candidates are arranged as answer choices, not in a first-angle or third-angle layout.
Use the self-checks to test your choices and read the explanations.
Use flat views from different directions, with dimensions and notes, to describe a part clearly.
Drawing views describe one part from different directions
Drawing views describe one part from different directions
A drawing view is a flat picture of a part seen from one direction. A set
of views, read together with dimensions and notes, describes one three-dimensional part so
someone can make or inspect it.
A front view shows width and height. Looking from above or from the side can show the
front-to-back depth that the front leaves out. In this stepped-block example,
the front explains the step heights, while the top shows how far the block extends back.
The picture on the left helps you recognize the part. The three flat views on
the right show the same part from separate directions.
Choosing views means selecting the directions that explain the shape clearly.
Orthographic Projection explains how the views line up and how
their positions tell you the viewing direction.
Choose the front view that explains the shape
Choose the front view that explains the shape
The front view is a drawing of the part from the direction chosen as the starting point
for the other views. The side shown need not be the one that happened to face you when you
picked up the part.
Start with a stable, understandable orientation. Prefer a view that shows characteristic
shapes directly and keeps important features out of hidden lines, the dashed lines used for
edges blocked from sight. For a stepped part, a profile that shows the steps is usually more
useful than a plain rectangle.
The front, top, and side are principal views: views along the part's main
directions. Once the front is chosen, the other principal views follow from it. Keep their orientation
and alignment consistent with Orthographic Projection and the Glass Box.
One or two views can be enough when the missing information is stated
One or two views can be enough when the missing information is stated
One view
A flat plate with a constant thickness can be defined by its face view
and a thickness note, provided the outline, holes, and other requirements are completely
specified. A circle alone does not say whether the part is a disk, a sphere, or a cylinder.
Two views
A constant-depth stepped shape can use a profile and a top view to
establish the step widths, heights, and front-to-back depth. A third view may add no new information.
A simple cylindrical part can often be described with a side view and an end view.
Three views
Front, top, and a side view are useful when features change across
all three directions. Each view should resolve a question the others leave open.
Three is a common arrangement, not a quota. Dimensions, notes, symmetry,
and repeated geometry can supply information without drawing every side. The remaining views
and written requirements must still define the whole part.
Add a view when it removes a real ambiguity
Add a view when it removes a real ambiguity
A view is useful when it answers a question the existing views leave open. For example,
the same circular front outline could belong to a thin disk or a long cylinder. A side view
or a length note can resolve that difference. If two different parts still fit the drawing,
identify the missing information and add the view or written callout that separates them.
Hidden interior
A section view can expose a bore or recess more clearly than
a tangle of dashed lines. Its cutting-plane arrows tell you which way to look.
Flat sloping surface
An auxiliary view looks straight at the surface from an
extra direction so its shape is clear. Another front, top, or side view may still make it
appear shortened. See Auxiliary and Detail Views for that construction.
Small feature
An enlarged detail view makes a crowded feature readable.
Read its stated scale; do not compare its apparent size directly with the main view.
Supporting detail: Addendum 16 — Why more pictures do not automatically mean more information.
Check the view set before moving on to dimensions; Checklist; Practice
Check the view set before moving on to dimensions
Confirm that the front view exposes the most useful shape.
Account for width, height, and depth without guessing.
Locate every hole, step, slot, or recess in enough views to explain its direction and extent.
Check hidden edges and the projection convention for consistency.
Remove a redundant view only if the remaining views and callouts still define the part.
Identify the projection symbol before interpreting where the top and side views sit on the sheet.
Check the projection convention before naming a side view
Check the projection convention before naming a side view
First-angle and third-angle projection can show the same part from the same
directions. What changes is where those views are arranged on the sheet.
Look for the projection symbol or an explicit note, often near the title block. Use it with
the view labels. If the symbol and the views disagree, resolve the inconsistency before
interpreting the part.
View placement relative to the front view
Named view
Third-angle
First-angle
Top
Above
Below
Bottom
Below
Above
Right side
To the right
To the left
Left side
To the left
To the right
A right-side view is always the view from the part's right. In first-angle projection,
it sits to the left of the front view. Do not rename it a left-side view because of its position.
The projection symbol is two views of a shortened cone
The projection symbol is two views of a shortened cone
The trapezoid is the side view of a cone with its tip removed, called a frustum.
The two concentric circles are its end view. Their arrangement tells you which projection
method is being used.
Read the circle's position together with the taper direction. These examples hold
the frustum orientation fixed so the difference is easy to see.
Supporting detail: Addendum 17 — Use the glass box to explain the swap.
Expect third-angle on U.S. mechanical drawings, then verify it; Practice
Expect third-angle on U.S. mechanical drawings, then verify it
Third-angle is the usual U.S. mechanical drawing convention. A shared convention lets the
designer and the person making or inspecting the part interpret the layout the same way.
It is a communication choice; neither method changes the part's geometry.
The drawing's declared convention is the deciding information. Country of
origin, inch units, or a familiar company name is not a substitute for checking. Drawings
cross borders, and CAD templates can use different defaults.
Supporting detail: Addendum 18 — A documented U.S. example, with its scope.
Block out height, width, and depth, then use light construction lines to develop a clear freehand pictorial.
Sketch the idea before committing to CAD
Sketch the idea before committing to CAD
A quick hand sketch lets you compare shapes, explain an idea, and find missing information before building a CAD model. Aim for a readable shape and sensible proportions. A sketch does not need mechanically perfect lines to be useful.
Use a pencil, eraser, and plain or grid paper. Isometric paper can help keep the three directions consistent. Start lightly so you can revise; darken the visible edges only after the overall form works. Add small features last.
Label important features and write any known dimensions. Do not expect someone to recover an exact size by measuring your freehand sketch. For line meanings, see The Alphabet of Lines. CAD sketch tools are covered separately in Sketch Entities and Planes.
Isometric sketches use three equally spaced directions
Isometric sketches use three equally spaced directions
Draw one axis vertically and the other two down to the left and right, each 30° from horizontal. The three outward rays are 120° apart. Edges parallel to these axes keep those directions throughout the sketch; they can extend either way along each axis line.
Use the same scale along all three axis directions. Lay out width, height, and depth along lines parallel to the axes; an isometric grid helps you keep equal intervals consistent.
Supporting detail: Addendum 19 — Isometric drawing and isometric projection use different scales.
Locate sloping edges by endpoints; sketch circles as ellipses
Locate sloping edges by endpoints; sketch circles as ellipses
A non-isometric line is not parallel to any of the three isometric axes. Locate both endpoints using width, depth, and height offsets, then join them. Do not lay the true sloping-edge length directly along its apparent direction on the paper.
For a circle on a face parallel to a principal plane, first sketch its enclosing square as an isometric rhombus. Mark the four side midpoints and sketch a smooth ellipse tangent there. Those are contact points, not sharp corners. Keep the curve inside the rhombus.
The circle-to-ellipse rule here applies to circles on the usual top, front, or side planes of the isometric sketch. Do not draw a round circle on one of these tilted faces.
Build a box, locate the cut, then remove material; Checklist
Build a box, locate the cut, then remove material
Start with the smallest simple box that encloses the part: height, width, depth. In this original example, a corner is removed uniformly through the depth. That makes the front profile a useful starting shape.
Compare the overall height, width, and depth before adding detail.
Mark where the cut begins and ends on the front profile.
Carry those points back along parallel depth lines.
Connect matching points to form the new face.
Check the remaining edges, then darken visible edges and lighten or erase construction lines.
“Extrude” means carry a profile through a distance. It is a useful mental model only when the cross-section stays constant over that distance. Check other views for features that stop partway through.
Choose isometric for three directions or oblique for a true front face; Practice
Choose isometric for three directions or oblique for a true front face
In an isometric sketch, the three principal directions share one scale, and none of the three principal faces appears in true shape. In an oblique sketch, draw the chosen front face in true shape at the drawing scale, then carry parallel edges back along one receding direction.
A 45° receding direction is common, but it is not required. Full-scale depth is called cavalier; half-scale depth is called cabinet. Keep the chosen depth scale consistent. A circle on the oblique front face stays circular; one on a receding face generally does not.
Both methods use parallel edges rather than perspective vanishing points. Pick the front direction deliberately; see Choosing Drawing Views.
Track the same surfaces through front, top, and side views, then reconstruct a pictorial without guessing hidden geometry.
Rebuild a part by combining shared dimensions; Checklist
Rebuild a part by combining shared dimensions
A multiview drawing gives several descriptions of one fixed part. Read them together: front and top share width, front and side share height, and top and side share depth. Review Orthographic Projection and the Glass Box and confirm the projection convention before interpreting positions on the sheet.
Identify the front direction and the overall width, height, and depth.
Choose a recognizable profile and locate its corners in the box.
Use the other views to decide which features continue, stop, or change along the depth.
Account for every visible and hidden edge before darkening the pictorial.
Do not assume that a front profile extends all the way through. The top or side view must support that interpretation. If two shapes still fit the information, identify the missing view or dimension rather than inventing a feature.
Match a surface by its boundaries, not its apparent shape
Match a surface by its boundaries, not its apparent shape
Face A in this original example is the front face. Face B is the sloping face made by removing a corner through the full depth. Follow their corner positions and shared boundaries across the views.
Views are individually labeled and stacked for a narrow screen; their positions do not specify a projection convention.
A appears in true shape in the front view. From above, all its points have the same front-to-back position, so it collapses to the front boundary line. From the right, it also appears edge-on. B appears as a sloping edge in front, but as a foreshortened area in top and right.
Supporting detail: Addendum 20 — One drawn line can represent several boundaries.
Normal, inclined, and oblique describe a flat surface relative to the view planes
Normal, inclined, and oblique describe a flat surface relative to the view planes
Normal surface
Parallel to one principal projection plane and perpendicular to the other two. It shows true shape in one principal view and an edge in the other two. Face A is an example.
Inclined surface
Perpendicular to one principal plane and tilted to the other two. It shows an edge in one principal view and a foreshortened area in the other two. Face B is an example.
Oblique surface
Tilted to all three principal planes, with none parallel or perpendicular to it. It shows a foreshortened area in all three principal views; none shows true shape or an edge view.
Here “oblique surface” describes a face orientation. “Oblique sketch” describes a pictorial drawing method. A part with an inclined face can be drawn with either isometric or oblique sketching.
Turn a pictorial back into views one direction at a time; Practice
Turn a pictorial back into views one direction at a time
Keep the front direction fixed. For the front view, discard depth and plot width against height. For the top, discard height and plot width against depth. For the side, discard width and plot depth against height. Include changes of surface inside the outside outline.
Before checking, explain which boundary remains visible from above and where it lies relative to the width. A matching outside rectangle alone is not enough.
Predict and reveal views in the projection explorer; Interactive; Practice
Predict and reveal views in the projection explorer
Choose a part, predict the missing view on paper, then reveal it. Change the part and repeat. Use the alignment guides to check shared dimensions. Changing the sheet layout changes view placement, not the part.
On paper: cover the top view, predict its outer rectangle and the line where the sloping face meets the flat top, then uncover it.
The explorer uses simple stepped solids of constant depth. Use the separate static example above to study the sloping surface.
Read imaginary cuts, choose a section type, and distinguish cut material from voids and conventional exceptions.
Use an imaginary cut to expose the interior
Use an imaginary cut to expose the interior
A section view shows what is inside a part without making you untangle a group of hidden lines. Imagine cutting the part, removing the material between you and the cutting plane, and looking at what remains.
The cut changes the drawing representation, not the manufactured part. Hatch the material crossed by the plane and show the useful visible edges beyond it. Hidden lines are usually omitted in sections unless needed to make the shape clear.
Follow the cutting-plane arrows and match the letters; Checklist
Follow the cutting-plane arrows and match the letters
The cutting-plane line locates the imaginary cut in a parent view. Its arrows point in the direction you look into the remaining part. Matching letters connect that line to a label such as SECTION A–A; the letters do not specify a dimension.
Use a prominent cutting-plane line that extends beyond the part, with thin section lining in the resulting view. Line weight, dash pattern, and arrow size follow the drawing standard and template. These teaching diagrams use blue for cutting planes; color is not required to interpret a drawing.
Find both cutting-plane ends and the matching section label.
Follow the arrows to decide which side is removed from sight.
Trace solid material and voids separately across the plane.
Compare the resulting section with the parent view.
Slide a cutting plane and predict the hatch; Interactive
Slide a cutting plane and predict the hatch
Practise reading what a cut exposes. Move plane A–A through a part, decide which regions of SECTION A–A are cut material, then check. Only material the plane passes through is hatched. A hole or slot that the plane crosses stays blank, and so do the surfaces you can see beyond the plane.
Worked example: a full section through the flanged bushing. Plane A–A runs through the axis. Its arrows point toward the back of the part, so the front half is imagined removed and you look at the cut face from the front. Only material the plane passes through is hatched: the bore and counterbore are empty, and the surfaces you see through them lie beyond the plane.
Full section: the two hatched walls include the flange; the counterbore step shows as a visible edge beyond the plane.Half section of the pulley: one quarter is removed, so the right half of the view is in section and the left half shows the outside. A center line divides them.Offset section of the bracket: the plane jogs to pass through the blind hole and the slot. Both cuts appear in one view, with no line at the jog.
Regions of the bushing section, top to bottom and left to right:
Region 1: Not cut: you see the far wall of the counterbore, about 15.0 mm behind the plane. Draw its edges, but do not hatch it.
Region 2: Cut material: the plane passes through the solid body and flange here, so it is hatched.
Region 3: Not cut: you see the far wall of the through bore, about 10.0 mm behind the plane. Draw its edges, but do not hatch it.
Region 4: Cut material: the plane passes through the solid body and flange here, so it is hatched.
Check the hatched area: each side of the bore contributes wall thickness × height, so 2 × [(20 − 10) × 30 + (30 − 10) × 2 + (30 − 15) × 8] = 920 mm². A hole crossed by the plane removes area from the cut face; it is never hatched.
The three parts are simplified teaching shapes, not dimensioned drawings. Round surfaces are modelled as 96-sided polygons, so every edge lies within 0.03 mm of a true circle at these sizes, and the hatched areas are exact for those polygons. The blind hole has a flat bottom; a drilled hole would end in a cone. Hidden lines are left out, as is usual in sections, and the explorer does not draw tangent edges where a flat face runs smoothly into a curve. It does not apply the rib, spoke and assembly exceptions described in “Hatch cut material, with conventional exceptions” below.
Supporting detail: Addendum 21 — How the explorer decides what is hatched, and its sources.
Full sections cut all the way through the part
Full sections cut all the way through the part
A full section uses one plane through the entire part. For this hollow cylinder, a plane through the axis exposes both walls and the bore. The bore is empty space and receives no hatching.
Half sections combine the exterior and interior
Half sections combine the exterior and interior
A half section is useful for a symmetric part. Imagine removing one quarter with two perpendicular cutting planes. The resulting view shows one half in section and the other half as an exterior view, usually divided by a center line.
It is not a full section with half its hatch erased. The unsectioned half shows the outside, and symmetry supplies the connection between the two halves.
Offset sections reach features that are not in one straight line
Offset sections reach features that are not in one straight line
An offset section jogs the cutting plane to pass through several features. Project the selected parallel portions into one section. The jogs help explain the cut location; they do not create physical edges on the part.
Read the parent view for the holes’ actual locations. Their appearance together in the section does not mean they lie in one straight row.
Broken-out sections expose only a local area
Broken-out sections expose only a local area
A broken-out section removes a limited patch to a chosen depth in an existing view. An irregular break line marks the boundary. Use it to expose a small passage or wall without adding a complete section view.
A separate cutting-plane line is normally unnecessary: the local boundary identifies the area. Depth still matters; a cut that stops before a bore will not reveal it. This differs from a broken view, which merely shortens a long part on the sheet.
Revolved sections show a cross section in place
Revolved sections show a cross section in place
A revolved section turns a cross-sectional slice 90° into the plane of the drawing and places it on the parent view. It is useful for the shape of a bar, spoke, or arm. Show the slice itself, rather than the features behind the cut.
Removed sections place the slice clear of the parent view
Removed sections place the slice clear of the parent view
A removed section places the cross section away from the parent view to keep it readable. Match its identifying letters to the cutting plane. Several removed sections can describe changes along a long part; keep each location unambiguous.
Aligned sections rotate an angled portion into the section plane
Aligned sections rotate an angled portion into the section plane
An aligned section uses intersecting cutting planes through features arranged around an axis. An angled portion is rotated into alignment before it is shown in the section. This makes radial features easier to read.
Do not infer angular spacing from the aligned result. In this disk, one small hole is rotated into the section plane; its original angular position is established by the top view.
Hatch cut material, with conventional exceptions
Hatch cut material, with conventional exceptions
Use thin, evenly spaced diagonal lines, commonly near 45° to the main outline. Change the angle when the hatch would be confused with an edge. Keep a part’s hatch consistent; distinguish adjacent assembly parts by changing hatch angle or spacing.
Voids: holes and open spaces are never hatched as solid material.
Ribs, webs, and spokes: a cut along their length generally leaves them unhatched so they do not look like a thick solid wall. A transverse cut through their thickness is hatched.
Shafts and fasteners in assembly sections: when cut lengthwise through their axes, solid shafts, bolts, nuts, washers, pins, and similar standard parts are commonly shown unsectioned. A transverse shaft section can be hatched; “never hatch a shaft” is too broad.
An unhatched region may be empty space, an uncut surface, or a conventionally unsectioned component. Use its outline and the other views to decide which.
Supporting detail: Addendum 22 — Drawing standards and scope.
Create the section from a CAD drawing view, then inspect it; Checklist; Practice
Create the section from a CAD drawing view, then inspect it
Start with a model-based parent drawing view. Choose a section command, define the cut, set its viewing direction, and place the result. These drawing operations do not remove material from the design model.
Full, half, and offset
Use a section-view command with a straight, half-section, or jogged cutting path. SOLIDWORKS calls the main tool Section View; Onshape uses Section view. Available half-section controls differ by application.
Aligned
Choose the aligned section option and define the intersection and angled portions. SOLIDWORKS uses its Section View PropertyManager; Onshape names the tool Aligned section view.
Broken-out
Define a closed local profile and a cut depth. The tools are Broken-out Section in SOLIDWORKS and Broken-out section view in Onshape.
Removed and revolved
Create a slice-only section, then place it apart or rotate and position it in the parent view. SOLIDWORKS documents Removed Section and a rotated-section workflow combining a break with section views. Onshape’s Show cut geometry only option can produce a slice without background geometry; check placement and rotation support in the installed version rather than assuming a dedicated revolved-section button.
Check that the plane crosses the intended features and the arrows face the intended direction.
Check the label, view scale, hidden-edge visibility, and hatch regions.
Exclude applicable assembly components from the cut and inspect ribs separately.
After a model change, update the drawing and recheck cut references and annotations.
Supporting detail: Addendum 23 — Vendor help for the drawing tools.
Show a flat sloping surface straight on, enlarge a small region, or shorten a long part on the sheet.
Extra views make sloping surfaces and small features easier to read
Extra views make sloping surfaces and small features easier to read
An auxiliary view is an extra drawing view that looks straight at a flat, sloping surface so its shape is clear. A tilted rectangular surface can look shortened from above; looking straight at it reveals its rectangular proportions.
A detail view is an enlarged picture of a selected small region, such as a hole with crowded edges or dimensions. The actual part stays the same size. Use an auxiliary when the viewing direction makes the shape hard to read, and a detail when a small region needs more room.
A view's scale tells you how large its picture is compared with the real part. Read the view labels and scale information to connect an added view to the original drawing. To expose an interior hidden behind solid material, use a section view.
Look perpendicular to a face to see its true shape
Look perpendicular to a face to see its true shape
A face is a surface on the part. Look straight at a flat face, perpendicular to it, to see its true shape. In projection terms, that face is parallel to the imaginary flat surface on which the view is drawn: the projection plane.
In the figure, the part is a wedge with a flat, sloping rectangular face. The front view sees that face edge-on, so the face is reduced to the line P–Q. The light-blue rectangle is the same face viewed straight on in the auxiliary view.
The same face looks different from different directions. P–Q is its edge in the front view; the auxiliary view shows its rectangular shape. The thin construction lines explain how the views connect.
In this example, the front view sees the inclined face on edge. The top view shows it foreshortened: its sloping length appears shorter because the view is not looking straight at the face. The top view's 160-unit length is not the face's true 200-unit length.
Scale is the ratio of a length on the drawing to its actual length. “True shape” still allows the stated drawing scale; it does not mean the image must be life size. The auxiliary view shows the face's correct proportions without the shortening caused by the viewing direction.
A primary auxiliary view is constructed directly from a principal view, such as the front, top, or side. Choose its projection plane parallel to the inclined face. Review Orthographic Projection and the Glass Box and Choosing Drawing Views for the principal views.
Supporting detail: Addendum 24 — When one auxiliary view is not enough.
A detail enlarges a feature; a break shortens the view
A detail enlarges a feature; a break shortens the view
The existing view from which a detail is taken is its parent view. A boundary and letter usually identify the selected region. In the figure, the circle marked B locates the region shown in Detail B.
Detail B makes the hole easier to read. The broken view below saves space along a long part; it does not show a shorter physical part.
Match the detail label and read its scale. 2:1 means a drawn length is twice the actual length; the hole itself has not grown. Enlargement alone does not change the viewing direction or reveal hidden features.
A broken view omits a middle length of a long, substantially uniform part so its ends and features fit on the sheet. Break lines identify the omission. The actual part remains continuous, and dimensions across the break state its full size. Use those dimensions rather than measuring the shortened illustration.
A broken view is different from a broken-out section, which shows interior geometry by representing a local portion of material as removed. See Section Views.
Project from the edge view and transfer the missing depth
Project from the edge view and transfer the missing depth
The auxiliary figure above uses the front view as its parent. Its thin projectors are construction lines used to line up corresponding points in the two views.
Find the principal view in which the face is a line. In the example, the front view shows the sloping face edge P–Q.
Draw a fold or reference line parallel to P–Q. It represents the hinge between the parent and auxiliary projection planes.
Draw thin projectors perpendicular to the fold line from the face’s corners.
Transfer each corner’s depth from the corresponding principal view, using the same reference and drawing scale. Here the top view supplies a constant depth of 80.
Connect corresponding points. The face is a 200-by-80 rectangle in the auxiliary view, although the top view shows its sloping length shortened to 160.
These are invented drawing units for the construction. The projectors and fold line are not physical edges on the part. The auxiliary view shows this face's true shape, not necessarily the true shape of every other face.
Use a partial auxiliary view when only one face matters
Use a partial auxiliary view when only one face matters
A partial auxiliary view shows the useful inclined face and enough nearby geometry to identify it. Omit unrelated geometry that would make the view crowded, using an appropriate break boundary where the view is interrupted.
Keep the viewing reference, label, and scale clear. Partial means limited coverage; it does not change the projection direction. The construction above isolates the inclined face for that reason.
Create auxiliary, detail, and break views from the parent in CAD; Practice
Create auxiliary, detail, and break views from the parent in CAD
Auxiliary view
Select the parent and a reference edge representing the inclined face edge-on. Use Auxiliary View in SOLIDWORKS or Auxiliary view in Onshape, check the direction, and place the view. For a partial view, limit the displayed region with the application’s crop or partial-view controls while retaining identifying references.
Detail view
Use Detail View in SOLIDWORKS or Detail view in Onshape. Define the region, place the enlarged view, and set its scale and label. Verify that dimensions reference the intended model edges.
Broken view
Use Break View in SOLIDWORKS or Break view in Onshape. Choose break direction and style, then position the two break boundaries. Check that no feature needed to define the part was omitted.
Review the result after every model revision. A generated view can be geometrically valid yet omit the feature the reader needs.
Supporting detail: Addendum 25 — Vendor help and dimensioning references.
Read the lines, arrows and text of a dimension, then arrange them so the part stays easy to understand.
A dimension connects a number to a specific feature
A dimension connects a number to a specific feature
A drawing shows the shape. Its dimensions tell the reader how big the features are and where they belong. Read the stated value; do not measure the picture.
Thin dimensioning lines keep the heavier part outline easy to follow. These teaching sketches illustrate dimensioning choices; they are not complete manufacturing drawings.
Dimension line
Runs in the direction being measured. Its arrowheads mark the extent of the dimension.
Extension line
Projects an edge, center or other point out to the dimension. Leave a visible gap at the part and continue a little beyond the last related dimension line.
Arrowheads and text
The arrows identify the endpoints; the text gives the value and any needed symbol. Use a consistent arrow style and readable text size.
Leader
A thin line connecting a note or callout to its feature. A hole leader ends with an arrow on the circle, directed toward its center.
Put dimensions outside the view, with the shortest nearest the part
Put dimensions outside the view, with the shortest nearest the part
Keep the outline clear. Put short dimensions close to the view and longer dimensions farther out. This also reduces the number of extension lines that cross dimension lines.
Good placement makes both the shape and the dimension’s endpoints easier to find.
A dimension inside the view can be appropriate when it is clearer there or avoids an excessively long leader. The aim is clarity, not an empty interior at any cost.
Leave room for the lines, arrows and text
Leave room for the lines, arrows and text
Use at least 10 mm from the part outline to the first dimension line and 6 mm between successive parallel dimension lines as layout guides. Those are distances on the drawing sheet, regardless of the part’s scale. The familiar inch drafting guides are about 3/8 in and 1/4 in; they are rounded guides, not exact conversions.
Check the final printed size. A readable CAD screen does not guarantee a readable reduced print.
Keep the gap at the part visible and extend the extension line slightly beyond the dimension line. About 2 mm of overrun is a useful drafting target. Increase spacing when the annotation needs more room.
Supporting detail: Addendum 26 — Which parts are standards, and which are layout guides?.
Keep text readable from the bottom of the sheet
Keep text readable from the bottom of the sheet
Use unidirectional text for the ordinary linear dimensions here: the numbers read from the bottom even when the dimension line is vertical. Leave clear space around the number. On a horizontal line, the text may sit above it or in a break in it.
Fit the value and arrows between the extension lines when there is room. Move them outside when there is not; do not shrink the lettering to squeeze it in.
Stagger values on several parallel dimension lines so they are easier to separate. Keep lettering free of part outlines, extension lines and leaders.
Rearrange crossing lines before accepting clutter; Practice
Rearrange crossing lines before accepting clutter
Move dimensions or notes to avoid crossing dimension lines, extension lines and leaders wherever practical. Keep a leader short, with a clear arrow target and a short horizontal landing next to the note.
A reader should be able to follow each line from value to feature without guessing.
If extension lines must cross, normally leave them continuous. Do not introduce gaps that make their endpoints ambiguous. A break near an arrowhead can preserve its readability.
Break a part into simple forms, define each feature’s size and location, and remove redundant requirements.
Ask what information is necessary to make this part
Ask what information is necessary to make this part
Start with the geometry, not with the dimension tool. Break the part into familiar forms: blocks, cylinders, holes, steps, slots and arcs.
For this simple plate, six independent numbers define the nominal geometry: length, height, thickness, hole diameter, and two center coordinates. THRU also defines the hole’s end condition.
Size dimensions
Describe the feature itself: a block’s length, width and thickness; a hole’s diameter; a slot’s width and length.
Location dimensions
Place that feature relative to other features or a chosen origin. A hole diameter alone does not say where the hole goes.
Locate a round hole by its center, not by a tangent edge that moves when the diameter changes. Choose reference surfaces that make sense for how the part fits and is checked. A formal datum has a specific meaning in geometric tolerancing; an arbitrary sketch origin is not automatically a datum.
Dimension a feature in the view that shows its shape
Dimension a feature in the view that shows its shape
Contour dimensioning keeps a feature’s dimensions with the view where its outline is clearest. Put a hole size on a view showing its circle. Put a step’s height where the step is visible. Use a section or another suitable view for an internal feature.
A hidden line tells you that an edge exists behind a surface; it is usually a poor place to attach a dimension.
For the beginner drawings here, do not dimension to hidden lines: choose a view that exposes the feature. Keep the dimensions of one feature together when practical. See the Reading Drawings group in Engineering Graphics for projection, section views and view selection.
Build the dimension scheme in a deliberate order; Checklist
Build the dimension scheme in a deliberate order
Identify the simple forms and list the features that need size, location or orientation information.
Choose the views that show those features clearly. Establish useful reference edges or surfaces.
Add the main body sizes. Leave space for smaller feature dimensions nearer the outline.
Add feature sizes and end conditions, such as a hole diameter and THRU.
Locate the feature centers, steps and other boundaries from the chosen references.
Check completeness, remove duplicate requirements, and arrange the lines for readability.
This sequence is a way to audit the information. CAD commands do not have to be clicked in this order.
Do not add dimensions just because the CAD system offers them. Review each imported model dimension for purpose, view, placement and duplication.
Give each independent requirement once
Give each independent requirement once
Completeness means every feature is defined. It does not mean every possible distance is dimensioned. A feature may need several dimensions, but the same size or location requirement should not be repeated in another view or restated by a closed chain.
The nominal difference is 2.30 − .80 = 1.50. Controlling all three distances adds a redundant requirement. Choose the dimensions that express the design intent.
A closed chain gives all the segments and their total as controlling dimensions. Remove one link, or make a useful derived value a reference dimension. Which link to remove depends on what the part must do.
Supporting detail: Addendum 28 — Why nominal arithmetic is not enough.
Parentheses mark information, not an extra acceptance requirement; Practice
Parentheses mark information, not an extra acceptance requirement
A reference dimension is shown in parentheses, such as (1.50). It helps the reader without imposing another manufacturing or inspection requirement. Use one when the derived value is useful; leave it out when it only adds clutter.
In the two-hole example, .80 and 2.30 can control the centers while (1.50) reports their nominal spacing. Parentheses do not mean that the physical distance cannot vary.
A basic dimension, shown in a rectangular box, is different: it supplies a theoretically exact value for a geometric tolerance scheme. It does not demand a physically perfect part. See Tolerances and Fits before interpreting limits or fits.
Read radii, diameters, slots, repeated features and hole notes, including the units and decimal places on an inch drawing.
Read the units before reading the numbers
Read the units before reading the numbers
Find the drawing’s unit note or title block first. On an inch drawing, .625 means 0.625 inch, not 625 inches and not millimeters. The unit need not be repeated beside every value when the drawing states it.
Decimal-inch dimensions conventionally omit the leading zero below one inch. Keep trailing zeros: .50 and .500 have the same nominal size, but may select different rows in the drawing’s general tolerance block. There is no universal “three decimals means ±.005” rule; read the actual block and any local tolerance.
An angle still needs its angle notation: 90°. Mixed units must be identified. For units and precision, use Measurement Language; for tolerance values, limits and fits, use Tolerances and Fits.
Use a diameter for a full circle and a radius for an arc
Use a diameter for a full circle and a radius for an arc
⌀ before a value means diameter. R before a value means radius. Thus ⌀.60 describes a full circular diameter of .60, while R.30 describes an arc radius of .30. The values are related, but the callouts describe different kinds of feature.
One 4X ⌀.20 THRU callout applies the same size and end condition to four identified holes. It does not locate them.
n X means the requirement applies in n places. A repeated size still needs an unambiguous pattern: center coordinates, spacing, or a fully defined bolt circle. A sketch that merely looks evenly spaced is not enough.
A round-ended slot needs size, location and direction
A round-ended slot needs size, location and direction
For a straight slot with semicircular ends, give its width and either its overall length or the distance between the end centers. Make the chosen meaning clear. Then locate the slot and establish its direction relative to the part.
For this geometry, overall length = center spacing + width: 1.30 + .50 = 1.80. The drawing must also specify the slot’s location and whether it goes through or stops at a depth.
Do not control the width, end radius, center spacing and overall length all at once. That repeats the relationships already built into the semicircular-ended shape. If a slot is not semicircular-ended, this shortcut does not apply.
Read a hole callout from the main hole to the added recess
Read a hole callout from the main hole to the added recess
The first size usually describes the main hole. Read the remaining symbols with the values immediately following them. All examples below are invented decimal-inch teaching values.
Callout
How it reads
⌀.30 THRU
A .30 diameter opening goes through the part. THRU is an end condition, not a numeric depth.
⌀.30 ↧ .55
A .30 diameter blind hole has .55 depth to the full-diameter portion. A drill-point cone, if present, extends farther unless otherwise specified.
⌀.30 THRU ⌴ ⌀.60 ↧ .15
The .30 through hole has a cylindrical, flat-bottomed counterbore: .60 diameter and .15 deep from the entry surface.
⌀.30 THRU ⌵ ⌀.60 × 90°
The .30 through hole has a conical countersink: .60 major diameter at the entry and a 90° included angle, measured across both sides of the cone.
⌀ = diameter; ↧ = depth; ⌴ = counterbore; ⌵ = countersink. Symbol shapes in a CAD font may look slightly different from browser text; the sketches show their meaning.
Read the leader and section view to identify the entry side. A hole callout supplies size and end condition; it still needs location dimensions. A countersink angle is not automatically 90°.
A spotface provides a local flat seat
A spotface provides a local flat seat
A spotface provides a flat circular seating surface around a hole. Its modern symbol puts SF inside the counterbore-shaped mark. Older drawings may use the counterbore mark with a note or context identifying the spotface.
The spotface diameter measures the flat seat, excluding an edge fillet. A shallow-looking counterbore is not enough by itself to identify a spotface.
A spotface may have a stated depth or remaining material thickness. If neither is specified, the ASME convention is the minimum depth needed to clean up the specified diameter. Do not invent a depth from the sketch.
Supporting detail: Addendum 29 — Reading old and new symbol styles.
Change a hole and watch its callout change; Interactive; Practice
Change a hole and watch its callout change
Predict which line will change before changing a control. Compare counterbore depth with countersink angle, then change the main diameter while keeping the recess diameter fixed.
Static example:2X ⌀.300 THRU / ⌴ ⌀.600 ↧ .150 means two holes, each .300 diameter through, each with a .600 diameter counterbore .150 deep. Their positions must be defined elsewhere.
The section sketches above provide a printable comparison of the same hole types. The live builder uses invented dimensions and an ideal section; it does not select a fastener, tolerance or manufacturing process.
Use sketches to explore ideas, models to develop geometry, and drawings to communicate a design for making and checking.
Choose a graphic for the question you need to answer; Practice
Choose a graphic for the question you need to answer
Engineering graphics communicate technical ideas and problem solutions. Aim for accuracy, simplicity, and clarity. A graphic succeeds when another person can use it for the intended task.
Ideation sketch
A quick drawing for exploring and comparing ideas. Designers and teammates use it to discuss shape, motion, or arrangement before committing to detailed geometry. Label uncertain sizes and assumptions.
CAD model
A digital description of geometry. Designers use it to develop parts, examine how components fit, and support analysis or manufacturing preparation. A realistic appearance alone does not prove that the design works.
Engineering drawing
Selected views with dimensions, tolerances, and notes. People making, assembling, and inspecting the product use this information to understand what is required. See Working Drawings and Title Blocks.
Use testing to send the design back for refinement; Practice
Use testing to send the design back for refinement
Begin with the task and its requirements: what must the design do, and what limits must it satisfy? Sketch alternatives, develop promising geometry, then test it against those requirements. Testing may involve calculations, simulation, a prototype, or a combination.
When a test reveals a problem, revise the design and test again. Update the affected graphics so that the model, drawings, and test record describe the same design.
Supporting detail: Addendum 30 — Why the process is a loop.
Release identifies the information approved for use
Release identifies the information approved for use
Release means approving a defined design state for its intended use through the organization's review process. Before release, check the model, drawing set, and supporting requirements together. A saved file is not automatically an approved file.
A maker needs part requirements; an assembler needs component relationships; an inspector needs criteria for deciding whether the result is acceptable. Match the information to the reader's job. For drawing-based work, use Creating Drawings from CAD Models to prepare the sheets and CAD History, Versions, and Sharing to distinguish an editable design from a preserved milestone.
Supporting detail: Addendum 31 — Does every design require a separate drawing?.
Follow the specified drawing standard and its applicable edition; Practice
Follow the specified drawing standard and its applicable edition
Standards give drawing readers shared rules for interpreting views, lines, dimensions, and symbols. The ASME Y14 series is widely used in US engineering drawing practice; ISO technical drawing standards are widely used internationally. These are not exclusive geographic boundaries. Read the drawing's stated requirements rather than choosing a convention from a country name.
A convention is an accepted way of presenting information. A company may add conventions for sheet layout or numbering, but those choices must remain consistent with the governing requirements. Use the current applicable edition specified for the work; do not silently apply an old classroom example or change an existing drawing's governing edition.
Check units, projection method, and the stated standards before interpreting a drawing. Continue with Orthographic Projection and the Glass Box and Choosing Drawing Views for view interpretation. This overview does not reproduce standard clauses or serve as a compliance checklist.
Distinguish part and assembly drawings, then use title blocks and revision records to identify the information that applies.
Send the drawing type that answers the reader's job; Practice
Send the drawing type that answers the reader's job
Detail or part drawing
Defines an individual part for making and inspection, using the necessary views, dimensions, tolerances, material information, and notes. A part drawing is not the same thing as an enlarged detail view.
Assembly drawing
Shows how components relate and fit together. It may include item identification, assembly requirements, and overall or interface dimensions. See Exploded Views and Bills of Materials for exploded views, item balloons, and parts lists.
Working-drawing set
The coordinated drawings needed to make and assemble a product: typically assembly drawings and the required part drawings, with supporting lists and notes as needed. A set may span several sheets and drawing numbers.
An assembly view alone usually does not provide every requirement needed to manufacture each component. Confirm that the recipient has the required sheets and revisions.
Read identity, units, and scale before reading dimensions; Practice
Read identity, units, and scale before reading dimensions
The title block identifies the drawing and records key information about it. Its layout varies. Read field labels; do not assume a familiar-looking border has familiar settings.
The part name tells you what the item is; the part or drawing number identifies the controlled record. Those numbers may be different. Units tell you how to interpret dimension values. Scale describes the displayed view size relative to the object, not the part's actual size. Check individual view labels for scale overrides, and use stated dimensions rather than measuring a print.
Find material, tolerances, and responsibility in the block or notes; Practice
Find material, tolerances, and responsibility in the block or notes
General practice includes fields or notes for material, general tolerances, revision, and drawn/checked information. Some templates also carry dates, approval status, finish requirements, or a projection symbol. A material field may refer to a separate specification; read that reference rather than guessing from the appearance of the model.
A tolerance states the permitted variation from a requirement. Read the scope of the general tolerance note and any specific tolerances at features. Displaying more decimal places is not, by itself, a complete tolerance instruction. See Dimension Anatomy and Placement, Choosing Dimensions, and Hole and Feature Callouts.
Drawn and checked entries record responsibility. They do not replace the organization's approval or release process. Missing or conflicting requirements need clarification before the drawing is used.
Match the revision record to the drawing being used; Checklist; Practice
Match the revision record to the drawing being used
The title block commonly shows the drawing's current revision identifier. A revision block or associated change record explains changes, often with a description, date, and authorization. Exact fields and identifier sequences depend on the organization's system.
A new file date alone does not prove that a drawing is the authorized revision. Match its number and revision to the release record for the job. Related parts may legitimately have different revision identifiers; they must be the approved combination.
Match the drawing and part identifiers to the item you need.
Confirm the required revision and approval status.
Confirm that every referenced sheet, note, and parts list is available.
Read change descriptions and inspect affected views and requirements.
Set up a sheet, place linked model views, add requirements, and check the drawing after every design change.
Choose the model and sheet settings before placing views
Choose the model and sheet settings before placing views
Start with the intended part or assembly and confirm its configuration or version: the selected design variant or saved design state. A drawing of the wrong variant can look convincing and still describe the wrong product. See CAD Files and Documents and CAD History, Versions, and Sharing.
A drawing template supplies starting settings. A sheet format supplies the border and title-block layout. CAD systems package these differently, so inspect the resulting sheet: size, units, projection method, scale, and dimension style all matter.
Use the workflow below as a sequence of tasks. Interface names vary by product and release; these are generic descriptions rather than menu instructions for SOLIDWORKS or Onshape.
Place a base view, then derive aligned projected views; Practice
Place a base view, then derive aligned projected views
Insert a base view from the model, choosing an orientation that communicates the shape clearly. Create projected views from that parent view, maintaining the required alignment and projection arrangement. Leave room for dimensions and notes.
The figure uses third-angle placement only as an example. Follow the drawing's declared projection method. Choose enough views to define the shape; three views are not a requirement for every part. Use Choosing Drawing Views, Section Views, and Auxiliary and Detail Views when ordinary views do not explain a feature clearly.
Distinguish dimensions that control geometry from dimensions that report it; Practice
Distinguish dimensions that control geometry from dimensions that report it
A driving model dimension controls geometry, such as the length of an extrusion. A dimension created by selecting drawing geometry usually reports that geometry. Changing a displayed label is not a sound way to change the part.
Some CAD workflows import model dimensions into drawings and allow linked edits to affect the model. Check the dimension's type and behavior before editing. Do not assume that all drawing dimensions are editable model controls, or that all are independent annotations.
Select dimensions to communicate manufacturing and inspection requirements, not merely every value used while modeling. Add needed tolerances, material information, and feature notes; CAD does not infer all design requirements from shape. Use Choosing Dimensions and Dimension Anatomy and Placement for the dimensioning method.
Update linked views and inspect the sheet before release; Checklist; Practice
Update linked views and inspect the sheet before release
Associativity is the connection between a model and the drawing information derived from it. When referenced geometry changes, linked views and dimensions can update to reflect it. Depending on the CAD system, update settings, and referenced version, an explicit update or reference change may be needed.
An update is not a completed review. Deleted or replaced edges can leave dimensions detached from their intended features. Notes can become obsolete. A previously exported PDF stays a snapshot; generate and check a new export after approved changes.
Confirm the referenced model, variant, and version, then update or rebuild the drawing as needed.
Inspect every affected view for the intended geometry, alignment, and readable line display.
Resolve detached dimensions and check that each dimension still refers to the intended feature.
Review units, view scales, material, tolerances, and notes for completeness and conflicts.
Complete the title block and required revision information; obtain the required review.
Export the approved sheets and inspect the actual output for missing views, clipped text, and readability.
Choose the right container for parts, assemblies, and drawings, then check templates, units, and references.
Choose a part, assembly, or drawing for the work you need to do
Choose a part, assembly, or drawing for the work you need to do
A part describes geometry. An assembly positions components relative to one another. A drawing communicates that design through views, dimensions, and notes. Start by deciding which job you need the document to do.
SOLIDWORKS part: .sldprt
Contains part geometry and its modeling features. A part can contain one body or multiple bodies; the file extension does not mean there is exactly one solid.
SOLIDWORKS assembly: .sldasm
References components, including parts and subassemblies, and stores their arrangement and assembly relationships.
SOLIDWORKS drawing: .slddrw
Usually references a part or assembly to generate drawing views. It is a separate document from the model.
An Onshape document is a container for related design information. Open a workspace to edit that information, then select the tab for the task.
Part Studio: create geometry using sketches and features. One Part Studio can produce several related parts.
Assembly: insert and position part or subassembly instances and define their relationships.
Drawing: create drawing sheets and views of models.
Tabs and tab folders: organize the document's contents. Use the Tab Manager to find a tab when the row becomes crowded. A tab folder organizes tabs; it does not mate parts together.
Supporting detail: Addendum 33 — Vendor help for the document model.
Check the template and units before entering dimensions; Checklist
Check the template and units before entering dimensions
A template supplies starting settings. In SOLIDWORKS, part, assembly, and drawing templates use .prtdot, .asmdot, and .drwdot. Choose the appropriate template, then verify the new document's units. A familiar template name is not proof that its settings are right.
In Onshape, check workspace units; account preferences provide defaults for new documents. Choose a suitable drawing template when creating a drawing, and check that drawing's units and sheet settings too.
Confirm the active document or workspace and the tab you are editing.
Check length and angle units before entering bare numbers.
Enter a known dimension and verify its displayed value and units.
Check drawing units and sheet scale separately from the model.
Changing the display from inches to millimeters should express the same physical length in another unit. It does not repair geometry created at the wrong size. Display precision controls how many digits you see; it is not a manufacturing tolerance.
Supporting detail: Addendum 34 — Template and unit references.
Keep referenced files together when you transfer a design; Practice
Keep referenced files together when you transfer a design
For a typical file-based SOLIDWORKS design, the assembly points to component files, and a drawing points to its model. Sending only the assembly file may leave the recipient without the parts. Renaming or moving files outside a reference-aware workflow can break those connections.
Use Pack and Go to gather a design's related files. Review the package contents, including required drawings, then open the transferred design and check for missing references. Files can be reorganized when references are updated; they do not have to remain permanently in the original folder.
Practice choosing a complete reference package; Interactive
Practice choosing a complete reference package
A reference is a stored relationship from one design document to another. In this lesson's declared graph, an arrow A → B means document A requires document B. A drawing may require a model; an assembly may require parts and subassemblies; each subassembly may require more components.
Start with the document you intend to deliver, then follow every required arrow. This is the dependency closure: the starting document plus every directly and transitively required document. A shared component appears once even when two parents require it.
Static worked case — clamp drawing: the drawing requires the clamp assembly. The assembly requires left and right arm subassemblies plus the base. Both arm subassemblies require the same pivot pin, so the complete six-document set contains the pin once.
Available but omitted
The source file exists, but it was not selected for this package. Add the required document.
Unavailable at source
The declared required document cannot be obtained in the scenario. Checking its box cannot create it; locate or restore the actual source first.
Changed symbolic locator
The intended node still has the same stable identity, but one declared edge expects an old locator. Explicitly retarget that edge. A same-looking or same-named substitute is not automatically the intended document.
This graph is a teaching model, not actual CAD file management. It performs no file operations, uploads, downloads, renames, Pack and Go command, cloud lookup, or PDM action. Real CAD systems can use paths, internal identifiers, search locations, platform records, and workflow rules beyond this declared graph.
Use a reference-aware workflow to inspect and collect the real design. In SOLIDWORKS, Find References can list documents referenced by the active file, Pack and Go can gather related files, and File Utilities can update references during supported rename, replace, or move operations. Review the result and open the transferred design to check it.
Supporting detail: Addendum 36 — Why this lab does not imitate a folder copy.
Engineering Graphics and CAD/CAD Modeling
CAD Model Views and Checks
Navigate a model, choose what edges to show, and check dimensions and mass without changing the design.
Zoom, pan, and rotate change your view of the model
Zoom, pan, and rotate change your view of the model
Zoom changes how large the model appears. Pan shifts it across the window. Rotate orbits the view so you can inspect another side. These viewing operations do not resize the part or move an assembly component.
Use zoom to fit to recover the whole model, zoom to window to enlarge a boxed region, and zoom to selection when you need a selected detail. Mouse buttons, modifier keys, and wheel direction depend on your device and control preferences. Check those settings instead of assuming two platforms use the same gestures.
Use Onshape's view cube or SOLIDWORKS view-orientation controls to return to a known direction. The axis triad helps you keep track of model directions while orbiting.
Normal to looks straight at a selected plane
Normal to looks straight at a selected plane
Front, rear, top, bottom, left, and right are standard model directions. Normal to a planar face or sketch plane means looking along a direction perpendicular to it. An inclined face can therefore have a normal view that is different from every standard view.
The face marked F establishes the front. Normal to depends on the selected plane, not on the name of a standard view.
Isometric, dimetric, and trimetric are angled parallel-projection views. The three principal axes have equal foreshortening in isometric, two equal in dimetric, and three different in trimetric. Perspective adds apparent size change with distance; turn it off when comparing parallel projected shapes.
Supporting detail: Addendum 37 — Viewing direction is separate from drawing layout.
Choose a display style for the edges you need to inspect
Choose a display style for the edges you need to inspect
Keep the viewing direction fixed while comparing styles. Shading shows surfaces; edge settings decide which boundaries you can see. Labels differ between platforms, so read the option's effect.
Shaded without edges
Filled surfaces emphasize overall form without drawn edge outlines.
Shaded with edges
Filled surfaces plus visible edge outlines make face boundaries easier to follow.
Hidden lines/edges removed
An unshaded view shows visible edges and leaves concealed edges out.
Hidden lines/edges visible
Concealed edges are also shown, distinguished from visible edges. Useful for finding geometry behind the front surface.
Wireframe
Shows the edge framework through the model without opaque shaded faces. Overlapping edges can make depth difficult to read.
Original schematic: dashed lines mark concealed edges where they are distinguished. Colors and exact edge treatments vary with software settings.
Onshape also provides translucent display and shaded display with hidden edges. Translucency lets you see through faces; hidden-edge display highlights concealed boundaries. Neither removes material.
Supporting detail: Addendum 38 — Find the view options in vendor help.
A model section view reveals the inside without cutting the part
A model section view reveals the inside without cutting the part
Use a section view in the model window to clip away the near portion visually. Choose a plane or planar face, set the cut position and direction, and inspect the exposed interior. Turn the section off afterward to see the complete model again.
A viewing section does not create an extruded cut feature. It also does not automatically create a documented section view on a drawing sheet. See Onshape Section View help for the available section controls.
Check the selection before trusting a measurement; Checklist
Check the selection before trusting a measurement
Select the actual entities you need, then use Measure. An edge can provide length; a circular edge can provide radius or diameter; two suitable entities can provide distance or angle. Read the result label: minimum distance, center distance, and distance along an axis answer different questions.
Quick selection properties or status-bar values are useful checks, but they depend on what is selected. A face, an edge, a body, and an assembly component are different selections. Clear old selections before starting a new measurement. Measurement reports geometry; editing a driving dimension changes geometry.
Clear the previous selection and select the intended entities.
Confirm the highlighted face, edge, or component belongs to the intended part.
Read the measurement type and unit with the value.
Compare the result with a known dimension or a simple estimate.
Supporting detail: Addendum 39 — Measurement reference.
Mass needs material density as well as geometry; Practice
Mass needs material density as well as geometry
Assign a material to the intended part or body before relying on mass properties. A color or metallic appearance alone is not proof that the material density is correct. Check which bodies or components are included, the units, and any overrides before accepting mass or center of mass.
For a uniform solid, mass = density × volume. A correct volume with the wrong density still gives the wrong mass. Center of mass describes how mass is distributed; it need not lie inside the solid material of a hollow or curved part.
Supporting detail: Addendum 40 — Material assignment and mass-property help.
Separate feature order from edit history, preserve useful design states, and share the intended model with the right access.
The feature list describes how geometry is built
The feature list describes how geometry is built
The SOLIDWORKS FeatureManager design tree and the Onshape feature list help you find sketches and modeling features. Later features can depend on earlier geometry. Rename important features so another reader can tell what they do.
A tree also contains items such as planes, bodies, or components; not every row is a modeling operation. To understand how features build a part, continue with Feature-based Modeling.
A rollback bar lets you work at an earlier position in the feature sequence while later features are temporarily left out of regeneration. Move it forward again to evaluate the complete model and check dependent features. Rolling back does not retrieve an old saved revision, and it is not the same operation as separately suppressing one feature.
Supporting detail: Addendum 41 — Rollback follows the regeneration sequence.
Onshape history records edits; versions preserve milestones; Interactive
Onshape history records edits; versions preserve milestones
Onshape records completed edits in document history. The feature list shows the modeling sequence; history records changes to the document over time. Editing an early sketch today changes the history today even though the sketch remains early in the feature list.
A version captures the design state of the workspace, including its tabs, at a named point. That captured design state is read-only. Use a meaningful milestone name and description so a reviewer knows which state you mean.
A branch starts from a version and provides a separate workspace for further edits. Use it to explore an alternative while preserving the starting version. Compare changes before merging; merging needs review, not just a button click.
Supporting detail: Addendum 42 — Viewing history, restoring, and branching serve different purposes.
Worked symbolic timeline: feature order stays put while edits accumulate
What: the feature list remains Mounting sketch → Base extrude → Edge fillet. Why: editing the first feature later should add a new history event, not move that feature to the end of the regeneration sequence.
Start Main workspace: sketch width 60 mm, extrude depth 12 mm, fillet radius 2 mm.
Edit the early Mounting sketch now: width 60 → 72 mm. It remains feature 1.
Create the fixed Design review snapshot: 72 / 12 / 2 mm.
Edit Main again: sketch width 72 → 84 mm. The snapshot still reads 72 / 12 / 2 mm.
Create Lightweight branch from Design review, then edit only its extrude depth 12 → 8 mm.
1 · Mounting sketch — width starts at 60 mm.
2 · Base extrude — depth starts at 12 mm.
3 · Edge fillet — radius starts at 2 mm.
State after the worked actions
Sketch width
Extrude depth
Fillet radius
Main workspace · editable
84 mm
12 mm
2 mm
Design review · fixed snapshot
72 mm
12 mm
2 mm
Lightweight branch · editable
72 mm
8 mm
2 mm
This is a symbolic in-memory model, not Onshape or SOLIDWORKS. It performs no rollback, restore, merge, save, file operation, or permission change.
A SOLIDWORKS save or file copy needs its own revision plan
A SOLIDWORKS save or file copy needs its own revision plan
In a local file workflow, Save writes the current document to disk. A deliberate copy can preserve an earlier state, but a filename alone does not establish a managed revision or capture all referenced files. Keep descriptive names and know which copy is the active design.
Before copying an assembly or drawing for an alternative, check what its references will point to. Two assembly copies can still use the same part file; editing that shared part can affect both. Use the transfer checks in CAD Files and Documents.
SOLIDWORKS installations may use PDM or connected data management for version and revision control. Follow that system's workflow when present; local Save and Save As are not a universal replacement for it.
Share the intended state and check the recipient's access; Checklist; Practice
Share the intended state and check the recipient's access
In Onshape, decide whether the recipient needs to inspect a fixed version or collaborate in an editable workspace. A link to a changing workspace can show later edits; a version identifies a fixed design state. Grant access using the document's sharing controls.
Confirm the document, workspace or version, and tab you intend to share.
Review document visibility and the intended recipient.
Choose view or edit access and inspect additional permissions such as export, copy, and resharing.
Check that the recipient can open the intended state with the intended access.
Do not assume that sending a URL grants access, or that view access prevents copying or exporting. Available sharing options depend on the account and organization. Review Onshape Share Documents for those permissions.
Choose where a 2D sketch lives, then build its shape from simple entities and construction geometry.
Choose the sketch plane before drawing the shape
Choose the sketch plane before drawing the shape
A 2D sketch is a set of points and curves on one plane. The plane places the sketch in the model; the sketch's origin and axes give you references for locating its geometry.
Standard plane: Front, Top, or Right is a useful starting reference for a new part. Choose the view that makes the intended profile easiest to describe.
Model face: use an existing planar face when the new sketch belongs on that face. A curved face is not itself a 2D sketch plane.
Reference plane: an added plane can locate a sketch where the standard planes and existing faces do not.
The origin is a point, not a plane. Starting a line or circle at the origin can anchor its position, but you still need a sketch plane. You may start elsewhere when that suits the design; then constrain the location relative to a deliberate reference.
Look normal to the sketch plane: straight at it, rather than at an angle. Horizontal and vertical refer to the sketch's axes, even when you rotate the model on screen.
Supporting detail: Addendum 43 — Sketch placement in Onshape.
Use the simplest entity that describes the shape
Use the simplest entity that describes the shape
Sketch entities and the information they need
Entity
What it describes
What to control
Line
A straight segment between two endpoints.
Position, direction, and length.
Circle
A complete round curve.
Center position and radius or diameter.
Arc
Part of a circle.
Center, radius, and where the arc begins and ends.
Rectangle
Four connected lines with right-angle corners.
Position, orientation, width, and height. Tool-created relations often supply some of these.
Slot
A constant-width path with rounded ends. A simple straight slot has two parallel sides and two semicircular ends.
Path position and direction, width, and length. State whether length means overall length or distance between end centers.
Spline
A curve shaped by fit points or control points and handles.
Point locations and curve shape. Use it when a line or circular arc cannot express the intended contour.
Rectangle and slot tools create useful groups of geometry. They do not guarantee that the resulting sketch is fully defined. Inspect their relations before adding more.
Supporting detail: Addendum 44 — Find the tools by their software names.
Construction geometry guides the sketch without outlining material
Construction geometry guides the sketch without outlining material
A centerline is a common use of construction geometry: a reference for a center, symmetry, angle, or axis. Construction geometry participates in dimensions and relations, but does not serve as the ordinary boundary of a filled profile.
The reference line and the profile have different jobs. A dashed line can still need constraints.
In SOLIDWORKS, Centerline creates construction geometry. In Onshape, use Construction to toggle selected sketch entities or to create construction geometry. Use a construction circle for a layout circle just as you would use a construction line for an axis.
Supporting detail: Addendum 45 — Vendor reference for construction geometry.
Check connections before moving on to a feature; Practice
Check connections before moving on to a feature
Two endpoints that look joined may still be separate. A tiny gap can prevent a profile from closing. Use a coincident relation to make the connection intentional, then inspect the sketch.
Closed and fully defined are different checks. A closed circle can still move or change size. A fully defined chain of lines can still be open. Later features such as extrude or revolve use sketches in different ways; choose the profile that the intended feature needs.
Match each relation to the motion it prevents, and distinguish shared position, direction, size, and curvature.
Relations preserve geometry when dimensions change
Relations preserve geometry when dimensions change
A geometric relation is a rule the sketch must continue to satisfy: two lines stay parallel, two circles keep one center, or an endpoint stays on a curve. Onshape generally calls these rules constraints; SOLIDWORKS calls them relations.
Choose the entities carefully. Selecting a circle's center is different from selecting its circumference. A relation can remove some motion while leaving other motion available. The diagrams show only the named rule, not a complete dimensioning scheme.
The before/after drawings are original geometry diagrams, not software icons. Their line colors do not indicate sketch status.
Coincident connects a point; midpoint puts it halfway along
Coincident connects a point; midpoint puts it halfway along
Coincident
Two points share a location, or a point lies on a selected line or curve. Joining two endpoints closes their gap. A point on a line can still slide along it unless another rule locates it.
Coincident controls connection. It does not by itself set either line's length or angle.
Midpoint
A point stays halfway between a segment's endpoints. It is more specific than simply putting the point somewhere on the line. Onshape also supports midpoint on an arc.
The two halves stay equal as the line changes length.
Supporting detail: Addendum 46 — Point selection and vendor names.
Collinear shares a line; parallel shares only its direction
Collinear shares a line; parallel shares only its direction
Collinear
Two straight segments lie on the same infinite line. They may have a gap between them; collinear does not join their endpoints.
Same underlying line does not mean same length or touching endpoints.
Parallel
Two lines keep the same direction. Their spacing, lengths, and positions along that direction still need other rules.
Parallel lines can rotate together; neither must be horizontal.
Software vocabulary: SOLIDWORKS has a Collinear relation. Onshape's documented toolbar has no separate Collinear entry. For two nonzero straight segments, placing both endpoints of one coincident with the other's underlying line enforces the same geometric condition. This is a construction from point-on-line constraints, not an Onshape command name.
Horizontal and vertical use the axes; perpendicular uses another line
Horizontal and vertical use the axes; perpendicular uses another line
Horizontal
A line's endpoints have the same vertical coordinate. For two selected points, horizontal aligns their heights without joining them.
Length and position can still change.
Vertical
A line's endpoints have the same horizontal coordinate. Two selected points can likewise be aligned vertically.
Use the sketch axes, not the edges of the rotated screen view.
Perpendicular
Two line directions form a right angle. They may rotate together while preserving that angle. The relation does not require their finite segments to meet.
If a joint is required, also connect the intended endpoints.
Supporting detail: Addendum 47 — Why horizontal plus vertical can already supply a right angle.
Concentric shares a center; equal shares size; coradial shares both
Concentric shares a center; equal shares size; coradial shares both
Concentric
Circles or circular arcs share a center. They can have different radii. For arcs, their endpoints and sweep angles are not determined by this relation.
Concentric suits two circular boundaries around the same axis.
Equal
Selected line segments keep equal lengths; selected circles or circular arcs keep equal radii. Equal does not move their centers together. Equal arc radii do not imply equal arc lengths when the sweep angles differ.
Dimension one size and relate the other to it when they must change together.
Coradial
Two circular arcs share both center and radius: they belong to the same underlying circle. They need not touch or have equal sweep angles. SOLIDWORKS names this relation Coradial. In Onshape, concentric plus equal radius expresses this condition.
Compare all three: same center, same size, or both.
Supporting detail: Addendum 48 — Check the circular relation definitions.
Tangent controls direction at contact; Fix holds a reference in place
Tangent controls direction at contact; Fix holds a reference in place
Tangent
A line and a circle touch without crossing: the line is perpendicular to the radius at contact. Curves meeting tangentially have a common tangent direction. Tangency alone does not necessarily join the endpoints you intended; add endpoint coincidence when a continuous profile needs it.
A smooth-looking connection still needs the correct relations. Tangency does not require equal radii.
Fix
Fix grounds selected geometry at its current location. Fixing a point removes its freedom to move in the sketch plane. It is useful for a deliberate fixed reference, but does not explain why an arbitrary location or size is correct.
The example fixes a point. Do not generalize it to every entity's endpoints.
SOLIDWORKS qualification: its relation reference says endpoints of a fixed line can still move along the underlying infinite line, and arc endpoints can move along the supporting circle. Check the entity and its endpoints. Onshape describes Fix as grounding the selected entity on the sketch plane.
Supporting detail: Addendum 49 — Vendor help for tangent and fixed geometry.
Watch automatic relations, then check what was stored; Practice
Watch automatic relations, then check what was stored
Sketching tools can add relations while you draw. A visual alignment is useful feedback; inspect the resulting relation icons before assuming the intended rule is present.
SOLIDWORKS: with Automatic Relations enabled, its documented cursor cues include horizontal, vertical, coincident, midpoint, perpendicular, and tangent. Hold Ctrl while sketching to suppress automatic relations temporarily.
Onshape: Automatic Inferencing documents horizontal, vertical, midpoint, parallel, and coincident as common inferences. Hover near existing geometry to activate the relevant inference; Shift suppresses inferencing while dragging.
These are documented examples, not an exhaustive promise for every tool. For equal, concentric, coradial, collinear, or fix, deliberately apply or verify the required rule. Rectangle, slot, and other creation tools can supply their own relations.
Remove unwanted freedom with relations and dimensions, then test whether edits preserve the intended shape.
Predict how an anchored rectangle grows, then test its remaining motion; Interactive; Practice
Predict how an anchored rectangle grows, then test its remaining motion
Rectangle constraint lab. Start with a 64 × 22 mm rectangular label blank. Predict where its left and right edges will be when the driving width changes to 80 mm. Compare a lower-left corner at the origin with a center at the origin.
Dashed: 64 mm width. Solid: 80 mm width. Left: corner anchored. Right: centered. Both retain 22 mm height.
Width changes from 64 to 80 mm; both sketches are fully defined before and after
Origin choice
Left x (mm)
Right x (mm)
Free motion
Lower-left corner
0 → 0
64 → 80
0 DOF
Center
−32 → −40
32 → 40
0 DOF
Diagnose the freedom: keep width and height driving, but remove only the horizontal anchor. The rectangle can translate horizontally: 1 DOF remains. Remove the width instead while retaining both anchors and height; the corner-anchored rectangle's right edge can move, or the centered rectangle can grow symmetrically. Restore the conditions before testing the intended size edit.
Measure versus constrain: a top-edge reference dimension reports the current width and adds no equation. A second driving width that agrees with the first repeats the same equation: five displayed conditions can still have only four independent conditions. A different second driving width contradicts the first; there is no feasible rectangle, so the lab retains its last valid drawing rather than displaying an invented solution.
Bounded model: one closed axis-aligned rectangle, with four variables [left x, right x, bottom y, top y]. Closure, rectangular shape and orientation are built in. For a feasible set, DOF = 4 − rank (the independent equation count). Width and height stay between 1 and 120 mm; these bounds restrict admissible sizes and do not count as equality constraints. The lab projects toward the nearest solution of the active equalities and rejects changes outside its size range. It models no rotation or other sketch entities and does not reproduce a vendor's solver or error colors.
With JavaScript enabled, use the prediction, size controls and two draggable corners. Keyboard: focus a corner and press arrow keys; Shift changes the requested step from 1 to 5 mm. Undo diagnostic motion restores the previous drawing.
Count independent ways the geometry can still change
Count independent ways the geometry can still change
A degree of freedom (DOF) is one independent variable still available to change. Constraints remove freedom. Count the geometry's possible motion, not the number of icons.
Simple, isolated 2D entities before any dimensions or relations
Entity
Free variables
DOF
Point
x and y position
2
Nonzero line segment
x and y for each endpoint
4
Circle
Center x, center y, radius
3
Circular arc
Center x, center y, radius, two endpoint angles
5
A circle's diameter dimension removes one DOF; its center can still move in two directions. Making its center coincident with the origin removes those two. A line with one endpoint at the origin still has length and direction to determine.
Supporting detail: Addendum 51 — Why subtracting one per relation gives wrong answers.
A driving dimension controls size; a driven dimension reports it
A driving dimension controls size; a driven dimension reports it
A driving dimension is a constraint: changing its value asks the solver to change the geometry while keeping the other rules. Length, angle, radius, diameter, and location dimensions can all supply constraints.
A driven or reference dimension measures a result already controlled elsewhere. It does not remove another DOF. For example, a circle whose size is set by a 24 mm driving diameter already has a 12 mm radius; a second driving radius dimension duplicates that control.
Use a relation for an enduring geometric rule and a dimension for the independent value you intend to change. Two lengths that must remain equal need an equal relation and one driving length, rather than two unrelated numbers that happen to match today.
Onshape automatically makes a newly added dimension driven if it would over-define the sketch. Check whether a displayed value is driving before expecting it to control geometry.
Supporting detail: Addendum 52 — Software treatment of redundant dimensions.
Read the sketch state in the software you are using
Read the sketch state in the software you are using
Under-defined / underconstrained: some position, orientation, or size remains free.
Fully defined / fully constrained: no free motion remains with the current driving values. Editing those values can still change the sketch.
Over-defined / overconstrained: dimensions or relations conflict or add control the solver treats as redundant. Repair the conflicting set.
Documented colors for sketch geometry while editing; selection and hover highlighting are separate
Software
Under-defined
Fully defined
Problems
SOLIDWORKS 2026
Blue
Black
Geometry-status help identifies yellow for conflicting or invalid items and red for unsolvable items; a redundant driving dimension can be red.
Onshape
Blue
Black
Red geometry indicates a constraint problem. A problem constraint icon is white on red.
Read status messages and inspect relations as well as color. One black edge does not prove that the entire sketch is fully defined. An under-defined construction line or endpoint can be easy to overlook.
Supporting detail: Addendum 53 — Current vendor references for status colors.
Fully define a sketch in a repeatable order; Checklist
Fully define a sketch in a repeatable order
State what must stay aligned, centered, equal, or tangent when the size changes.
Choose the plane and an origin reference that suit that intent. Confirm the working units.
Draw the simplest useful entities. Check the automatic relations and remove unintended ones.
Connect the intended endpoints and apply the geometric relations that describe the shape.
Anchor the sketch's position to the origin or other stable references; control its orientation.
Add independent driving dimensions for the remaining sizes and locations.
Inspect the remaining free points and curves. Drag gently to diagnose motion, then undo the diagnostic move.
Resolve conflicts before adding more constraints. Inspect the whole sketch, including construction geometry.
Change one intended driving value, check that the sketch behaves correctly, then restore the value.
Fully defined is a useful check, not proof of good design intent. Fixing a misplaced point can remove freedom without giving it the correct location. A sketch can be completely constrained by dimensions that make future edits awkward.
Test design intent with a change, not just the starting shape; Practice
Test design intent with a change, not just the starting shape
Fresh practice part: a circular inspection plate. Sketch two circular boundaries for an annular plate. Put their common center at the origin; use concentric and separate diameter dimensions of 46 mm and 18 mm. Increasing the outer diameter to 58 mm should leave the inner opening centered and unchanged in size.
Fresh practice part: a rectangular label blank. Use an axis-aligned rectangle with its lower-left corner at the origin, width 64 mm, and height 22 mm. Increasing the width to 80 mm should move the right edge while the left edge stays at the origin. If the intended part must grow equally left and right, choose a centered construction instead.
These two origin choices describe different editing behavior. There is no single best anchor for every part. Decide what should stay put before dimensioning.
Repair the unwanted rule, then check the intended change again
Repair the unwanted rule, then check the intended change again
When an added dimension causes an error, inspect what already controls that measurement. Keep the relation or dimension that expresses the intended design. Remove the duplicate, or make a measurement driven if it is only there to report a result.
A horizontal line cannot also have a nonzero vertical separation between its endpoints. Equal circles cannot have different driving diameters. These are contradictions; adding still more dimensions will not solve them.
SOLIDWORKS offers Display/Delete Relations and SketchXpert for diagnosis. Onshape's Constraint manager filters constraints and dimensions to help locate problems. A suggested deletion is still a design decision: check what behavior you would lose.
Supporting detail: Addendum 54 — Redundancy is not the same as contradiction.
Plan a solid part as a sequence of features, choose stable references, and test whether the model survives a change.
Build the main shape, then add and remove material
Build the main shape, then add and remove material
A parametric model stores instructions for building a shape. Dimensions and relationships are inputs; the solid is the result. Change an input and rebuild to see the result update.
The base feature creates the initial solid. Later features add material, remove material, or modify faces and edges. For a simple spacer, start with its main cross-section and extrude it. For a stepped round knob, a revolved section may describe the main shape more directly. There is often more than one valid feature sequence.
A body is a connected piece of solid geometry. A SOLIDWORKS part file can contain multiple bodies. An Onshape Part Studio can create multiple parts from a shared feature list. Neither arrangement, by itself, defines assembly motion or assembly relationships.
The feature tree records a build sequence and its dependencies
The feature tree records a build sequence and its dependencies
Read the tree from the base feature toward the end. A feature that supplies a sketch, face, edge, or other reference is a parent; a feature that uses that reference is a child. A child can depend on more than one parent. Being later in the list does not, by itself, make a feature a direct child of every earlier feature.
For example: a plate extrusion supplies a top face for a hole-position sketch. A hole feature uses that sketch. A pattern uses that hole as its seed. Delete the hole and the pattern loses its seed; delete the plate and the sketch loses its support as well. Inspect the deletion dialog before accepting dependent deletions.
Rename features for their purpose, such as Main plate, Locating hole, and Hole row. Renaming a feature in the tree is different from renaming a referenced part file. File references need their own reference-aware workflow.
Supporting detail: Addendum 55 — Why a small edit can break a later feature.
Rollback lets you inspect an earlier stage without deleting later work; Checklist
Rollback lets you inspect an earlier stage without deleting later work
Move the rollback bar above later features to inspect or edit an earlier stage. Return it to the end when checking the completed part. Rollback is a temporary stopping point in regeneration. Suppression instead leaves a selected feature in the tree but excludes it from the active model; dependent features may also be affected. Hiding changes visibility, not the solid's definition.
Find the earliest feature that fails or produces the wrong shape.
Roll back to inspect the geometry and references available at that point.
Edit the sketch for its dimensions or relations; edit the feature for its operation, depth, direction, or selected references.
Roll forward to the end, rebuild, and inspect the downstream results.
Supporting detail: Addendum 56 — Vendor help for history and rollback.
Choose references that express what must stay aligned
Choose references that express what must stay aligned
A reference plane locates a sketch or defines symmetry. A reference axis supplies a direction or center of rotation. Neither adds material. Use the origin and default planes when they express the design; add offset, angled, or mid-planes when needed. Reference geometry can also have parents.
Design intent is what should stay true when dimensions change. A centered plate should grow equally on both sides of its center plane. A hole required to pass through the plate should remain through when the plate gets thicker. A row of identical holes should share one seed definition and a spacing rule.
Put major shape and functional references early. Add small edge treatments later when they are finishing details. This is a useful starting order, not a rule that every fillet must be last: a large blend that defines the main shape may belong before shelling or other features.
Supporting detail: Addendum 57 — Fewest features is not always the best model.
Check units, bodies, material, and mass after a change; Checklist; Practice
Check units, bodies, material, and mass after a change
Assign the intended material or density before relying on mass. A surface color is not evidence that density is correct. For a uniform solid, mass = density × volume. Compare volume with a simple estimate, and inspect unexpected mass or center-of-mass changes.
A fresh example: a solid rectangular spacer measuring 30 × 20 × 8 mm has a volume of 4,800 mm³ = 4.8 cm³. With an assumed density of 2.50 g/cm³, its mass is 12.0 g. These are practice values, not a material specification. A hole should reduce that mass if the same body and density remain selected.
Confirm the document units and overall dimensions.
Confirm the expected body or part count and the scope of each add or cut.
Change one important dimension, rebuild, and check the intended relationships.
Check material assignment, selected bodies, and any mass overrides before trusting the result.
Supporting detail: Addendum 58 — Mass properties are a check, not proof of a correct part.
Engineering Graphics and CAD/CAD Modeling
Extrude and Revolve
Turn a sketch into a straight or rotational solid, and choose an end condition that preserves the intended shape when dimensions change.
Extrude carries a cross-section in a straight direction
Extrude carries a cross-section in a straight direction
For a plain solid extrusion, select a closed sketch region and give it depth. A rectangular region makes a block; a circular region makes a cylinder. Without draft, the cross-section remains constant along the extrusion.
A boss/base extrusion creates or adds solid material. An extruded cut removes material where the extrusion intersects the target solid. Check the arrow, preview, and selected bodies. A cut pointing away from the part cannot remove material from it.
Sketch → straight depth → solid. This schematic shows the geometry, not a software dialog.Section through a rectangular cut: the floor and surrounding body remain.
In Onshape, choose the result operation New, Add, or Remove. In SOLIDWORKS, check the boss/cut command and merge or feature scope settings. Adding touching material and creating a separate body are different intentions.
Choose the end condition for what should happen after an edit; Interactive; Practice
Choose the end condition for what should happen after an edit
Condition
What controls the end
Use when
Blind
A specified distance in the selected direction.
A pocket must keep a particular depth.
Through all
All target material along the selected direction.
A cut must remain through as the part thickens. Check body scope and one- versus two-direction settings.
Up to next
The next terminating surface that intercepts the entire profile.
The next suitable boundary is the intended stop. It is not simply the first edge encountered.
Up to surface / face
A selected terminating surface or face.
The feature must follow that particular boundary when it moves. The selection becomes a dependency.
Mid-plane
A total depth split equally about the sketch plane.
The part must stay centered. In SOLIDWORKS, a 14 mm Mid Plane depth extends 7 mm each way.
Worked thickness edit. One rectangular cut starts on the top face of one flat plate, travels downward normal to that face, and removes material from that selected body only. Compare a distance-controlled blind cut with a through-all cut before and after the plate becomes thicker.
All three sections use the same vertical scale: 8 drawing units per millimeter.
The requested blind distance reaches beyond this plate; actual removal stops at the body boundary.The blind distance stays 12 mm, so the later thickness edit leaves a floor.Through all follows this selected plate in the stated direction.
Design goal
Choice that survives the edit
Why
Opening must stay through
Through all
The termination follows the selected plate thickness.
Pocket must retain a floor
Blind, with a depth smaller than the final thickness
The fixed distance intentionally stops before the far face.
This teaching model does not cover up-to-face, up-to-next, multiple bodies, opposite directions or revolved cuts. Check the selected sketch region, direction and body scope in the CAD preview.
Do not substitute an oversized blind cut for a through-all requirement. It may work today and leave a thin floor after a later edit. Conversely, through all is wrong for a pocket that must retain its floor.
Onshape uses a Symmetric option for supported end types. Dialog names and available conditions depend on the selected operation; inspect the preview and measured result rather than transferring every setting by name.
Supporting detail: Addendum 60 — Vendor help for extrusion boundaries.
Revolve rotates a section around an axis
Revolve rotates a section around an axis
Select a section, an axis of rotation, and an angle. A full turn is 360°; a smaller angle produces a partial rotational shape. A boss revolve adds material, and a revolved cut removes it. Start with a closed section on one side of the axis for a straightforward solid revolve.
The gap between the section and the axis becomes the bore. Rotating a section that reaches the axis can instead make a solid center.
A straight sketch line, centerline, or reference axis can define rotation when supported by the command. The axis must be deliberately located. A diameter describes the distance across a round shape; the distance from the axis to its outer wall is the radius.
A stepped sleeve can often be built with one revolved section including its bore. Repeated extrusions and cuts can also build it, but put the coaxial steps under separate controls. Choose the sequence that makes the important dimensions easiest to change.
Supporting detail: Addendum 61 — Check overlap and axis selection before adding complexity.
Pick the base feature from the shape's main organizing rule; Practice
Pick the base feature from the shape's main organizing rule
Use extrusion when a useful section stays the same along a straight direction. Use revolution when a useful section repeats around an axis. A cylinder can be made either way. A rotationally stepped part often makes the reason for choosing revolve clearer than a plain cylinder does.
Before accepting either feature, confirm the profile, direction or axis, end condition or angle, and result body. Then make one trial dimension change. Does the model still express the intent described in Feature-based Modeling?
Use a sweep to carry a section along a path and a loft to transition through ordered sections, with references that control the result.
A sweep needs a profile and a path
A sweep needs a profile and a path
A profile describes the cross-section; a path describes where it travels. A circular profile swept around a smooth bend makes a bent solid rod. An annular profile can make a tube. For a basic sweep, keep the section size constant and choose how it stays oriented along the path.
Profile + path → sweep → bent rod. The path is a reference curve, not another solid.
Place the profile on a plane normal (perpendicular) to the path at its start for an easy first construction. Constrain its position to the path. A shape that looks connected in one view can still be separated in three dimensions. Select the complete intended path, not a neighboring model edge.
A sweep can create material or remove it from an existing part. Advanced sweep options can control twist or scaling; a constant circular section is a simpler starting case. See Onshape: Sweep.
Sweep lab: how tight can a bend be before a thick profile folds?; Interactive
Sweep lab: how tight can a bend be before a thick profile folds?
Choose a profile and a path, then tighten the bend. Watch where the inside of the sweep turns red: there, the profile reaches the centre of the bend and the inner wall has to fold back through itself.
The rule this lab tests. Carry a profile along a path. At each point the path has a bend radius ρ: the radius of the circle that best fits the path there, measured to its centre of curvature. The profile also has a reach toward that centre: how far its edge extends from the path toward the inside of the bend. The inner wall folds through itself where
reach toward the centre of curvature ≥ local bend radius ρ
For a round rod centred on the path, the reach is its radius, so a rod of diameter D fails around a bend when D/2 ≥ ρ. Exactly equal is already a failure: the inner wall shrinks to an edge at the centre of curvature.
Reach 8 mm is less than the 12 mm bend radius, so the inner edge stays a smaller arc with 4 mm to spare.Reach 15 mm passes the 12 mm bend radius. The inner edge (red) passes the centre of curvature and runs backwards on the far side, folding the wall through itself.
Profile on a 12 mm arc
Reach toward centre
Result
Ø16 mm rod
8 mm
Builds (8 < 12)
Ø24 mm rod
12 mm
Fails: inner wall collapses to an edge (12 = 12)
Ø30 mm rod
15 mm
Fails: folds (15 > 12)
30 × 15 mm bar, 30 mm side across the bend
15 mm
Fails: folds
Same bar turned, 15 mm side across the bend
7.5 mm
Builds
Only the local bend matters for this test. On an S-curve the bend radius changes along the path, so the failure appears only near the tightest bends. Here a Ø20 mm rod (reach 10 mm) follows an S-curve whose tightest bend radius is 8 mm: 6% of the path fails.
Where the reach line rises above the bend-radius line, that stretch of the sweep folds (red bands).
A passing local test is not a complete check. This lab calls a sweep “builds” only on the U-bend, where the geometry also rules out clashes; anywhere else a passing local test is reported as only that, with global clearance not established. A Ø20 mm wire wound with a 30 mm coil radius bends gently (bend radius 30.2 mm), but with a 16 mm pitch neighbouring turns are only 15.9 mm apart, so the wire hits the next coil. Coils collide: neighbouring turns are 15.94 mm apart along the chord between them, but the profile needs 20 mm. The local bend test cannot see this clash.
The local test passes everywhere, yet the turns overlap. A real CAD check also looks for clashes between distant parts of the same feature.
Teaching model: the profile is centred on the path and carried without avoidable twist (a rotation-minimising frame). The red regions come from the local test only. It is not a complete validity check. The helix chord check can prove that neighbouring coils collide, never that they clear. A given CAD product may report failures differently or offer other orientation options. Sources: Patrikalakis, Maekawa and Cho, Local self-intersection of pipe surfaces and Global self-intersection of pipe surfaces; Onshape: Sweep.
A loft passes through profiles selected in order
A loft passes through profiles selected in order
A loft transitions between two or more sections. Put sketches on suitable planes, then select the sections in the order the shape should pass through them. A broad oval transitioning to a smaller oval is a simple example; the section size changes along the length.
Ordered sections → transition → solid. A guide can control the side between the sections.
Use a guide curve when the profiles alone do not control the shape between them. For a straightforward boundary guide, constrain it to meet every profile at the intended boundary point. A Pierce relation can locate a sketch point where a curve crosses that sketch plane. Do not accept a connection solely because it looks right in an isometric view.
Match corresponding locations around successive profiles. If one section's corner connects to an unrelated corner on the next, the loft can twist. Inspect connection handles and a section view before adding more profiles.
Supporting detail: Addendum 62 — More profiles do not automatically make a better surface.
Loft lab: what moving a start point or reordering profiles does; Interactive
Loft lab: what moving a start point or reordering profiles does
Three profiles stay in place: a square, a circle and a slot. Change only which points the loft pairs and the order you select the profiles, then watch the connector lines twist, pinch or double back.
What decides a loft’s shape. Each profile is divided into the same number of points, counted from its start point (the connector) in the same direction. Point 1 of the first profile joins point 1 of the next, and so on; the loft passes through the profiles in the order selected. Three profiles sit on parallel planes: a 60 mm square at the bottom, a Ø44 mm circle 45 mm up, and a 56 × 24 mm slot at 90 mm.
Matched start points: each connector runs straight from square to circle to slot.Circle start point moved 90°: the connectors spiral. No checked section crosses itself, but it is twisted.Circle start point moved 180°: paired vertices sit on opposite sides, so sections pass through the middle and cross themselves (red).Selected square, slot, circle: the loft climbs to the slot, then comes back down to the circle through heights it already occupies (red).
Change
Result
Fix
Start points do not correspond
Twist; a large mismatch pinches or crosses itself
Line up the connectors or start points
Profiles selected out of their order along the part
Loft doubles back across heights already occupied
Select profiles in sequence
Whole selection reversed
Same surface, built from the other end
Nothing to fix
Teaching model: every profile runs counter-clockwise, and corresponding points are joined by a smooth curve through all three profiles. A profile drawn in the opposite direction is a separate problem, not modelled here. Twist and crossing come from the actual sections. Source: Onshape: Loft (sequential profile order; connections control twist).
Use the controlling geometry to choose sweep or loft; Practice
Use the controlling geometry to choose sweep or loft
What you know
First feature to consider
What to inspect
One section following a bent centerline
Sweep
Path continuity, section position, and orientation.
Different sections at several locations
Loft
Profile order, connections, and shape between sections.
One section along a straight direction
Extrude
Depth or end condition.
A section repeated around an axis
Revolve
Axis position and rotation angle.
These are starting choices, not exclusive capabilities. For example, a loft can follow a centerline, and a sweep can vary with advanced controls. Prefer the feature that states the intended change clearly.
Challenge: choose the feature, then the one input that fixes it; Interactive
Challenge: choose the feature, then the one input that fixes it
Each target below comes with a failing attempt. Name the feature that states the shape, then pick the change that makes the attempt match the target.
Choose the feature, then the input to change. For each target, decide whether a sweep, loft or extrude states it, then which change fixes the failing attempt.
U-shaped handrail. One Ø20 mm round section follows a U-shaped centreline with a 30 mm bend radius. Current attempt: fails: the inner wall folds through itself.
Answer
Sweep. Yes: one constant section follows a bent centreline, which is what a sweep states. Change: Open the bend radius to 30 mm.
Square-to-round duct transition. A duct changes from a 60 mm square, through a Ø44 mm circle, to a 56 × 24 mm slot, with straight, untwisted sides. Current attempt: twisted: no crossing section found.
Answer
Loft. Yes: the section changes shape at known positions, which is what a loft states. Change: Move the circle’s start point back to 0° so it lines up with the square and slot.
Three-section transition built out of order. The same square → circle → slot duct, built bottom to top. Current attempt: wrong shape: the loft doubles back.
Answer
Loft. Yes: three different sections at fixed heights. Change: Select square, circle, slot: the order the profiles sit along the part.
Compression spring. Ø16 mm round wire wound with a 24 mm coil radius and a 28 mm pitch. Current attempt: fails: neighbouring coils collide.
Answer
Sweep. Yes: one wire section follows a helical path. Change: Increase the pitch to 28 mm.
Troubleshoot the inputs before changing every option; Checklist
Troubleshoot the inputs before changing every option
Check that the selected profile regions match the intended solid, surface, or thin result.
For a sweep, check path continuity and the profile's location and orientation.
For a loft, check profile order and each intended guide intersection.
Look for self-intersection: a thick swept section may overlap itself around a tight bend.
Inspect sections and confirm the expected part count; repair the first failed reference.
Shelling a complicated loft is a separate geometry problem: offset walls can collide where the shape becomes tight. Build and inspect the outer shape first, then check the wall thickness. See shell and other applied features.
Engineering Graphics and CAD/CAD Modeling
Patterns, Mirror, and Applied Features
Repeat geometry with a rule, model useful hole information, and finish a solid with edge treatments, shell, draft, and ribs.
Pattern a seed when the copies should change together; Practice
Pattern a seed when the copies should change together
A seed is the original feature being repeated. A feature pattern makes the repetition explicit: edit the seed's size once and rebuild the copies. Model independent features when their sizes or locations must change independently.
A linear pattern uses a direction, spacing, and count. For a single-direction row with N total instances including the seed, the distance from first center to last is (N − 1) × spacing. Some dialogs also offer a total-span mode; check which distance the field means.
Seed → direction and spacing → repeated features.
A circular pattern repeats around an axis. N evenly spaced instances around a complete circle have an angular pitch of 360°/N. A partial arc with both endpoints occupied instead has N − 1 intervals across that arc. Inspect whether the dialog asks for total angle or angle between instances.
Seed + axis → full-circle spacing → four total holes.
Choose feature, face, or body/part pattern deliberately. A feature pattern repeats selected operations; a body/part pattern repeats a larger solid. Check target bodies, skipped instances, and whether every copy actually intersects the intended material.
Supporting detail: Addendum 63 — Copied geometry and recalculated end conditions can differ.
Mirror across a plane when symmetry is the rule; Practice
Mirror across a plane when symmetry is the rule
A mirror reflects selected features or bodies across a plane. Corresponding points lie at equal distances on opposite sides. It is not a rotation: an asymmetric shape changes handedness.
A stable center plane is usually a better symmetry reference than a face likely to move independently. Check whether the mirror should join material into one body or create another. Assemblies use separate tools to position components; part-level mirror features do not define assembly motion.
Hole features store type and size as well as position
Hole features store type and size as well as position
Use a hole feature when the hole needs structured information such as a fastener size, fit, counterbore, countersink, or tapped-hole specification. A counterbore is a larger cylindrical recess; a countersink is a conical recess. A plain circular cut can make geometry, but does not automatically carry the same hole definition.
Position + hole definition → modeled hole. Section view shows the recess; no thread geometry is implied.
In SOLIDWORKS Hole Wizard, use Type for the hole parameters and Positions for its centers. Select the appropriate standard, type, size, fit where offered, and end condition. Locate the centers with dimensions and relations. Different hole types require separate Hole Wizard features.
For tapped holes, distinguish drill depth from thread depth. A cosmetic thread represents thread information without cutting a helical groove in the solid. Inspect the selected thread option before expecting detailed thread geometry in an export.
Supporting detail: Addendum 64 — Hole options depend on type and software version.
Fillet rounds an edge; chamfer bevels it
Fillet rounds an edge; chamfer bevels it
A fillet creates a rounded transition. A chamfer creates a beveled transition. Select the intended edges, set the radius or chamfer dimensions, and inspect the preview all the way around the selection. A small radius can still fail where neighboring faces leave too little room.
Keep edge treatments separate when they have different functions or are likely to change independently. Cosmetic edge breaks often belong late; a large blend that controls the main shape may belong early. See planning feature order.
Shell hollows a solid and leaves a controlled wall; Practice
Shell hollows a solid and leaves a controlled wall
Select faces to remove and specify the remaining wall thickness. Removing the top face of a block makes an open container; keeping all faces can make an enclosed cavity. Check whether the thickness is offset inward or outward.
Solid + opening face → wall thickness → hollow part, shown in section.
If shell fails, inspect small radii and narrow regions where offset faces collide. Try a simpler outer shape or revisit the intended thickness. Do not silently reduce a required wall just to make the command succeed. See Onshape: Shell.
Draft tapers faces; a rib adds a thin support; Practice
Draft tapers faces; a rib adds a thin support
Draft inclines faces relative to a pull direction, often to help a molded part release. In a neutral-plane construction, that reference keeps its size while selected side faces tilt. Check the direction and which end grows or shrinks. There is no universal draft angle for every material and process.
A rib adds a thin web between supporting regions. It usually starts from sketch curves plus a thickness and direction. Although grouped here with finishing features, a rib needs sketch geometry. Check that it meets the intended walls and merges with the intended part.
Support + sketch → thickness → reinforcing web. Thickness runs across the sketch plane.
See Onshape: Draft, Rib, and the feature tool glossary. After any applied feature, rebuild, inspect the section, and make a trial change to its parent geometry.
Keep component references intact and choose mates that locate parts while preserving their intended motion.
An assembly records which parts belong together and how they fit
An assembly records which parts belong together and how they fit
A part defines a component's shape. An assembly places instances of parts and subassemblies and records relationships between them. Two instances of one part can occupy different positions while using the same part definition.
In a file-based SOLIDWORKS assembly, the .SLDASM normally references external .SLDPRT and other assembly files. An assembly drawing references the assembly. Sending only the assembly file can leave the recipient without its components. Virtual components are an exception: their definitions can be stored inside the assembly.
Onshape organizes Part Studios, Assemblies, and Drawings as tabs in documents. Inserted instances reference their source definitions; a tab name is not a Windows filename. Share the document with the appropriate access and identify the intended version when a fixed design state matters.
Supporting detail: Addendum 65 — Definitions, instances, and design changes.
Rename and package files with their references; Checklist
Rename and package files with their references
Renaming or moving a component in ordinary File Explorer can leave an assembly looking for its old name or location. Use the CAD system's reference-aware rename or move workflow. Changing a display name in the tree is not necessarily changing the file name.
Save a recoverable copy before reorganizing an assembly's files.
Use the supported rename workflow, include affected assemblies and drawings, and save the referencing documents.
For file-based SOLIDWORKS sharing, use Pack and Go where available. Review the file list, drawing inclusion, library components, and destination.
Open the packaged assembly from its destination and inspect the resolved reference paths. Confirm it is not quietly loading parts from the original folders.
Supporting detail: Addendum 66 — Vendor help for renaming and sharing.
Ground a base, then count the motion you intend to keep
Ground a base, then count the motion you intend to keep
A free rigid component in three-dimensional space has six degrees of freedom (DOF): translation along three axes and rotation about three axes. A degree of freedom is an independent motion, not a count of arrows or mates.
Grounding removes motion relative to the assembly reference frame.
Choose a base or housing as the reference. Fix it, or fully locate it to the assembly origin and planes. In SOLIDWORKS, insertion options include fixing only the first component, fixing inserted components, or leaving them floating. Check the actual state; do not assume that the first component is always fixed. Fixing a base away from the origin holds it there; it does not move it to the origin.
A lever should still rotate about its pivot. A cover should stay put. Fully locating every moving part would turn a mechanism into a rigid model.
Supporting detail: Addendum 67 — Check the insertion setting.
Use geometric mates to describe the intended contact
Use geometric mates to describe the intended contact
Select the actual locating faces, axes, or reference planes. The same mate name can accept different geometry, so its effect depends on what you select. The diagrams below are schematic before/after comparisons, not complete constraints for whole assemblies.
Coincident
For two planar faces, put their supporting planes together. The faces can still slide in that plane and rotate about its normal. Coincident planes do not guarantee that finite faces overlap.
Concentric
Put two cylindrical axes on the same line. Without a rotation lock or other mates, a shaft can still slide along and rotate about that line.
Supporting detail: Addendum 68 — Why subtracting one DOF per mate gives the wrong answer.
Test a shaft joint: keep the motion the design needs; Interactive; Practice
Test a shaft joint: keep the motion the design needs
The housing is grounded. The shaft and its attached lever start with their axes aligned to the housing bore. Predict the motions left, test them, then seat the shoulder. Finally add angular alignment: does a hinge still work?
Worked experiment: 2 → 1 → 0 independent motions
This original ideal joint begins after axis alignment, not as a free rigid body. Its only coordinates are axial position z in millimeters and spin θ in degrees. The housing is grounded; the lever moves with the shaft.
Worked hinge state: shoulder at the housing datum, z = 0 mm; lever at θ = 65°. Looking toward −Z in the end view, positive spin is counterclockwise. Dashed lines show the joint axis and reference datums.
Conditions remove independent motions, not one freedom per mate icon
Condition after built-in axis alignment
Example coordinates
What can move?
Neither additional condition
z = 12 mm, θ = 35° → test: 22 mm, 65°
Slide + spin: 2 DOF
Seat shoulder at z = 0
z = 0 mm, θ = 65°
Spin only: 1 DOF. Hinge goal met.
Also align lever at θ = 0°
z = 0 mm, θ = 0°
Neither: 0 DOF. Fixed goal met; hinge goal defeated.
Angular alignment only
z may vary, θ = 0°
Slide only: 1 DOF. Slider goal met.
Diagnose and recover: to restore the hinge, remove angular alignment while keeping the shoulder seated. The shaft can turn again. For a slider, remove the shoulder condition and retain angular alignment. Choosing a goal alone does not change conditions.
The shoulder condition enforces z = 0; angular alignment enforces θ = 0°. They do not freeze an arbitrary current placement. Removing a condition permits motion without itself moving the component. Angles wrap every 360°.
Model limits: axial travel −30 to +30 mm is a declared lab range, not physical stops. Axis alignment and rigid components are built in. Shoulder seating means ideal plane coincidence, holding z = 0 in both directions; physical shoulder contact alone would not retain a shaft against separation. Contact, collision/interference, friction and load capacity are outside this model. Schematic overlap does not establish a fit or clearance.
In a SOLIDWORKS geometric-mate sequence, concentric alignment followed by shoulder-face coincidence can leave shaft rotation free. This lab's conditions illustrate the resulting motion; they are not a vendor command recorder. Onshape expresses joint motion through mate connectors: Cylindrical permits axial translation and rotation (Tz, Rz), while Revolute permits rotation (Rz). These are not a one-to-one mapping of the SOLIDWORKS steps.
Parallel keeps selected planes parallel without setting their separation. Perpendicular keeps selected planes at a right angle. Neither condition alone fully locates the part. These diagrams show the planes edge-on.
Distance, angle, and tangent mates control gaps and contact
Distance, angle, and tangent mates control gaps and contact
Distance sets a separation between selected entities. For parallel planar faces, use the normal gap, not a slanted edge length. Angle sets the angle between selected entities; check alignment and direction so the model uses the intended side of the angle.
Tangent keeps compatible curved and planar or curved surfaces touching tangentially. Tangency alone does not enforce rolling without slipping.
Choose a joint or mechanical relationship when motion is the point
Choose a joint or mechanical relationship when motion is the point
For a simple lever on a grounded pin, align the pivot axes and locate the lever axially. Leave rotation free. A hinge mate expresses this single rotational freedom directly. In Onshape, a Revolute mate serves that joint purpose; Cylindrical allows axial slide and spin, Slider allows one translation, and Fastened allows no relative motion. Mate connectors establish the joint frames.
A slot mate locates a pin or similar feature relative to a slot. Select free travel or a prescribed position to match the design; other motions depend on the selections and remaining mates. Onshape's Pin Slot mate allows rotation about the connector's Z axis and translation along its X axis. Set appropriate travel limits; it is not an identical set of SOLIDWORKS slot options.
A gear mate or gear relation couples rotations by a ratio. Locate the shafts first. The relation does not create teeth or prove they mesh without interference. Use Gear Ratios for the ratio calculation and Torque for the separate question of turning effort.
Build reusable parts and subassemblies with deliberate dependencies; Practice
Build reusable parts and subassemblies with deliberate dependencies
Bottom-up design starts with existing parts and brings them into an assembly. Top-down design starts with an overall layout or shared design references and develops parts around them. A mixed approach is common: use a shared layout for custom plates and insert purchased hardware.
A subassembly groups parts into a reusable unit. Give it a useful function, such as a pivot cartridge, rather than hiding unrelated parts in it. Check whether its internal joints are allowed to move at the parent level; a rigid subassembly can make a working joint appear locked.
Top-down references can keep mating holes aligned when the layout changes, but they also create dependencies. Keep the direction of those dependencies understandable and check them when copying or sharing the design.
Supporting detail: Addendum 70 — What makes a feature top-down?.
Use SOLIDWORKS Toolbox or Onshape Standard Content, where available, for standard hardware. Choose the standard, size, thread pitch, length, and material or grade deliberately. A visually similar bolt or an automatic size suggestion is not a completed fastener selection.
Supporting detail: Addendum 71 — Library hardware still needs checking.
Diagnose mate errors, inspect overlap and clearance, and test the intended motion before trusting an assembly model.
Judge remaining motion against the design intent
Judge remaining motion against the design intent
A successful rebuild means the CAD system can solve the model. It does not mean the model describes the mechanism you intended. Try moving each component and name the motion that should remain.
Under-mated means freedom remains. That is a defect for a loose cover, but rotation at a lever pivot can be intentional. Over-mated or conflicting constraints ask for relationships that the solver cannot satisfy together. A redundant constraint repeats an existing condition; it adds no useful location and can complicate diagnosis.
For a shaft with concentric axes and seated shoulder faces, one rotation remains. Adding another mate that merely keeps those axes parallel is redundant. Adding an angle mate to lock that remaining rotation may be correct for a stationary shaft and wrong for a rotating lever. Review Assembly Files and Mates for the geometry.
Repair the cause of a mate error before adding more mates; Checklist
Repair the cause of a mate error before adding more mates
Read the reported mate error and identify the first failed relationship, rather than only the later errors it causes.
Check which component is grounded and whether a moving part was fixed accidentally.
Inspect selected faces and axes, alignment direction, offsets, and angle values.
Check whether an edit removed or replaced the geometry used by a mate.
Temporarily suppress a suspect mate to isolate the conflict, then repair or remove the unnecessary relationship.
Rebuild and test motion again, including motion inside subassemblies at the parent level.
Do not force incompatible hole locations together by adding duplicate constraints. Determine whether the parts, the chosen references, or the intended fit are wrong.
Check interference and clearance as different questions
Check interference and clearance as different questions
Interference is shared volume: two solid parts occupy the same space. Clearance is the gap between parts. A model with no overlap may still lack enough room for movement, manufacturing variation, or tool access.
Run interference detection on the relevant components in the intended configuration and position. Inspect each result. An intentional press fit or simplified thread representation can produce overlap, but an unwanted bolt tip inside a moving path needs attention. Record the reason for any accepted interference.
Supporting detail: Addendum 72 — Selection scope can hide an interference.
Move the mechanism through its intended range; Checklist; Practice
Move the mechanism through its intended range
Move the input joint slowly and watch the connected parts. Test intermediate positions as well as endpoints: a lever can clear a housing at both ends and strike it halfway through. Check which mate limits apply and whether the model passes through solid geometry because collision checking is not active.
A motion preview checks the constraints represented in that preview. It does not automatically prove contact behavior, load capacity, friction, or real-world operation. In particular, a gear relation can drive two rotations even when the modeled teeth do not mesh correctly.
Confirm that the input moves and connected parts follow in the expected direction.
Inspect travel limits and intermediate positions for collisions and small gaps.
Check that the components can be assembled and tools can reach the fasteners.
Rebuild after changes and repeat the affected motion and interference checks.
Review the final drawing and BOM against the checked assembly.
Supporting detail: Addendum 73 — A joint preview is not always a full-assembly test.
Show how components fit together and connect drawing balloons to clear part identities and quantities.
An exploded view separates parts to explain their relationship
An exploded view separates parts to explain their relationship
An assembled view shows the working arrangement. An exploded view spaces components apart so the reader can identify them and follow how they fit. The separation is for communication; it is not an operating clearance or a change to the part geometry.
Separate components along understandable directions, keep related parts aligned, and use explode lines where the connection would otherwise be unclear. Preserve the working assembly and create a saved exploded view rather than deleting mates to pull the model apart.
Original teaching schematic: the pin passes through the aligned holes; a retainer holds its end. Both washers use item 4. No manufacturing dimensions or fit are implied.
Supporting detail: Addendum 74 — Use the saved view in a drawing.
A balloon finds a BOM row; a part number identifies the component
A balloon finds a BOM row; a part number identifies the component
A bill of materials (BOM) lists the components required for the stated assembly. A drawing balloon points to a component and usually shows its BOM item number. The item number is a row identifier in that drawing's list. The part number identifies the part for reuse, manufacture, or purchase.
One teaching pivot assembly — quantities per assembly
Item
Part number
Description
Quantity
1
PV-110
Support
1
2
PV-210
Lever
1
3
PV-310
Pivot pin
1
4
HW-410
Thrust washer
2
5
HW-510
Pin retainer
1
Balloon 4 identifies HW-410, not four washers. Its quantity is two per assembly. This list has five distinct rows and six component instances. Repeated instances of the same specified part share an item number; different sizes or variants need distinguishable identities.
Decide whether the BOM lists units or their internal parts
Decide whether the BOM lists units or their internal parts
A top-level list can show a purchased subassembly as one unit. A structured list can show the assembly hierarchy, while a flattened list collects the underlying components without that hierarchy. State the scope before interpreting a quantity. Do not order a complete unit and all its contents accidentally.
Verify part numbers, descriptions, quantities, and relevant configuration or revision information. A library model's filename is not automatically a useful purchasing description. The teaching identifiers above are examples, not an orderable hardware specification.
Supporting detail: Addendum 76 — Subassembly display changes what the table means.
Review the assembly drawing as an identification tool; Checklist; Practice
Review the assembly drawing as an identification tool
Show an assembled view that makes the working arrangement understandable.
Add an exploded or section view where hidden relationships need explanation.
Follow each balloon leader to the correct component and match its number to the BOM.
Count repeated components and compare the counts with the stated BOM scope.
Check the drawing's design state, units, scale, and necessary assembly notes.
An assembly drawing explains how parts belong together. Individual part drawings supply the manufacturing detail for those parts; do not crowd every part dimension onto an assembly view. See Choosing Drawing Views and the Engineering Graphics and CAD collection for related drawing topics.
Compare current mechanical CAD certification paths, distinguish requirements from recommendations, and verify the route before registering.
Use a certification to document assessed skills, not to replace design experience
Use a certification to document assessed skills, not to replace design experience
A CAD certification is a provider's record that you passed a defined assessment. Depending on the program, that assessment may cover drawing interpretation, sketches, parts, assemblies, documentation, collaboration, manufacturing, or analysis. It can give a learner a concrete practice goal and give an employer one more piece of evidence about a specific product or workflow.
Its meaning is bounded. A credential does not guarantee employment, prove that every model is manufacturable, or replace a portfolio, coursework, supervised practice, and engineering judgment. Product names and versions also matter: proficiency in one CAD system does not automatically transfer to every other system.
This overview leads with mechanical CAD. Architecture and construction, CAM, simulation, additive manufacturing, product-data management, and platform roles are useful branches when they match the work you want to do. Program information below was checked against official sources on October 29, 2026; recheck the linked catalog before registering.
Choose the product and work first, then the credential level
Choose the product and work first, then the credential level
Do not begin by looking for a universal Associate → Professional → Expert ladder. Providers use those words differently, and some products offer only selected levels. Begin with the software and tasks used in your course, internship, workplace, or intended field.
Core mechanical design
Look for sketching, parametric part modeling, assemblies, drawings, dimensions, materials, and model checks.
Specialized design
Sheet metal, surfacing, weldments, mold tools, drawing tools, and generative design usually require narrower practice than a general design credential.
Manufacturing and additive
CAM, turning, milling, additive-process, and design-for-manufacturing credentials connect geometry to process planning. They are not substitutes for machine or shop authorization.
Simulation
Static, thermal, flow, frequency, nonlinear, and other analysis credentials assess both software operation and interpretation. Passing does not make an unchecked result physically valid.
Platform and data roles
Cloud collaboration, revisions, lifecycle, PDM, and administrator credentials may assess data workflows rather than only geometry creation.
Read the assessed skills on the exact credential page. A badge for completing a course, a training certificate, and a certification earned by passing an assessment are not automatically the same thing.
Compare SOLIDWORKS and Autodesk mechanical paths
Compare SOLIDWORKS and Autodesk mechanical paths
SOLIDWORKS
The official SOLIDWORKS catalog groups the general design path as Design Associate, Design Professional, and Design Expert, but the levels assess different depth rather than the same checklist three times.
Foundational sketches, common part features, patterns, dimensions, materials and mass properties, component insertion and mates, drawing views, and annotations.
Professional parametric part design from drawings, linked dimensions and equations, configurations and design tables, mass-property changes, and assembly modeling across three segments.
Advanced part and assembly problem solving, including multibody/imported geometry, complex features, in-context work, configurations, and advanced bills of materials. Eligibility requires CSWP plus at least four of exactly these five advanced-topic exams: Sheet Metal, Weldments, Surfacing, Mold Tools/Mold Making, and Drawing Tools.
Those five design specialties form the CSWE prerequisite set. Other Professional credentials—such as CAM, MBD, API, and Flow Simulation—assess valuable but different work and are not listed as substitutes in the CSWE requirement. Additive Manufacturing Associate assesses processes, materials, design, slicing, and preparation without requiring SOLIDWORKS software during the assessment.
The simulation family is separate: Simulation Associate covers statics, materials, loads, mesh, and result checks; Simulation Professional adds static, frequency, thermal, beam/shell, and convergence work; Simulation Expert requires CSWP, CSWA-S, and CSWP-S and adds advanced contact, composites, thermal, dynamics, and nonlinear analysis. Flow Simulation Professional is another specialty, not a step in that three-credential prerequisite chain.
Cloud xDesign and xShape credentials are not alternate names for desktop CSWA/CSWP. The xDesign Professional and xShape Professional pages require the relevant app, prescribed training, 3DSwymer Associate, ENOVIA Collaborative Industry Innovator Associate, and a new collaboration space. Exact student-cloud bundle mapping remains unclear, so confirm access before choosing one.
Route matters for students. Through the Academic Certification program, free exams depend on the school being an Academic Certification Provider, an active subscription, and region-specific license minimums; this is not an entitlement for every student. The current Design Premium for Students offer separately lists CSWA and CSWP attempts, while free Design Standard software does not list them. Recheck the current offer before purchase. Ordinary CSWP publishes no general prior-certification requirement, except that K–12 students using an Academic Certification Provider must first pass CSWA. The distinct CSWP-Academic route requires CSWA-Academic at least 30 days earlier and qualified, proctored institutional delivery.
Autodesk
Autodesk names four broad levels: Certified User (ACU), Certified Associate (ACA), Certified Professional (ACP), and Certified Expert (ACE). Not every product has every level, and the official overview does not establish a universal prerequisite ladder.
Mechanical starting points include ACU exams for AutoCAD, Inventor, and Fusion; ACA in CAD for Mechanical Design; ACP in Inventor for Mechanical Design, AutoCAD for Design and Drafting, and Design for Manufacturing; and ACE in Generative Design for Manufacturing. Optional extensions include Fusion CAM credentials, ACP in Simulation for Static Stress Analysis, and AEC credentials for Revit, Civil 3D, and BIM management.
ACU registration runs through Certiport; Autodesk's current ACU guidance says exams may be delivered online or in person, so do not assume a testing-center-only route. ACA, ACP, and ACE pages instead route candidates through Autodesk's application/dashboard to Pearson VUE or OnVUE. Those ACA/ACP/ACE exams use selected-response questions rather than live CAD software, so preparation should include concepts and workflow decisions as well as software practice. See Autodesk certification support for current policies and preparation routes. Free Autodesk education software and free learning resources do not establish a free exam or student discount.
Compare Onshape, Creo, NX, and Solid Edge
Compare Onshape, Creo, NX, and Solid Edge
Onshape
The live Learning Center certification catalog lists Certified Onshape Associate for parts, multipart design, assemblies, drawings, and collaboration, and Certified Onshape Professional for advanced modeling, motion, in-context work, versioning, branching, and linked-data collaboration. No Associate prerequisite is published for Professional. Register through the Learning Center and its Training Dashboard. A student Associate voucher has been described only through a conditional preparation route; current course access and voucher availability must be confirmed.
PTC Creo
The current PTC Learning Connector uses Product Proficiency for foundational sketches, features, assemblies, properties, and analysis; Modeling Specialist for advanced design intent, sketches, and solids; and Surfacing, Sheetmetal, Assembly, and Documentation specialists for their named workflows. Older User/Associate/Professional labels should not replace the live catalog. Enroll through the specific Learning Connector exam with appropriate active LEARN access; learning paths are recommended, and the current FAQ says prior certifications are not prerequisites. A separate academic certification-only route offers Product Proficiency, Modeling Specialist, Assembly Specialist, and Documentation Specialist after Proxi.id academic verification. It does not include every specialist or prove a universal student entitlement.
Siemens NX
The live Siemens Xcelerator Academy catalog lists NX Design Associate for solid and assembly models, modeling strategies, parametric/non-parametric methods, and interpart links; NX Design Professional adds curves and surfaces, PMI, validation, downstream model use, and drafting. The NX Design learning map makes Associate a prerequisite for Professional. Register from the catalog's Buy route. Optional NX CAM Associate/Professional and Additive Manufacturing Associate paths assess manufacturing work. Academic discounts or free vouchers may depend on institutional licensing; no universal student entitlement is established.
Siemens Solid Edge
The Solid Edge registry publishes Associate, Professional, and Expert. Associate covers introductory parts, assemblies, sketches, and drawings; Professional adds advanced synchronous, sheet-metal, assembly, and documentation work. Associate before Professional is recommended, not stated as mandatory; Expert requires Professional and assesses advanced ordered/synchronous modeling and detailing. Use Getting Started to register, complete the profile, review the guide, and select an exam. Enrollment pages currently display the exams as free, but verify region and delivered software version.
Keep CATIA V5 and 3DEXPERIENCE credentials separate
Keep CATIA V5 and 3DEXPERIENCE credentials separate
Dassault Systèmes publishes two different families. 3DEXPERIENCE role certifications include Associate roles such as Mechanical Designer, Mechanical & Shape Designer, SheetMetal Designer, and Function Driven Generative Designer. Associate exams use the Edu Space and certification-credit route with access to the appropriate roles/apps. The Professional registry covers advanced Mechanical Designer, Function Driven Generative Designer, and SheetMetal Designer work through authorized certification centers—public centers for general candidates or private academic centers for their students. Role trigrams identify software roles, not separate marketed exam codes.
CATIA V5 certification is another center-delivered family, marketed at Associate and Expert levels for Part Design, Assembly Design, and Surface Design. Its catalog describes training and regular practice as preparation, but the inspected pages do not publish a prior Associate credential as a universal Expert gate. Contact an authorized center for the available V5 route rather than registering through the 3DEXPERIENCE Associate Edu Space.
Student CATIA/3DEXPERIENCE offers can bundle software and exams under eligibility, billing-country, age, and noncommercial-use conditions. Official pages conflict on the exact bundled exam roster and renewal wording, so confirm the cart and current student terms rather than promising a particular set of credentials.
Separate prerequisites, preparation, access, and payment; Checklist
Separate prerequisites, preparation, access, and payment
Credential prerequisite: a prior certification the exact exam page says you must hold. Examples include the published CSWE, SOLIDWORKS Simulation Expert, NX Design Professional, and Solid Edge Expert chains.
Recommended preparation: experience hours, courses, learning paths, or practice described as readiness guidance. Do not silently convert a recommendation into an admission rule.
Software or platform access: the app, version, role, testing client, collaboration space, or live software needed to prepare for or take that route.
Payment condition: a public purchase, institutional voucher, subscription benefit, bundle, or conditional student offer. Free student software is not the same as a free exam.
Voucher expiration and credential validity are also different. For example, Certiport governs ACU credential policy while Autodesk's other credentials use Autodesk/Pearson routes. Confirm the exact program, country, tax, proctoring, retake, voucher, and validity terms immediately before paying or scheduling.
Use one verified route from comparison through preparation
Use one verified route from comparison through preparation
Name the product and work you want to demonstrate: general mechanical design, drawings, manufacturing, simulation, or data workflow.
Open the provider's current catalog and the exact credential page. Record the title, assessed skills, delivery route, and published prerequisites.
Mark recommendations separately from requirements. Confirm that you can access the needed software, account, testing center, or remote-proctor setup.
Ask your institution about participation or vouchers without assuming it has them. Verify any student offer, region, expiration, and checkout total directly.
Use official preparation materials without copying exam questions, answer keys, or protected sample parts. Practise the underlying workflow with original drawings and models.
For a worked preparation case, continue to CAD Certification Preparation. It uses CSWA to organize drawing, modeling, assembly, units, material, mass-property, checking, and revision practice while keeping the official exam specification outside CourseWiki.
Engineering Graphics and CAD/CAD Modeling
CAD Certification Preparation
Build dependable modeling habits, check your work, and use official sources to plan an entry-level CAD certification attempt.
Use certification as a goal for building dependable CAD skills
Use certification as a goal for building dependable CAD skills
A CAD certification gives you a way to demonstrate skills assessed by its provider. Preparing for one can help you become more productive, build models that survive changes, and describe your skills on a resume. Passing does not guarantee a job or prove that every design you make will work.
The Certified SOLIDWORKS Associate (CSWA) is the worked case here, offered through Dassault Systèmes' SOLIDWORKS certification program. Its hands-on modeling workflow does not describe every vendor exam: some routes use selected-response questions, testing-center delivery, platform roles, or different software-access rules. Compare those routes first in CAD Certifications. CourseWiki is an independent learning resource and is not affiliated with or endorsed by Dassault Systèmes.
Find the current exam rules before you register; Checklist
Read the current exam description, skill coverage, format, length, question count, passing rules, and any section weights on the official page.
Follow the official registration or purchase route; confirm the current price and any voucher conditions before paying.
Check software, computer, account, and testing-client requirements, plus the rules for permitted resources and retakes.
Find the official sample or practice resources linked from the certification page and read their use instructions.
For current numerical exam details, see the official page. This guide does not reproduce an exam specification, exam questions, answer keys, or sample parts. The official certification FAQ is another starting point for registration and testing questions. Academic and ordinary CSWP routes have different conditions, and student software access does not by itself prove an exam voucher is included.
Practise reading, modeling, assembling, and checking
Practise reading, modeling, assembling, and checking
Use these general skill areas to organize practice; use the official description to confirm what your chosen certification assesses.
Read a drawing: identify views, dimensions, and feature notes before building. Start with Drawing Terminology Review.
Sketch deliberately: use dimensions and geometric relations to control size and shape. Review Geometric Relations in Sketches.
Build and revise parts: choose features that express the shape, then change a dimension and check the result. Review Feature-based Modeling.
Assemble components: place parts and constrain their intended positions or motion with mates. Review Assembly Files and Mates.
Inspect the result: measure dimensions, check mass properties, and confirm the correct model state. Review CAD Model Views and Checks.
Check geometry, units, and material before trusting mass; Checklist; Practice
Check geometry, units, and material before trusting mass
For a uniform solid, mass = density × volume. Use compatible units: density in g/cm³ multiplied by volume in cm³ gives mass in g. To convert mm³ to cm³, divide by 1,000 because 1 cm³ = 10 × 10 × 10 mm³.
Changing only the displayed units changes the number and unit label, not the physical size or mass. Entering a dimension in the wrong units changes the geometry. Choosing a different density changes mass even when the shape stays the same.
Confirm the drawing's units and the units used when entering dimensions.
Check overall dimensions, holes, and removed material against all relevant views.
Assign the specified material or density to the intended bodies or components.
Rebuild after edits; confirm the intended configuration and which bodies or components are included.
Read the requested quantity and its output units before recording an answer.
Supporting detail: Addendum 77 — Why matching mass does not prove the shape is right.
Build accuracy first, then practise with a time limit
Build accuracy first, then practise with a time limit
Choose an original, ungraded drawing you have permission to use. Build the part without following a click-by-click demonstration. Explain how each view supports the geometry, then check the dimensions and material. Repeat with a changed dimension to see whether the model updates as intended.
Once that process is reliable, set a practice time limit. Include time to read, model, check, and save. Record where you lose time and practise that skill next. During an actual attempt, follow the provider's rules about navigation, returning to questions, and saving work.
Keep a short error log: drawing interpretation, sketch control, feature choice, assembly position, units, or material. Rebuild after correcting the cause instead of memorizing the previous answer.
Engineering Graphics and CAD/Reading Drawings
Drawing Terminology Review
Recognize drawing terms used when turning a drawing into a CAD model, then follow links for the full methods.
Identify the view before interpreting the shape
Identify the view before interpreting the shape
This short vocabulary review supports CAD certification preparation. It is general drawing language, not a list of guaranteed exam terms.
A view is a picture of the part from a chosen direction. First identify how
the picture represents the part; then read its lines, dimensions, and notes.
Orthographic view
The principal orthographic views look straight at the part
from the front, above, or a side, using parallel lines of sight perpendicular to each viewing
plane. Front shows width and height; top shows width and depth; a side view shows depth and
height. Read the views together to understand one three-dimensional part.
The pictorial on the left helps you recognize the block. The front, top, and right
views on the right show the same fixed part from separate directions. This example uses
third-angle placement; Orthographic Projection explains the views
and First-Angle and Third-Angle Projection explains their placement on the sheet.
Isometric view
An angled pictorial that helps you see width, height, and depth
together. Its three principal axis directions are 120° apart and use the same scale.
An isometric projection foreshortens lengths equally along all three axes; an ordinary
isometric drawing lays out axis-parallel lengths at the chosen drawing scale. Use stated
dimensions to model the part rather than measuring its apparent lengths on the picture.
The block is an isometric drawing: its edges follow three consistent directions.
The dashed grid on its top is a construction aid, not hidden edges of this part. See
Pictorial Sketching for making the sketch and the distinction between drawing and projection
scales; compare isometric with dimetric and trimetric in CAD Model Views and Checks.
Line conventions describe edges and centers within a view
Line conventions describe edges and centers within a view
A view type tells you how the part is represented. A line convention tells you what a
particular mark means within that view. Visible, hidden, and center lines are line conventions,
not additional view types.
Visible line
A continuous line shows an edge or outline you can see from
this viewing direction.
Hidden line
Short dashes show an edge concealed by material.
Center line
A long-short pattern identifies an axis, center, or symmetry
reference. It is not a physical seam in the part.
The first three samples match the terms above. The fourth, phantom, can indicate
an alternate position or reference. Read the pattern together with its context; the dashed
construction grid in the isometric figure above is a teaching aid. Review the full conventions
in The Alphabet of Lines.
Read dimensions and callouts as instructions about features; Practice
Read dimensions and callouts as instructions about features
Dimension and extension lines
A dimension gives a size or location. A dimension line is a thin line, usually ending in arrowheads, that shows the extent of the measurement; extension lines carry the edges of the measured feature out to it. Read the value and units instead of measuring a picture. See Dimension Anatomy and Placement.
Diameter and radius
Diameter spans a circle through its center; radius runs from its center to its edge. The diameter symbol is Ø; R denotes radius. Confusing them changes the modeled size. See how holes and arcs are called out in Hole and Feature Callouts.
Hole and feature callout
A note describing a feature, possibly including quantity, size, depth, or thread information. A through hole passes through the material; a blind hole stops within it. See Hole and Feature Callouts.
Tolerance
The permitted variation in a specified dimension. Read the stated limits or applicable drawing note; do not assume that every dimension has the same tolerance. See Dimension Anatomy and Placement.
Distinguish a section, a detail, and an auxiliary view; Practice
Distinguish a section, a detail, and an auxiliary view
Section view: shows the part as if cut by an imaginary plane so internal features can be read. A cutting-plane indication locates the cut; section lining identifies material crossed by it. See Section Views.
Detail view: enlarges a selected area so small features are easier to read. Check its scale and labels.
Auxiliary view: looks perpendicular to an inclined surface to show its true shape. Compare it with a detail view in Auxiliary and Detail Views.
Before modeling, point to the view or callout that establishes each feature. If a shape is unclear, look for another view rather than guessing from a pictorial.
Identify an additive process by what it places, what joins the material, and what the part still needs after the build.
Classify the mechanism before comparing process names
Classify the mechanism before comparing process names
Additive manufacturing builds three-dimensional geometry by adding material. The standard process families describe how material is placed and joined. They are different from this course's five purpose categories, which describe what an operation is intended to accomplish.
Use three questions when you meet an unfamiliar name: What feedstock enters?What places or selects each region?What joins or solidifies it? Then ask what must happen after the build before the part is ready to inspect or use.
For the course's purpose model, additive shape-building is primarily Forming. Removing supports is a later Separating operation; curing or heat treatment can be Conditioning; finishing can change a surface. The seven AM families below do not replace those five purpose categories.
Seven families place and join material in different ways
Seven families place and join material in different ways
Family
Feedstock and joining mechanism
A useful boundary
Material extrusion
Material is pushed through a nozzle and selectively deposited. A common filament route softens thermoplastic, then adjacent roads bond as they cool.
FDM is a registered trademark of Stratasys; FFF is generic usage for filament fabrication. Neither name covers every extrusion feedstock.
Vat photopolymerization
Light selectively cures liquid photopolymer held in a vat. SLA, DLP and masked exposure systems select regions differently.
Cleaning, support removal and material-specific post-curing may remain. “Resin printing” does not identify one universal exposure method.
Powder bed fusion
A thin powder layer is spread, then thermal energy selectively fuses regions. Polymer SLS uses a laser; HP Multi Jet Fusion applies agents and heat. Metal routes use laser or electron-beam energy.
Polymer and metal PBF share a family, not one identical workflow. Loose powder can support polymer SLS parts, while some metal routes need supports for anchoring or heat flow; process-specific exceptions exist.
Binder jetting
A printhead selectively deposits binder into a powder layer. Repeating the powder-and-binder cycle produces a fragile green shape.
The printed shape is not automatically a finished dense part. Curing, depowdering, debinding, sintering or infiltration depend on the material and route.
Material jetting
Droplets containing build material are selectively deposited, then solidified or cured. PolyJet is a Stratasys photopolymer-and-UV example.
The jetted liquid is build material, not merely binder placed into a powder bed. PolyJet is one branded implementation, not the family name.
Directed energy deposition
Powder or wire is delivered to a target while focused energy creates a local melt zone. Deposited tracks solidify on a substrate or existing part.
The feed arrives at the deposition point rather than being spread as a complete powder layer. Repair and large features are useful contexts; finishing and inspection still matter.
Sheet lamination
Sheets are bonded to build thickness, with shape developed layer by layer.
The family name alone does not establish the sheet material, bonding method, accuracy or present-day machine capability.
Material names do not move freely between families. A printer, process version and qualified feedstock must be considered together. Polymer, metal, ceramic, composite, sand and cementitious examples exist in particular systems; that does not mean every material works in every printer.
Powder and droplets can play three different roles
Powder and droplets can play three different roles
Similar words do not mean the same mechanism. Follow what the droplets contain and when the material becomes the intended solid.
Powder bed fusion
The powder is the build material; selected regions are thermally fused during the build.
Binder jetting
The powder is the build material; jetted binder holds a green shape that may require later densification.
Material jetting
The droplets themselves contain build material; a separate support material may also be deposited in some systems.
HP Multi Jet Fusion belongs with powder bed fusion because agents help control where powder is fused by heat. It is not binder jetting simply because a printhead deposits an agent. See the manufacturer's mechanism comparison for that distinction.
The build is one stage of the manufacturing route; Checklist; Practice
The build is one stage of the manufacturing route
Judge a route from feedstock through the inspected part, not from the printer alone. Depending on the family and material, the route may include cooling, unpacking and depowdering; washing and post-curing; support removal; debinding and sintering; heat treatment; machining; surface finishing; or inspection.
State the material, required geometry, load direction, critical surfaces and fit.
Identify what carries an overhang during the build and whether that material can be removed afterward.
Trace trapped powder, uncured resin, support material or internal passages to an exit or cleanup method.
Name the state at the end of the machine cycle: finished solid, green part, supported part, powder-filled part or another intermediate state.
List the post-build and inspection steps required before the part can meet its intended requirement.
No family is the universal best choice. Surface, accuracy, properties, cost and throughput depend on the actual material-process-machine combination, build use, postprocessing and acceptance requirements. Continue to FDM 3D Printing for the material-extrusion mechanism and 3D Printing from CAD for the filament CAD-to-slicer workflow.
Follow the shared powder-layer cycle, then distinguish polymer SLS and MJF from stated metal laser and electron-beam routes.
Powder bed fusion repeats a spread, select, and lower cycle
Powder bed fusion repeats a spread, select, and lower cycle
Powder bed fusion (PBF) is one additive-manufacturing family. A machine spreads a thin powder layer, applies thermal energy to selected regions, lowers or advances the build, and repeats. Unselected powder remains around the growing parts until they are unpacked.
The family name does not specify one material or energy source. Polymer and metal examples can share the layer cycle while differing in temperature, atmosphere, thermal behavior, support strategy, cooldown, powder recovery, postprocessing and inspection.
Start with Additive Manufacturing Process Families for the seven-family map. PBF thermally fuses powder during the build; it is not binder jetting, where deposited binder first creates a green shape.
Supporting detail: Addendum 79 — Readable process sources.
Polymer SLS and MJF select powder in different ways
Polymer SLS and MJF select powder in different ways
Selective laser sintering (SLS)
A laser scans selected regions of a polymer powder layer and thermally joins the particles. Unfused powder surrounds the parts in the stated process, so dedicated support structures are generally unnecessary; the build must cool before unpacking and depowdering.
Multi Jet Fusion (MJF)
A printhead places fusing and detailing agents on polymer powder, then applied heat fuses selected regions. The agents control fusion; they are not binder that leaves a green part for later sintering.
Both examples belong to PBF because powder is thermally fused during the build. Neither description proves that any polymer powder, color, wall, gap or enclosed cavity will work on a particular machine.
Loose powder can carry surrounding geometry during these stated polymer builds, but it must still be removed. A sealed hollow region can trap powder. An internal passage needs an accessible route for cleaning and inspection; “no dedicated supports” does not mean “no design constraints.”
Metal laser and electron-beam PBF need process-specific thermal reasoning
Metal laser and electron-beam PBF need process-specific thermal reasoning
The metal examples here use a laser or electron beam to melt or fuse selected regions of metal powder. The part develops through repeated melt-and-solidify events, so orientation and connection to the build system can affect heat flow, residual stress, distortion and later removal.
In a stated laser PBF case, sacrificial supports may anchor an overhang to the build plate and conduct heat away. Loose metal powder surrounding the part is not automatically an adequate thermal path. That does not create a universal rule that every metal PBF system and geometry needs the same supports.
Electron-beam PBF has process-specific strategies and exceptions. Current commercial examples can reduce or replace traditional supports for some parts. Record the exact machine, material, melt strategy, orientation and acceptance plan instead of transferring one support rule to every metal powder process.
Supporting detail: Addendum 80 — Why the support statement is qualified.
Design powder access and the post-build route with the part; Checklist; Practice
Design powder access and the post-build route with the part
The layer cycle is shared; support, thermal and post-build assumptions are material- and process-specific. Geometry must allow powder removal and inspection.
Mark enclosed volumes, channels and lattice spaces; give loose powder a stated removal and inspection route.
State the material, machine/process variant, energy route and build orientation rather than writing only “PBF.”
Identify what supports geometry and, for the stated thermal case, what anchors the part and conducts heat.
Plan cooldown, unpacking, depowdering and any support removal before choosing inaccessible geometry.
List required postprocessing and inspection. A completed build is not automatically a qualified service part.
Export a solid model, choose how its layers carry load, and inspect the sliced toolpaths before printing.
Build the part by adding layers
Build the part by adding layers
Additive manufacturing makes a shape by adding material. This page uses thermoplastic-filament material extrusion: a printer feeds filament through a heated nozzle and deposits it along paths, much like a controlled hot-glue gun. Fused filament fabrication (FFF) is generic usage for this route; fused deposition modeling (FDM) is a registered trademark of Stratasys.
A slicer divides the model into horizontal cross sections and plans the paths for each layer. The nozzle and build surface move relative to one another to build the next layer. A CAD model describes the desired shape; the sliced file describes how a particular printer will make it.
This page focuses on filament printing. Resin, powder and metal routes use different placement, joining and post-build mechanisms; compare them in Additive Manufacturing Process Families. Their preparation, handling and finishing procedures are not interchangeable.
Export the model, then check its size in the slicer; Checklist
Export the model, then check its size in the slicer
Finish and save the editable CAD model. Check that the intended part is a closed solid; see Feature-based Modeling.
Export the intended body as STL or 3MF if supported by both programs. Inspect curved surfaces for coarse facets.
Import into the slicer and compare a known dimension with the CAD model. Check units, scale, and the number of bodies.
Select the actual printer, nozzle, and approved material profile. Do not assume settings imported with a file match the available machine.
Orient the part, set walls, infill, layer height, and supports, then slice and inspect the layer preview.
Export the printer's required job format using the posted procedure. Save the slicer project so you can revise the setup.
Supporting detail: Addendum 81 — STL and 3MF carry different information.
Use walls for the shell, infill for the interior, and supports where needed
Use walls for the shell, infill for the interior, and supports where needed
Walls, also called perimeters, trace the outside and hole boundaries. Infill fills some of the interior. Solid top and bottom layers close the part. Increasing infill is not a substitute for choosing suitable walls and orientation.
Layer height sets the thickness of each deposited layer. Smaller layers can reduce the steps on sloped surfaces but usually add print time. They do not by themselves make a thin wall or tiny hole printable: nozzle size and extrusion width matter too.
Supports are temporary material beneath regions that cannot print reliably in the chosen orientation. They use material and time, may leave rough contact surfaces, and must be reachable for removal. A short bridge between two supported edges differs from an unsupported overhang; check the machine's demonstrated capability instead of assuming one universal angle limit.
Supporting detail: Addendum 82 — Why more infill does not solve every strength problem.
Orient for load direction, surface quality, and support removal; Practice
Orient for load direction, surface quality, and support removal
Ask which way the part will be pulled or bent. Filament prints are often weaker when a load pulls adjacent layers apart. For a straight bar pulled along its length, laying its length in the build plane is usually a better starting point than printing it upright. Test a representative part before relying on it under load.
Then consider the important faces. A face against the bed takes the bed's texture; a supported underside may need cleanup; a slope shows layer steps. Rotating the part can improve one surface while making another worse. A broad, stable bed contact usually makes the start easier than a narrow footprint.
Try it: orient a bracket for support, layer direction and load; Interactive
Try it: orient a bracket for support, layer direction and load
Turn an L-bracket on the build plate and read three consequences together: which downward faces would need support, whether the load in use runs parallel to the layers or must cross the bonds between them, and how layer height leaves steps on the curved faces.
Challenge: this bracket will be screwed to a wall and carry a weight hanging from its arm. Which way up should it print? Read three consequences together: overhangs that need support, the direction of the load relative to the layers, and the steps that layers leave on curved faces.
The bracket: arm 60 mm, back plate 50 mm, both 8 mm thick and 30 mm wide, a 10 mm inner fillet with a concentric 18 mm outer round, and a 6 mm gusset across the inside corner. These are chosen illustrative dimensions.
Needs support: downward and flatter than the threshold
Downward but at or steeper than the threshold
Resting on the plate, or inside the first layer
Upward or vertical: never flagged
Stretched path: blue = parallel to layers, red-orange = normal to them
Unsupported overhang (proxy)
329 mm²329 mm² of downward faces flatter than 45°, projected onto the plate. Flagged faces do not overlap in plan; plate footprint about 330 mm².
Resting on the plate
1,260 mm²Downward faces on the plate are supported by it.
Height and layers
50.0 mm · 250 layers⌈50.0 ÷ 0.20⌉ at 0.20 mm
Load-to-layer angle
up to 90°Around the bend the stretched direction ranges from 0° to 90° from the layer planes. Part of it is mostly normal to the layers, so that load must cross the bonds between layers.
Layer steps on the curves
inner 0.08 mm, outer 0.09 mmMeasured in the drawn cut; not a roughness value.
Unsupported overhang (proxy)
428 mm²428 mm² of downward faces flatter than 45°, projected onto the plate. Flagged faces do not overlap in plan; plate footprint about 430 mm².
Resting on the plate
768 mm²Downward faces on the plate are supported by it.
Height and layers
30.0 mm · 150 layers⌈30.0 ÷ 0.20⌉ at 0.20 mm
Load-to-layer angle
up to 0°Every stretched direction lies within the layers (0°): no part of the load has to cross the bonds between layers. The road (raster) direction inside each layer is set by the slicer and is not modelled here.
Layer steps on the curves
none on the curved faces (vertical walls)Measured in the drawn cut; not a roughness value.
Two orientations of the same bracket, 0.20 mm layers, 45° threshold, hanging weight
Orientation
Unsupported overhang (projected)
On the plate
Height · layers
Load-to-layer angle (max)
A. Arm flat on the plate
329 mm²
1,260 mm²
50.0 mm · 250
90° (hanging weight)
B. On its side
428 mm²
768 mm²
30.0 mm · 150
0° (hanging weight)
What the comparison shows: standing up (A), the bend's stretched path must turn through the layer stack, so part of it pulls layers apart, and the lower outer round needs support. On its side (B), the stretched path lies within the layers and the curves print as vertical walls, but the gusset now overhangs the open corner. Neither is free: you choose which consequence to accept, or change the design (for example a chamfer instead of a downward-facing round, or no gusset).
Layer steps on a curved face
Vertical cut through the front of the bracket: thin line = CAD shape, stepped line = 167 layers of 0.30 mm.1 Inner fillet: largest gap between the true curve and the layer steps in this cut 0.12 mm2 Outer round: largest gap between the true curve and the layer steps in this cut 0.12 mm
How the numbers are worked out
Build direction: +z, from the plate toward later layers. Layers are horizontal planes.
Face inclination θ = arccos|nz| from the horizontal plate (0° horizontal, 90° vertical), where n is the face's outward unit normal. A face is downward when nz < 0.
Needs support when downward and θ is less than the threshold (45° here; 44° is flagged, 46° and exactly 45° are not). A face resting on the plate, or lying wholly within the first layer, is supported by the plate. Upward and vertical faces are never flagged.
Unsupported-overhang proxy As = Σ Ai·|nz,i| over flagged faces: their area projected onto the plate. Example A: the outer round is flagged from 30 × (18 sin 45° − 18 sin 5.6°) ≈ 329 mm² (the lowest facet sits inside the first layer).
Layers N = ⌈H ÷ h⌉. Example A: ⌈50 ÷ 0.20⌉ = 250.
Load-to-layer angle φ = arcsin|dz| for the stretched direction d: 0° lies within the layers; 90° is normal to them and must cross the bonds between layers. Within a layer, the slicer also chooses the road (raster) direction; this model does not include it.
Layer steps: each layer is the cut at its mid-height, extruded straight up through the layer. The figure measures the largest gap between that stepped outline and the CAD curve in one vertical cut.
Model limits: a geometric teaching model, not a slicer. The support figure is a projected-area proxy: it is not support volume, print time or a promise that a face will print. Bridging between two supported edges, support landing on the part, interface gaps, cooling and removal are not modelled. The 45° threshold is an adjustable guideline, not a universal limit. The load angle is a direction only: no strength value, failure prediction or material data.
Supporting detail: Addendum 83 — Where the threshold and the load rule come from.
Use the preview and the failed part to find the next check
Use the preview and the failed part to find the next check
Missing thin feature
Inspect the sliced paths. A feature visible in CAD may be too thin for the selected extrusion width; revise the feature or an approved setup.
Loose first layer or lifted corners
Check bed preparation, first-layer setup, and the material profile against the machine procedure. Warping involves shrinkage as the part cools.
Sagging underside
Check the orientation, unsupported spans, and support placement before repeating the same job.
Gaps, strings, or shifted layers
Check material condition, extrusion, temperature/profile, and machine motion as appropriate. These symptoms have several possible causes; change one justified factor at a time and record the result.
In the preview, inspect the first layer, small holes, supports, and the final top layers. Estimate time and material before starting. Follow Equipment Operating Procedure and Machine Hazards and Housekeeping for operation and handling; the nozzle and build surface may remain hot after motion stops.
Separate cutting paths from engraved areas, preserve scale, and account for the material removed by the laser.
Use vector paths for outlines and raster scans for filled marks; Practice
Use vector paths for outlines and raster scans for filled marks
A vector operation follows lines and curves. A raster operation scans across an area to make a surface image or filled mark.
A vector path can cut through a sheet or make a shallow score, depending on the material and settings. Raster engraving typically changes the surface without cutting out the part. A bitmap picture of an outline is not automatically a usable vector cutting path.
Prepare a full-size profile and assign each operation deliberately; Checklist
Prepare a full-size profile and assign each operation deliberately
From CAD, export the intended planar face or sketch as a supported vector format such as DXF. View the face normal to its plane; a perspective picture is not a true-size profile.
In the vector editor, set units and page/piece size. Import the file and measure a known feature to confirm 1:1 scale.
Remove unwanted dimensions, notes, borders, and duplicate paths from the fabrication copy. Check for gaps in outlines that should be closed.
Assign cut paths, score paths if used, and raster areas to the correct operations. Inspect fills as well as strokes.
Match page/piece size and placement in the artwork and machine software. Preview the job and check its extent against the actual sheet.
CorelDraw is one possible vector editor. Line weight and color can tell a particular driver how to treat an object, but those conventions are not universal. Follow the posted procedure for that driver and confirm the operation in its preview.
Supporting detail: Addendum 84 — Why a hairline is a workflow setting, not a cutting guarantee.
Offset the path toward the waste by half the kerf; Practice
Offset the path toward the waste by half the kerf
Kerf is the width of material removed by a cut. In the simple model below, the laser follows the center of a constant-width kerf. Half the removed width lies on each side of the path.
For an outside part boundary, move the path outward by kerf / 2. For an opening, move the path inward toward the material being removed. Without compensation, a cutout part becomes smaller and a hole becomes larger.
For a desired outside width W, the path-to-path width is W + k, where k is kerf. For a desired opening width H, it is H − k. These are whole-width changes; the offset at each edge is only k / 2.
Measure a test cut in the same material and setup. Kerf can vary with thickness, focus, and settings, and cut edges may taper. If software already compensates the path, do not apply the same allowance again. See Tolerances and Fits for fit requirements.
Treat power, speed, and pulse settings as a matched setup
Treat power, speed, and pulse settings as a matched setup
Power controls laser output; speed controls how quickly the spot travels. With other conditions held fixed, higher power or slower travel generally puts more energy into a length of cut. That can also increase scorching or melting rather than improve the edge.
Frequency or pulse settings control how pulses are delivered. Controls may use pulses per second, pulses per distance, or a machine-specific scale; read the manual's definition. A percentage from one machine is not a transferable recipe for another.
Use the posted procedure and the manufacturer's starting settings for the exact machine, material, and thickness. Confirm the result on an approved test piece. Check that the cut separates and that engraving is readable before running the complete job.
Supporting detail: Addendum 85 — Manufacturer guidance for selecting a starting setup.
Confirm the material and stay with the operating laser
Confirm the material and stay with the operating laser
Only process materials approved for that machine. Suitable grades of wood and acrylic are common CO₂-laser examples, but coatings, adhesives, thickness, and machine capability matter. A material that can be marked is not necessarily one the machine can cut through.
Do not cut or engrave PVC or vinyl containing PVC. Do not guess the identity of an unknown plastic. Never leave an operating laser unattended. Use the required extraction and follow the machine procedure for a flare-up or other abnormal condition.
Supporting detail: Addendum 86 — Manufacturer safety reference.
Engineering Graphics and CAD/Digital Fabrication
Choosing a Fabrication Process
Match geometry, load, surfaces, and fit to filament printing or laser-cut sheet construction.
Choose from the required shape and material first
Choose from the required shape and material first
Start with what the part must do. A process is useful only if it can produce the geometry in a suitable material with the required performance.
Filament printing
Builds three-dimensional shapes in layers. It suits changing cross sections, bosses, and internal features when those features can be printed and supports can be removed. Layer direction and service temperature affect the choice.
Laser-cut sheet
Produces planar profiles from a sheet of existing thickness. It suits flat panels, plates, and repeated outlines. Three-dimensional structures need joints, stacked layers, or another forming operation.
A flat nameplate with surface lettering is a natural laser candidate if the sheet is approved. A one-piece curved knob with a raised boss is a natural printing candidate if a suitable printable material meets the load and temperature requirements. Neither choice establishes production time without a job estimate.
Design features the selected process can actually make
Design features the selected process can actually make
Printed walls and holes
Check that the slicer generates the intended paths. Leave access for support removal. Do not assume a CAD hole prints at its nominal size; measure a representative sample.
Laser-cut webs and corners
Leave enough material between cuts for the part to survive fabrication and use. Account for kerf and heat effects. An infinitely sharp CAD corner does not guarantee an infinitely sharp cut corner.
Sheet joints
Design slots from measured sheet thickness and the intended clearance. Kerf compensation controls the cut edge; clearance controls how two finished parts fit. They solve different problems.
Assembly
Plan how pieces enter their final position and how they are held. A collision-free CAD assembly does not prove that real parts will fit or can be assembled; see Assembly Files and Mates.
Supporting detail: Addendum 87 — Why there is no universal minimum wall or perfect press-fit allowance.
Test the critical feature before making the full part; Checklist; Practice
Test the critical feature before making the full part
State the required shape, material, load direction, surface, and fit.
Identify the feature most likely to fail: a thin wall, loaded layer joint, supported surface, or mating slot.
Make an approved small sample that preserves that feature and the intended process setup.
Measure or test the sample against the requirement. Record the setup and the result.
Revise the design or setup, then compare time, material, cleanup, and assembly effort before making the full part.
Before starting: check the blade, guide and feed path; Checklist
Before starting: check the blade, guide and feed path
Confirm that the blade suits the material and cut. With the machine stopped and isolated for setup, expose only the blade height needed for the cut, following the installed saw's instructions.
Check the blade guard and the saw's anti-kickback equipment. A missing or malfunctioning device means the setup is not ready. No one removes a guard in this lab. A machine that needs a guard off is the instructor's to deal with, out of class (see Machine Hazards and Housekeeping).
Choose the guide for the cut: the rip fence for ripping, or the approved crosscut setup. In our labs, do not use the sled with the rip fence.
Plan support for the board throughout the cut and place the push stick within reach before starting. Check where both hands will go as the trailing end approaches the blade.
Control blade contact and kickback throughout the cut
Control blade contact and kickback throughout the cut
Kickback is material thrown back toward the feed side by the blade. Binding between the blade and fence is one cause. Do not make a cut that traps a loose cutoff there.
Use the approved guide to keep the board aligned; do not steer it freehand.
For a rip cut, push the part between the fence and blade. Use the push stick to keep hands out of the blade path, including at the end of the cut.
Feed steadily at a rate the blade can cut. Ease the feed through harder areas; do not force a struggling cut.
Keep clear of the blade while it coasts. Stop it completely before removing scraps or reaching for a finished piece near it.
Supporting detail: Addendum 88 — Why one feed rate does not fit every cut.
If material binds or kicks back: stop and report it
If material binds or kicks back: stop and report it
Do not reach after a thrown piece or try to free material beside a moving blade. Stop the saw from a safe position and notify the instructor. Have the setup checked before restarting; clearing a jam follows the isolation procedure in Machine Hazards and Housekeeping.
Support the work, keep the exposed blade short and feed without twisting or pinching the band.
Category 3 in both labs; vertical and horizontal setups differ
Category 3 in both labs; vertical and horizontal setups differ
A band saw cuts with a continuous toothed band. A vertical saw can follow a wood outline; a horizontal saw lowers its blade through clamped material. See How Saws Cut Wood and Choosing a Woodworking Machine.
Before starting: match the blade and stabilize the work; Checklist
Before starting: match the blade and stabilize the work
Confirm that the installed blade suits the material, thickness and intended curve. Teeth per inch (TPI) alone do not establish suitability.
Check that wheel covers are closed. On the vertical saw, in our labs, set the upper blade guard approximately 1/4 inch above the work, with the machine off.
In our labs, use stock with a flat supporting surface. On the vertical saw it rests flat on the table; on the horizontal saw it seats against the vise's fixed surface and is firmly clamped.
Plan forward exits from the cut and hand positions that stay out of the blade path. Avoid a layout that requires twisting the band or repeatedly backing out.
Feed steadily; do not force a curve or withdraw against a moving band
Feed steadily; do not force a curve or withdraw against a moving band
Vertical saw: hold the work flat against the table and feed at a moderate, steady rate the blade can cut. Keep hands away from the line of cut. Do not twist the blade to force a tighter turn. In our labs, stop the machine before backing out of a long cut; wait until the band has stopped.
Horizontal saw: keep the work clamped. Where the saw has a hydraulic feed control, use the trained adjustment procedure to set a controlled descent for the material and section. Do not apply the vertical saw's hand-feeding method to this setup.
Supporting detail: Addendum 89 — Why thickness matters as well as material.
If the blade breaks or pinches: stand clear and stop
If the blade breaks or pinches: stand clear and stop
If the band breaks, step clear and use the emergency stop if safely reachable. Do not open wheel covers or try to catch the band. If the blade pinches, stop and get the instructor before freeing the work under the isolation procedure in Machine Hazards and Housekeeping.
Support the board against the fence, keep clear of the full blade path and use the cutting motion taught for the installed saw.
Crosscuts and angled ends: Category 3 in the woods lab
Crosscuts and angled ends: Category 3 in the woods lab
A miter saw cuts a board to length or cuts an angled end. The miter setting turns the cut across the table; the bevel setting tilts the blade. See How Saws Cut Wood and Choosing a Woodworking Machine.
Before starting: set angles, support the board and check clearance; Checklist
Before starting: set angles, support the board and check clearance
With the machine off and isolated for setup, set and secure the miter and bevel angles. Mark the cut and check its alignment with the stationary blade's path; a laser, if fitted, is an alignment aid.
Seat the board against the fence and table. Support long ends at the same height as the saw table so the board cannot tip during the cut.
Check that the moving guard works and shields the blade. If a dust collector is fitted, check that it is ready for use.
Check the entire blade path at the selected angles, including clearance from clamps. In our labs, keep all body parts at least 6 inches from the blade and never cut small pieces. If the piece cannot be supported while maintaining that clearance, stop and ask for another method.
Keep the work still and use the motion taught for this saw
Keep the work still and use the motion taught for this saw
Secure the work against the fence using the trained holding or clamping method. Do not improvise a stacked-board cut; have the instructor establish the setup.
With hands outside the blade path and the blade clear of the work, start the saw and let it reach cutting speed.
Make the cut with controlled feed using the motion demonstrated for the installed saw. A sliding saw needs its own cutting sequence. Have that demonstrated before using the slide; do not interpret “pull through” as permission to pull a spinning blade toward you through the board.
At the end of the cut, release the trigger, keep the head controlled and wait for the blade to stop before lifting it or removing the work and cutoff.
Use a blade and material combination approved for the installed saw. Changing the blade alone does not make a woodworking miter saw suitable for metal, masonry or wet cutting.
If the board shifts or the blade binds: release the trigger
If the board shifts or the blade binds: release the trigger
Keep clear of the blade and let it stop. Do not reach in to reposition the work or free a cutoff while it moves. Notify the instructor and follow the isolation procedure before clearing a jam.
Use push blocks, suitable stock and shallow cuts to keep hands clear of the cutterhead while establishing a flat face or straight edge.
Flat faces and straight edges: Category 3 in the woods lab
Flat faces and straight edges: Category 3 in the woods lab
A jointer establishes a flat face or a straight edge at a set angle to an adjacent face. It does not by itself make opposite faces parallel. See Milling Rough Lumber Square for the sequence and Choosing a Woodworking Machine for machine selection.
Before starting: check the stock, guard and depth of cut; Checklist
Before starting: check the stock, guard and depth of cut
In our labs:
Check for nails, screws, loose knots, splits and other defects. Do not feed wood containing metal; ask the instructor about defective or unstable stock.
Use stock at least 1/4 inch thick and 10 inches long. These minimums do not make an otherwise unstable setup acceptable.
Set the infeed table for no more than 1/16 inch removal per pass, with the machine isolated for setup.
Check that the swinging cutterhead guard covers the cutter and returns freely. Do not use a setup that defeats it.
Plan the feed with the grain, with a cupped face concave-side down so the board does not roll. Have the instructor check stock that will not sit stably.
Have push blocks ready. Turn on dust collection and open the machine's collection gate before cutting.
Keep hands 4 inches away and transfer pressure with push blocks
Keep hands 4 inches away and transfer pressure with push blocks
In our labs, keep hands at least 4 inches from the cutterhead and never pass hands over it. Do not hook fingers around the end or side of the board. Use push blocks or the trained push-assist device; plan hand transfers before starting.
Stand to the side of the board near the cutter, not behind its feed line. Start the jointer and wait for full speed.
Feed with slight, even pressure against the table and fence. Keep the board stable rather than forcing it flat.
Once the leading portion has passed the cutter by more than the 4-inch margin, use the push block to apply downward pressure on the outfeed side. Transfer hands without passing them over the cutterhead.
Complete the pass while maintaining control and clearance. Let the guard return over the cutter before lifting the board away.
If the board kicks back or control is lost: stop the jointer
If the board kicks back or control is lost: stop the jointer
The cutter can throw a board opposite the feed direction. Do not chase it or reach toward the cutter. Stop the jointer from a safe position and notify the instructor before another pass.
Before starting: secure the bit, work and vise; Checklist
Before starting: secure the bit, work and vise
Select a bit and spindle speed suitable for the material and hole diameter. Have the instructor confirm an unfamiliar setup; a list of bit types is not approval to use every type in this press.
With the machine isolated for setup, seat and tighten the bit using the installed chuck's procedure. The chuck key never leaves your hand. It is not released until it is out of the chuck. Do not count on a key ejecting itself (see the chuck-key rule).
Clamp wood and metal to the table, or grip the work in a vise secured to the table. Secure small parts in a suitable vise or fixture; clamp larger parts with adequate support. Handholding is not workholding.
Check that the bit's full travel clears the table, vise and clamps. For a through-hole, provide clearance beneath the work or suitable sacrificial backing.
Secure the table at the required height and check that the work cannot rotate or lift when the bit catches.
Feed steadily and keep hands away from the rotating work
Feed steadily and keep hands away from the rotating work
A bit can catch and turn an unsecured part into a spinning lever. That is why a vise must be secured as well as tightened around the work.
Start with the bit clear of the work. Feed steadily so it cuts without being forced.
Ease the feed as the bit breaks through the underside. Keep hands clear rather than reaching underneath to support the exit.
Withdraw the bit under control, then stop the spindle before releasing or moving the work.
Supporting detail: Addendum 90 — Why larger drills usually need fewer revolutions per minute.
If the bit breaks or the part comes loose: stand clear
If the bit breaks or the part comes loose: stand clear
Do not grab a spinning part. Step clear and stop the drill press using a safely reachable stop control. For a broken bit, use the emergency stop if safely reachable. Wait for motion to cease and notify the instructor; do not restart until the fault and workholding have been checked.
In VCarve: match the material, preview the paths, then post
In VCarve: match the material, preview the paths, then post
Create or open the .crv job. Measure the material and match its width, height, thickness and units. In the lab's demonstrated setup, XY zero is the bottom-left corner and Z zero is the material surface.
Import the DXF vectors, remove unwanted geometry and join the outlines needed for the paths. Leave space for clamps and check the actual cutter path against their positions.
Create the pocket and profile toolpaths. Match the selected tool to the installed cutter; check cutting depths, feeds and speeds. Plan tabs or other workholding so the cut pieces remain secured.
Preview all toolpaths in their cutting order: pockets first, outside profiles last in this workflow. Check the first cutting location, remaining tabs, cut depth and clearance above clamps.
Save the intended toolpaths with the demonstrated Axiom HHC CNC (mm) (*.mmg) post processor and transfer the .MMG file to the supplied USB drive. Confirm the file selected at the machine is the one you previewed.
The preview checks the programmed cut; it does not prove that the real clamps are clear. The material position and zero settings at the router must match the job.
Before running: secure the cutter, material and every cut piece; Checklist
Before running: secure the cutter, material and every cut piece
With router power off and the machine made safe for tool setup, remove the magnetic dust boot. Check cutter insertion and tighten the collet with the appropriate wrenches, as demonstrated.
Use the installed power-up procedure, insert the USB drive, and select All axis home on the controller with the travel area clear. Homing finds the machine's references; it does not locate the workpiece.
Clamp the material on the spoilboard, the sacrificial surface above the machine bed. Keep clamps out of the entire tool path, leave the zero corner accessible, and tighten clamps progressively in the demonstrated zig-zag order.
Check that the material and the pieces cut from it will remain held throughout cutting. A loose piece can be struck and thrown by the cutter.
Set XY zero at the job's datum and Z zero at the material surface, using the demonstrated touch-off or tool-setting puck method. Clear the puck and its cord from the tool's path after setting.
Raise the router as demonstrated, refit the dust boot, turn on router power, open the dust-collection gate and start dust collection.
Keep clear of the cutter and the moving carriage throughout operation. The dust boot helps collect debris; it does not make the cutting area safe to reach into.
At Run, check the spindle and first movement against the preview
At Run, check the spindle and first movement against the preview
In our lab's demonstrated controller workflow, press RUN/PAUSE, choose UDisk File, select the intended .mmg file and review SetWorkParam. Confirm the parameters with the checkout instruction before accepting them. Accepting starts a countdown, followed by spindle startup and travel to the first toolpath location.
If the spindle does not start or the first location is wrong, press STOP/CANCEL. Resolve the cause with the instructor before restarting. Do not reach in to change the router switch while the program continues moving.
In our labs, watch the process and listen for unusual noises. Keep the controller accessible. Use STOP/CANCEL for a problem with the run or the emergency stop for an emergency, as demonstrated during checkout. Notify the instructor and use Lab Conduct and Emergencies when needed.
After cutting, switch off the router before removing the work
After cutting, switch off the router before removing the work
In our lab's sequence, turn router power off, wait for the cutter to stop, raise it to the demonstrated Z clearance, and remove the dust boot before unclamping and removing the workpiece. Refit the dust boot afterward.
Cut the retaining tabs using an approved tool and its own operating procedure; the lab instruction advises against popping the parts out. Stop dust collection when it is no longer needed, return tools and clamps, and complete shutdown and cleanup.
Safety/Equipment
Manual Lathe
Check workholding and material support before starting; keep clear of the rotating work and stop for hazardous chip strings.
Manual lathe: Category 3 in the Metals lab
Manual lathe: Category 3 in the Metals lab
A lathe rotates the workpiece against a cutting tool. See Lathe Operations for chucks, work support and turning operations.
Check the setup and the material extending through the spindle; Checklist
Check the setup and the material extending through the spindle
In our labs, check the setup before starting the lathe.
Check that the chuck or other workholding grips the part securely and that the cutting tool is secured.
The chuck key never leaves your hand. It is not released until it is out of the chuck (see the chuck-key rule).
Check the support for long material, including material extending through the back of the spindle. In our labs, never run long, unsupported material through the spindle.
Check the planned movement of the tool and carriage against the chuck, workpiece and supports.
Locate the emergency stop and foot brake, and confirm how to operate them before starting.
A long unsupported bar can whip as it rotates. Support at the cutting end does not establish that the part behind the spindle is safe.
The whole workpiece rotates; chip strings can catch and cut
The whole workpiece rotates; chip strings can catch and cut
The chuck, workpiece and any material projecting from the spindle are rotating hazards. Apply the entanglement rules to the entire setup, including its back side.
In our labs, stop and clear long chip strings when they become a hazard. Never pull a chip string by hand. Use Metal Chips and Swarf for removal and cleanup. If long strings keep forming, have the instructor review the cutting setup before continuing.
If the work shifts or the setup behaves unexpectedly, stop safely
If the work shifts or the setup behaves unexpectedly, stop safely
Do not try to steady rotating work or catch a loose part. Use the stopping controls you were shown if you can reach them safely, keep clear, and notify the instructor. Use Lab Conduct and Emergencies for an injury or emergency.
Check workholding, cutter clearance and cutting settings; recognize the different categories for manual and CNC mills.
Manual mill: Category 3; CNC mill: Category 2 in the Metals lab
Manual mill: Category 3; CNC mill: Category 2 in the Metals lab
A vertical mill uses a rotating cutter to remove material held in a vise or clamps. See Vertical Mill Anatomy and Motion for the machine's parts.
The manual mill is Category 3 in the Metals lab; the CNC mill is Category 2 there. Use Equipment Categories and Supervision for the corresponding permission and supervision requirements.
Check clamping, cutter travel and cutting settings before the cut; Checklist
Check clamping, cutter travel and cutting settings before the cut
In our labs, check and recheck the workpiece clamping before beginning an operation.
Check the vise or clamps and the cutter's retention. Confirm the tool can follow the planned path without striking the workholding.
Identify the closing gaps between the moving table, workholding and machine frame. Keep the planned travel clear.
Check spindle speed, feed, depth of cut and width of cut for the planned operation.
Check coolant and slide lubrication as directed for the installed mill. Report low levels, damage or a maintenance need rather than adjusting the machine's sliding fits yourself.
A rotating cutter and a moving table create different hazards
A rotating cutter and a moving table create different hazards
The cutter can cut or catch what touches it; the table can close a gap against the column, vise or clamps. Keep clear of both the cutting area and the table's travel. CNC motion follows the program, so a pause in motion is not permission to reach in.
Use Machine Hazards and Housekeeping for stopping before measurements and for isolation before adjustments or maintenance. Use Metal Chips and Swarf for chip removal, including the required controls if compressed air is used.
If a tool breaks or the work comes loose, step away
If a tool breaks or the work comes loose, step away
In our labs, step away if a tool breaks or the workpiece becomes loose. Stop the mill if it is safe to do so; do not endanger yourself to reach a control. Notify the instructor in every case.
Keep hands away from the cutting nozzle and clear of its travel. The jet cuts material, and the moving head can trap a hand. See Machine Hazards and Housekeeping for movement, guards and stopping. OMAX safety information is further reading for the installed-machine training.
Prepare the file and toolpath: lab steps 1–10
Prepare the file and toolpath: lab steps 1–10
This is our lab's OMAX operating sequence. Follow it with the machine-specific instruction you received at checkout.
Export the CAD file to DXF or DWG, as for a laser-cut part.
Turn on the OMAX machine.
Turn on the water: the top water line under the sink.
Open ProtoMAX Layout software.
Click File → “Open file for other CAD software.”
Use the move, rotate and duplicate tools to lay out the parts. One square is equal to one inch.
Click Autopath to create toolpaths. Check that the path cuts on the correct side of each line and cuts inside items before outside items, so the part is not cut loose before its interior features are cut.
Click Post.
Select the starting position, normally the bottom left.
Save the post. It saves as an .omax file.
Verify settings, follow the prompts and dry-run: lab steps 11–15
Verify settings, follow the prompts and dry-run: lab steps 11–15
Right-click on Post and open the .omax file in ProtoMAX Make.
When Make asks for cutting parameters, select the appropriate material and enter its thickness. The lab procedure says to oversize the thickness “by just a bit”; confirm that allowance with the instructor.
If the machine was just turned on, Make shows a red homing button at the top of the screen. Make sure nothing obstructs the nozzle's movement before clicking it to home the machine.
Follow all the on-screen steps. These include, but are not limited to:
Attaching the abrasive hose.
Testing the nozzle for abrasive flow.
Placing and securing the material.
Homing the nozzle to the starting position on the material.
Adjusting the water height if necessary.
Dry-running the program.
Flipping down the splash guard.
Run the program.
In step 14, “homing” to the material means the job's starting position; it is distinct from the machine-homing step in step 13. Have both positions demonstrated during checkout.
A dropped part or a fault needs a safe stop, not a reach into the tank
A dropped part or a fault needs a safe stop, not a reach into the tank
Do not reach into the cutting area to retrieve a part while the machine is operating. If the material moves or the cut behaves unexpectedly, keep clear and use the stopping procedure demonstrated during checkout. Notify the instructor; follow Lab Conduct and Emergencies for an emergency.
The lab sequence above ends at running the program. Have the instructor demonstrate shutdown and safe part recovery before using the machine; a part falling into the tank is not a recovery procedure. Use Equipment Operating Procedure for the general shutdown and reporting requirements.
Materials and Manufacturing Processes/Foundations
What Is Manufacturing?
Turn materials into useful products by choosing processes that fit the material, quantity, cost and required quality.
Manufacturing turns materials into useful products
Manufacturing turns materials into useful products
Manufacturing changes materials into parts and products people can use. A board becomes a shelf, plastic pellets become a bottle, and metal sheet becomes a bracket. Shape, properties, joints and surfaces all contribute to the result.
A process is an operation that makes one of those changes. Most products need several processes. A useful plan states what each operation must achieve and how the result will be checked.
Primary processing makes usable material; secondary processing makes parts
Primary processing makes usable material; secondary processing makes parts
Primary processing converts raw resources into usable materials and common supply forms. Secondary processing turns those materials into parts or products. Stock means material supplied for further work, such as sheet, rod, boards or pellets.
Metal
Ore is refined into metal and made into stock such as sheet; sheet is then cut and bent into a bracket.
Plastic
Chemical feedstocks are made into polymer resin, often supplied as pellets; pellets are then molded into a bottle cap.
Wood
Logs are sawn into lumber; boards are then cut, joined and finished as furniture.
Glass
Mineral ingredients are melted and made into sheet glass; sheets are then cut and edge-finished for a window.
These terms describe a material's place in the supply chain. They do not replace the five process categories: sawing a log and sawing a furniture part are both separating.
Supporting detail: Addendum 91 — Why the boundary needs context.
Choose a process that fits material, quantity, cost and quality
Choose a process that fits material, quantity, cost and quality
Material
Can it tolerate the heat, force or chemical exposure? A process that bends metal sheet may crack a ceramic plate.
Quantity
A few parts favor flexible methods with little dedicated tooling. Repeated production can justify a mold or other tool made specifically for that part.
Cost
Count material, setup, tooling, labor, processing time, scrap and inspection. Cheap starting material can be expensive to turn into an acceptable part.
Required quality
Specify dimensions, allowable variation, strength and surface condition. Choose a route that can meet them consistently, then verify it.
For a small plastic cover, 3D printing may be useful for a few trial pieces; molding may suit repeated production after the design settles. Neither route wins from quantity alone: material behavior, geometry and acceptance requirements still matter.
Prototype, batch and mass production describe production situations, not universal numerical cutoffs. Manufacturing economics and design for manufacturing develop this comparison further.
Characteristics: What is the material like? Compare properties, useful forms and limitations.
Forming: How can it take a shape?
Separating: How can material be removed or cut apart?
Fabricating: How can parts be joined?
Conditioning: How can its internal properties be changed?
Finishing: How can its surface be protected or improved?
This is the collection's learning map for the later plastics, wood and metals topics. Characteristics is the starting description, not a sixth process category.
The map is not a mandatory factory sequence. Wood may be dried before cutting; a metal part may be annealed between forming steps; some surfaces are finished before assembly. A product may repeat a category or omit one.
Materials and Manufacturing Processes/Foundations
Manufacturing Process Categories
Classify an operation by its main purpose: separating, forming, fabricating, conditioning or finishing.
Five categories describe the change an operation makes
Five categories describe the change an operation makes
Name the operation's intended result. Are we removing material, creating shape, joining parts, changing internal properties or treating a surface?
These are five kinds of change, not five steps that every product must follow in order.
This collection uses the course's five-category model. In this model, forming includes casting, molding and additive manufacturing such as 3D printing. Other technical references may separate those into their own process groups.
Separating removes material to make a size, shape or opening
Separating removes material to make a size, shape or opening
Separating cuts material apart or removes it from a workpiece, the piece being worked on. Look for a cut edge, hole, slot or reduced dimension as the intended result.
Sawing: cut a wooden board or plastic rod to length.
Drilling: remove material to make a hole in a metal bracket or wooden panel.
Milling: a rotating cutter removes material to make a flat face, pocket or slot.
Laser cutting: remove material along a narrow path to cut a suitable sheet material.
Supporting detail: Addendum 92 — A laser cut does not have to vaporize all the removed material.
Forming creates shape without using material removal as the shaping method
Forming creates shape without using material removal as the shaping method
Forming gives material a shape by filling a mold, deforming it or building it up. The central action creates the shape rather than cutting unwanted material away.
Casting and molding: pour metal into a mold, mold a plastic cap, or cast a concrete planter.
Bending: bend sheet metal into a bracket or bend prepared wood around a form.
Forging: press or hammer metal into a new shape.
3D printing: build a plastic part in layers.
Forming can still produce excess material. Trimming a molded edge or cutting away printed supports is a separate separating operation. “Forming” does not promise zero waste.
Fabricating joins parts into an assembly
Fabricating joins parts into an assembly
Fabricating brings separate parts together so they work as one assembly. Ask whether the intended result is a joint.
Welding: join metal frame members or suitable plastic parts.
Adhesive bonding: glue wooden strips together or bond a panel to a frame.
Fasteners: use screws, bolts or rivets to hold parts together.
Joinery: assemble matching wooden joint features, such as a mortise and tenon.
Cutting the joint features is separating; fitting and securing the parts is fabricating. In industry, “fabrication” can describe a whole production job. Here it has the narrower meaning joining.
Conditioning changes internal properties
Conditioning changes internal properties
Conditioning changes how the material behaves through its structure, moisture content or chemical state. A new outline or a decorative coating is not its main goal.
Heat treating: use a controlled heating and cooling cycle to change properties of a suitable metal.
Drying or seasoning wood: reduce moisture content before later processing or service.
Curing: allow a resin's chemical reaction to develop its intended properties.
Annealing: use a controlled thermal cycle to relieve stress or change structure, as appropriate to the metal, plastic or glass.
Conditioning can also change dimensions. Drying wood may shrink; heat treatment may distort a part. “Changes properties” does not mean “leaves every dimension unchanged.”
Finishing treats the surface for protection or appearance
Finishing treats the surface for protection or appearance
Finishing changes surface condition, appearance or protection. It may add a layer, remove a little material or alter the surface itself.
Painting: coat a wooden panel or metal housing.
Plating: deposit a metal layer on a part.
Staining: change wood's color; stain alone does not necessarily provide a protective film.
Polishing: improve the surface of metal, suitable plastic or glass.
A surface location alone does not decide the category. Surface hardening primarily changes material properties, so it belongs under conditioning in this model.
For overlapping processes, state the purpose and pick the primary category; Practice
For overlapping processes, state the purpose and pick the primary category
Identify one operation. Break a long manufacturing description into separate actions.
State its acceptance goal. What result tells you this operation is complete?
Choose the category that best matches that goal. Name any secondary effect in the explanation.
Sanding
Sanding a block down to a specified thickness is primarily separating. Sanding out visible scratches before a clear coat is primarily finishing, although both remove material.
Bent lamination
Bonding thin wood layers around a curved form combines fabricating and forming. If the stated goal is the curve, call forming primary; if the question focuses on the bond between layers, call fabricating primary.
Resin and adhesive curing
Curing a resin part to develop properties is conditioning. Bonding two parts with that resin is primarily fabricating; curing is the property-changing step that enables the joint.
Welding
A weld can change nearby material properties, but a step intended to join two frame members is primarily fabricating.
If the description only says “sanding” or “curing,” explain what purpose you are assuming. A defensible classification includes the reason.
Compare exactly four families: Metals, Plastics (polymers), Wood & Composites, and Ceramics & Glass.
Use four material families as the starting point
Use four material families as the starting point
The course uses exactly four families: Metals; Plastics (polymers); Wood & Composites; Ceramics & Glass. A family helps you predict useful behavior. It does not specify a material well enough to manufacture a part.
Classify the material in the named part, not the entire product. A kettle can have a metal body, a plastic handle and a glass window.
Supporting detail: Addendum 93 — Why another book may show a different family list.
Metals combine useful strength, stiffness and conductivity
Metals combine useful strength, stiffness and conductivity
Metals include metallic elements and alloys, mixtures designed for useful properties. Steel, aluminum and copper are everyday examples.
Many metals conduct heat and electricity well and can deform permanently without breaking. Many are strong and stiff compared with unreinforced plastics. Density varies: aluminum is much less dense than steel, so “metal” does not always mean the heaviest choice.
Typical matches include copper wire for electrical conduction, aluminum cookware for heat transfer, and steel fasteners for carrying loads. Corrosion behavior depends on the alloy and environment. Rust specifically concerns iron-containing materials; other metals can corrode without rusting.
Metals may be cast, formed, cut, joined, heat treated and coated. Those process choices depend on the specific alloy and condition. Detailed metal processing belongs in the later metals topics; Milling Operations and Lathe Operations show separating operations.
Plastics are usually light, moldable and poor conductors
Plastics are usually light, moldable and poor conductors
Plastics (polymers) are materials based on long molecular chains, usually with additives to adjust their behavior. Polyethylene containers, acrylic display panels and nylon gears belong here.
Common unfilled plastics have relatively low density and low thermal and electrical conductivity. They can range from flexible to rigid, and from tough to brittle. Heat, sunlight and chemicals affect different grades differently.
Thermoplastics can soften on heating and be reshaped under suitable conditions. Thermosets develop a chemically linked structure during curing and cannot simply be remelted into a new shape.
“Light” does not mean “floats.” Solid acrylic is denser than water. A hollow product may float because its overall density includes the trapped air.
Supporting detail: Addendum 94 — A supplier value that checks the floating claim.
Wood & Composites depend on grain, layers and reinforcement
Wood & Composites depend on grain, layers and reinforcement
Wood has a cellular structure and grain. It is often light for its useful stiffness, relatively easy to cut and join, and a poor heat conductor. Strength and movement depend on direction and moisture content.
A composite combines materials so they work together. Examples include plywood, wood-fiber board, glass-fiber-reinforced plastic and carbon-fiber-reinforced plastic. The material surrounding and holding reinforcement is the matrix; the reinforcement helps carry load.
Do not assume every composite behaves like wood or like unfilled plastic. Fiber direction, layer arrangement, binder and moisture exposure affect the result. A composite can offer useful strength or stiffness for its mass while still being difficult to cut, join or repair.
Plywood shelves and glass-fiber-reinforced boat panels belong to the same course family, but need different processing choices. Later wood topics develop grain and moisture behavior.
Ceramics & Glass often resist heat and wear but can fracture abruptly
Ceramics & Glass often resist heat and wear but can fracture abruptly
Ceramics & Glass include fired clay products, porcelain, window glass and engineering ceramics such as alumina. Many are hard, resist chemical attack and carry compression well. Many also have little ability to deform permanently before fracture.
A tile can resist scratching yet break when struck. Hardness is not toughness. Many familiar ceramics and glasses are electrical insulators, but the family contains exceptions; thermal conductivity also varies widely.
Shaping may occur before firing, while hot, or through suitable cutting and grinding afterward. Glass can be formed while hot and annealed to reduce residual stress. Finished ceramic parts are often harder to machine than common metals or plastics.
Supporting detail: Addendum 95 — Hard to machine does not mean impossible to machine.
Compare typical behavior, then check the specific material; Practice
Compare typical behavior, then check the specific material
Common tendencies, not design values or a ranking from best to worst. Compare materials at the same temperature, condition and loading direction.
Use Material Properties to put a precise name to the requirement. Then select a grade, species or composite construction and check its data. No family wins on every property.
Distinguish strength, stiffness, hardness and toughness, then compare physical and chemical behavior, cost and workability.
State the requirement before choosing the material
State the requirement before choosing the material
“Strong,” “light” and “durable” are starting points. A useful comparison says what load, temperature, environment and lifetime the part must handle.
Mechanical properties describe behavior under force. Physical properties describe features such as density and heat or electrical behavior. Chemical properties describe interaction with the environment. Cost and workability determine whether a suitable material can become a practical product.
Start with the four material families, then compare actual materials within them. Processing and condition matter: a material name alone does not tell you its final properties.
Strength describes the stress a material can withstand before a specified limit, such as permanent deformation or fracture. Stress relates force to the area carrying it. A thicker part may carry more load without being made of a stronger material.
Tensile strength
Resistance to a pulling load. Think of a tie rod being pulled along its length.
Compressive strength
Resistance to a pushing or crushing load. Think of a block squeezed between two surfaces. A material good in compression may be much less capable in tension.
Stiffness
Resistance to elastic deformation, the change that recovers when the load is removed. A shelf that sags too far may be strong enough to avoid failure but insufficiently stiff.
A part's stiffness depends on both its material and its geometry. Compare similarly shaped specimens when comparing materials; do not infer material stiffness by comparing a thin wire with a thick bar.
Supporting detail: Addendum 96 — Stress, strain and modulus give the comparison units.
Hardness, toughness, brittleness and ductility answer different questions
Hardness, toughness, brittleness and ductility answer different questions
Hardness
Resistance to local indentation or scratching, depending on the test. It can help resist wear, but hardness alone does not determine wear performance.
Toughness
Ability to absorb energy before fracturing. A part that must survive a blow needs more than a hard surface.
Brittleness
A tendency to fracture with little permanent deformation. Glass may resist scratching but crack instead of bending permanently.
Ductility
Ability to deform permanently in tension before fracture. A ductile metal can be drawn into wire. Elastic stretch that disappears when unloaded is not the same as ductility.
Do not treat these as synonyms. A hard ceramic tile can be brittle; a ductile metal can bend before it breaks. Toughness depends on both the stress sustained and the deformation before fracture, as well as test conditions.
Supporting detail: Addendum 97 — Why a single “toughness number” needs its test method.
Density and thermal behavior decide weight and temperature limits
Density and thermal behavior decide weight and temperature limits
Density
Mass per unit volume. At equal volume, lower density gives lower mass. A large hollow metal part can weigh less than a small solid plastic part, so compare the whole design too.
Melting point or melting range
The temperature or range where a material melts. It helps choose processing conditions, but it is not the allowable service temperature: a loaded part may lose useful stiffness or strength earlier.
Thermal conductivity
How readily heat travels through a material. A heat spreader benefits from high conductivity; an insulating handle usually benefits from low conductivity.
Electrical conductivity
How readily electric current passes through a material. A wire needs a conductor; its surrounding insulation needs low conductivity under the intended conditions.
Many common metals conduct heat and electricity well. Many unfilled plastics, dry woods and familiar ceramics are poor electrical conductors. Additives, moisture and temperature can change those tendencies.
Supporting detail: Addendum 98 — Not every material has one useful melting-point number.
Corrosion resistance is resistance to a particular environment
Corrosion resistance is resistance to a particular environment
Corrosion resistance is the ability to resist chemical or electrochemical deterioration in service. A metal that works well indoors may perform differently in salt water or against another metal.
Rust is one form of corrosion involving iron. Aluminum and stainless steel can resist many exposures, but neither is immune to every environment. Coatings can protect a surface, and their condition matters.
For plastics, wood and composites, also consider chemical attack, sunlight, moisture and decay as appropriate. “Does not rust” is not the same as “will last outdoors.” Name the exposure before selecting a family or grade.
Cost and workability belong in the same comparison
Cost and workability belong in the same comparison
Workability means how readily a material can be processed into an acceptable part. It is specific to the operation: a material that molds well may be difficult to bond, and one that cuts readily may be unsuitable for bending.
Cost includes more than price per mass. Consider how much material the design needs, available supply forms, tooling, processing time, waste, inspection and any protective finish.
A family profile narrows the search: common metals often offer stiffness and conductivity; plastics often offer low mass and moldability; wood and composites offer useful directional performance; ceramics and glass often offer hardness and chemical resistance. The particular material decides whether those benefits meet the job.
Use Manufacturing Process Categories to describe the required operations. Detailed manufacturing economics and design for manufacturing extend the cost comparison.
Choose a candidate, give a reason, and name what still needs checking; Checklist; Practice
Choose a candidate, give a reason, and name what still needs checking
Write the required function and service conditions.
Name the properties that control success.
Screen the four families, then identify a specific candidate material.
Check direction, temperature, moisture, processing condition and data source.
Check workability and total cost, then verify the finished part against its requirements.
For a heat-spreading plate, Metals is a sensible starting family because common choices such as aluminum and copper conduct heat well. The next checks include temperature, dimensions, corrosion exposure and cost. That is a justified candidate, not a complete design specification.
Polymer chains, thermoplastics and thermosets, common plastics, and what resin identification codes actually tell you.
Plastics get their behavior from polymer chains
Plastics get their behavior from polymer chains
A polymer is a substance made of very large molecules built from repeating units. Small starting molecules called monomers react to build those molecules. Many polymers have long chains; some also have branches or chemical links between chains.
A plastic combines a polymer with ingredients that may change its color, flexibility, processing behavior or resistance to weather. The polymer name is a starting point, not a complete material specification. Two grades of the same plastic can behave differently.
Plastics is one of the four material families in the material-family foundations topic. A polymer reinforced with glass or carbon fibers is a composite; the course places composites in Wood & Composites.
Thermoplastics soften again; cured thermosets do not remelt
Thermoplastics soften again; cured thermosets do not remelt
The useful distinction is behavior on reheating
Type
What happens
Examples and recycling
Thermoplastic
Heating makes the material soft enough to reshape or flow. Cooling makes it firm again. Reheating can repeat this change, within the material's processing limits.
PE, PP, PVC, PLA, ABS, PETG, acrylic, polycarbonate and nylon. Clean, compatible material can often be remelted for recycling; contamination, degradation and available collection systems limit actual recovery.
Thermoset
Curing forms a network of chemical links between molecules. The cured material cannot be melted back into a moldable liquid. Excessive heating degrades it.
Cured epoxy and unsaturated polyester resin. They cannot be recycled by ordinary melt-and-remold processing; specialized recovery methods may exist.
Curing is a chemical change; cooling is a temperature change. A two-part epoxy becoming solid is not simply a hot plastic cooling down.
Supporting detail: Addendum 99 — Softening, melting and heat resistance are different questions.
Light weight and corrosion resistance come with limits
Light weight and corrosion resistance come with limits
Light weight: many unfilled plastics have much lower density than metals. Low weight does not automatically mean high stiffness.
Chemical resistance: plastics do not rust like steel, but a chemical may soften, swell or crack a particular plastic. Check the material, chemical, temperature and exposure time together.
Low softening or melting temperatures: many common thermoplastics are easy to form with heat but unsuitable for hot, loaded service.
Creep: slow deformation under a sustained load. A plastic shelf can keep sagging even when its load stays constant.
UV degradation: sunlight can discolor or embrittle susceptible grades. Outdoor service calls for a suitable resin and stabilization, not just a preferred color.
Electrical insulation: many unfilled plastics resist current flow. Conductive fillers and special formulations can change that behavior.
Supporting detail: Addendum 100 — Why a short strength test does not settle a long service life.
Match common thermoplastics to their useful properties
Match common thermoplastics to their useful properties
These are typical uses and tradeoffs, not design ratings for every grade. All materials in this table are thermoplastics.
Common plastics: a first selection, followed by a grade data sheet
Material
Typical uses and strengths
Watch for
PLA — polylactic acid
Models, packaging and filament; stiff, often made from renewable feedstocks.
Ordinary grades have limited heat resistance and can be brittle. Bio-based does not mean an item belongs in home compost or a recycling bin.
ABS — acrylonitrile butadiene styrene
Housings and toys; a useful balance of toughness and rigidity.
Ordinary grades weather poorly outdoors; some solvents attack it.
PETG — glycol-modified PET
Clear displays, formed packaging and filament; tough and readily thermoformed.
Scratches and limited service temperature. PETG is not interchangeable with bottle-grade PET.
Acrylic / PMMA — polymethyl methacrylate
Signs, displays and glazing; clarity, stiffness and good weathering.
More prone to cracking under impact than polycarbonate; vulnerable to some solvents.
PC — polycarbonate
Impact-resistant glazing and housings; transparent and tough.
Scratching and chemical attack; select an appropriate UV-resistant grade for outdoor exposure.
HDPE — high-density polyethylene
Bottles, tanks and pipe; tough with useful chemical resistance.
Low stiffness compared with metals, creep and substantial thermal expansion.
LDPE — low-density polyethylene
Film and squeeze bottles; flexible and tough.
Less stiff than HDPE and limited temperature capability.
PP — polypropylene
Containers, caps and living hinges (thin flexible connections); light and chemically resistant.
Creep, UV sensitivity in unstabilized grades and reduced toughness in cold service.
PVC — polyvinyl chloride
Rigid pipe and window profiles; plasticized grades make flexible tubing and cable insulation.
Properties depend strongly on additives; limited temperature range.
Nylon / PA — polyamide
Gears, bearings and cable ties; strength, toughness and wear resistance.
Absorbed moisture changes dimensions and mechanical properties.
Supporting detail: Addendum 101 — Material references for checking a particular choice.
Epoxy and polyester resin cure into thermosets
Epoxy and polyester resin cure into thermosets
Two common thermosetting resin systems
Resin
Typical uses and strengths
Limitations
Epoxy
Adhesives, cast parts and composite matrices; good adhesion and generally low cure shrinkage.
Mixing and cure conditions affect properties. Often costs more than general-purpose polyester resin; unprotected epoxy can degrade in sunlight.
Unsaturated polyester resin
Fiberglass boat shells and panels; economical for many composite parts.
Typically greater cure shrinkage and lower adhesive performance than epoxy. Cured resin cannot be remelted.
“Polyester” alone is ambiguous. PET packaging is a thermoplastic polyester. The unsaturated polyester resin used in a conventional fiberglass layup cures into a thermoset. See the hand-layup card in Plastic Forming Processes.
Supporting detail: Addendum 102 — Where the resin comparison comes from.
Resin codes identify plastic; they do not promise recycling; Practice
Resin codes identify plastic; they do not promise recycling
The number on a container is a resin identification code (RIC). It can help sorting, but it does not say whether the local recycling program accepts that product.
The seven code-to-resin matches, checked against current public guidance
Code
Plastic
1 — PET / PETE
Polyethylene terephthalate
2 — HDPE
High-density polyethylene
3 — PVC
Polyvinyl chloride (vinyl)
4 — LDPE
Low-density polyethylene
5 — PP
Polypropylene
6 — PS
Polystyrene
7 — OTHER
Resins outside the first six categories; also some combinations of resins. It is not one particular plastic.
For example, code 5 identifies PP; it does not prove that a PP lid is accepted with PP containers. Use the collector's instructions for that item. Do not assign PETG to code 1 just because its name contains PET.
Supporting detail: Addendum 103 — Verified code sources and the standard's exact distinction.
How eight plastic and composite processes shape material, what they can make, and where tooling and geometry limit the choice.
Start with the shape and how the material becomes solid
Start with the shape and how the material becomes solid
These processes make a shape by moving softened material, stretching sheet or curing resin in tooling. A mold shapes a part against its surfaces; a die gives flowing material a cross-section. Tooling is the equipment made specifically to produce the part.
Use the process-category foundations topic for the five-category framework. Here, follow what happens to the material: thermoplastics usually set by cooling; thermosets set by curing. Review Plastics as Materials if that distinction is unclear.
The starting form and the finished shape narrow the choice before cost enters the discussion. The diagrams show typical versions of each process.
Injection molding fills a closed cavity, then repeats the cycle
Injection molding fills a closed cavity, then repeats the cycle
In conventional thermoplastic injection molding, a heated barrel and screw prepare the melt. The screw advances to push a measured shot (the material delivered in one injection) through a nozzle into a clamped mold.
A thermoplastic cycle. Cooling overlaps filling and packing; the five labels describe the main jobs, not five completely separate thermal events.
Clamp: close the mold and hold it against the pressure of the incoming melt.
Inject: fill the cavity.
Hold/pack: maintain pressure to feed additional material as it shrinks, while the gate can still pass melt.
Cool: allow enough heat to leave for the part to keep its shape during removal.
Eject: open the mold and push the part free, commonly with ejector pins. Close for the next cycle.
Materials and products: thermoplastics such as ABS, PP and nylon become housings, caps, clips and gears. Specialized injection systems also mold thermosets; those require curing, so the cooling-based cycle above is not universal.
Tooling and quantity: detailed, pressure-resistant molds are a substantial initial investment. Repeated cycles and multiple cavities can make the investment worthwhile for many identical parts.
Supporting detail: Addendum 104 — See the machine and cycle in a public explainer.
Sprue, runner and gate carry melt into the part
Sprue, runner and gate carry melt into the part
In a conventional sprue-and-runner layout, the sprue receives melt from the nozzle, a runner distributes it, and a gate is the restricted entrance to a part cavity. One mold may contain several cavities, and one cavity may have several gates.
Draft is a slight taper on a surface in the mold-opening direction. It helps the part release instead of scraping along the tool. Injection molding can produce ribs, bosses (raised features around holes) and fine detail, but every feature must have a way out of the mold.
An undercut traps material behind a tool feature. It may require a moving side core, another special mechanism or a redesigned part. A simple two-part mold cannot produce every enclosed hollow shape.
Uniform walls reduce sink marks and uneven shrinkage; Practice
Uniform walls reduce sink marks and uneven shrinkage
Aim for a reasonably uniform wall thickness, with gradual transitions where thickness must change. A thick mass cools differently from an adjacent thin wall. Its shrinkage can pull the surface inward, leaving a sink mark, or contribute to distortion.
A solid block under a thin housing wall is therefore a warning sign. Hollow out the bulky region where possible and use appropriately sized ribs for support. Packing and cooling settings also matter; changing the drawing is not the only remedy.
Supporting detail: Addendum 105 — Three design clues to recognize.
Blow molding inflates a hot tube or preform into a hollow part
Blow molding inflates a hot tube or preform into a hollow part
A mold closes around a hot parison (tube), or a previously molded preform. Air pressure expands the material against the mold, then it cools. Extrusion blow molding starts with a tube; injection-based versions start with a molded preform.
Materials and products: thermoplastics; HDPE detergent bottles and PET beverage bottles are familiar examples made by different blow-molding variants.
Tooling and quantity: dedicated molds and machinery favor repeated production, especially large packaging runs. Mold complexity and the chosen variant affect cost; lower forming pressure does not make the whole production line inexpensive.
Geometry: good for thin-walled hollow containers. Stretching affects wall thickness; external detail is controlled better than internal detail. It does not directly make a solid gear or complex internal ribs. Mold parting lines, and pinch-off seams in extrusion-blown parts, may remain visible.
Supporting detail: Addendum 106 — Public process reference.
Rotational molding coats a mold to make a large hollow shell
Rotational molding coats a mold to make a large hollow shell
A measured charge, usually thermoplastic powder, goes inside a mold. Heating and slow rotation about two axes distribute material over the inside surface as it melts. The mold keeps moving during cooling before the shell is removed.
Materials and products: predominantly polyethylene; tanks, playground shells and kayaks.
Tooling and quantity: molds do not withstand injection pressure, so tooling is often less costly for a large part. Heating and cooling the mold takes time, making low-to-medium quantities attractive compared with faster processes.
Geometry: large hollow parts with relatively even walls are a strength. Local thickness, corners and fine tolerances still need care. Tiny details, very thin walls and solid precision parts are poor fits. This is slow coating of the mold, not high-speed centrifugal casting.
Supporting detail: Addendum 107 — Public process reference.
Thermoforming stretches a sheet into a tray or shell
Thermoforming stretches a sheet into a tray or shell
Heat thermoplastic sheet until it is pliable, form it against a tool, cool it and trim the edge. In vacuum forming, removing air between sheet and tool lets outside air pressure press the sheet against the tool. Pressure forming adds pressure on the other side.
Materials and products: thermoplastic sheets such as PETG, ABS and polystyrene; packaging trays, display covers and equipment liners.
Tooling and quantity: a simple one-sided tool can suit prototypes or short runs. Durable tools and automated equipment also support very large packaging volumes.
Geometry: best for open, sheet-like shapes with draft. Deep draws stretch and thin the sheet; the tool controls one surface most directly. It cannot create a solid boss or a closed bottle from one sheet in this basic process. Undercuts complicate release.
Supporting detail: Addendum 108 — Public process reference.
Extrusion makes a continuous, constant cross-section
Extrusion makes a continuous, constant cross-section
A screw moves and melts plastic, then pushes it continuously through a shaped die. Cooling and sizing equipment establish the final dimensions. The product is cut to length or wound.
Materials and products: commonly thermoplastics such as PVC and PE; pipe, tubing, sheet, film and window profiles.
Tooling and quantity: a profile die is often simpler than a complex injection mold, but the production line and setup still cost money. Long runs spread those costs over many meters of product.
Geometry: the die can make solid or hollow cross-sections. It cannot directly put a cap on the end of a tube or create isolated holes along one side; those require other operations. A long product with the same section everywhere is the main clue.
Supporting detail: Addendum 109 — Public process reference.
Compression molding presses a charge between matched tools
Compression molding presses a charge between matched tools
Place a measured amount of material in an open mold. Closing the heated tool applies pressure and spreads the charge into shape. With a thermosetting compound, the part cures before removal; cooling alone is not what hardens it.
Materials and products: often thermosets or fiber-filled thermosetting compounds; electrical components and composite body panels. Thermoplastic sheet composites can also be compression molded, with a cooling-based solidification step.
Tooling and quantity: matched tools and a press require investment, often justified by repeated medium-to-high production. Tooling is not automatically cheap; size, surface quality and precision matter.
Geometry: both faces can be shaped, including ribs and shaped panels. Material must flow before it cures; extremely thin features, deep narrow details and trapped undercuts are difficult.
Supporting detail: Addendum 110 — Public process reference.
Casting fills a mold with liquid resin for small quantities
Casting fills a mold with liquid resin for small quantities
Liquid resin fills a mold and hardens. In common small-batch resin casting, mixed components react and cure. A flexible mold made from a master pattern can reproduce surface detail.
Materials and products: often thermosets such as epoxy, polyurethane or unsaturated polyester; prototypes, decorative replicas and electrical encapsulation. Casting is broader than polyurethane casting; some cast plastics, such as cast acrylic, are thermoplastic after polymerization.
Tooling and quantity: flexible molds can have a low initial cost but limited life. Labor and cure time make this useful for short runs rather than a default for millions of pieces.
Geometry: good detail and some undercuts are possible with flexible tooling. Trapped air, cure shrinkage and heat from the reaction limit thin passages and thick pours. A closed hollow space still needs a removable or sacrificial core, or a different casting method.
Supporting detail: Addendum 111 — Public process reference.
Hand layup builds a fiber-reinforced composite against a tool
Hand layup builds a fiber-reinforced composite against a tool
In wet hand layup, reinforcing fabric or mat is placed against a mold, wetted with liquid resin and consolidated to reduce trapped air. Layers build thickness, then the resin cures.
Materials and products: usually a thermosetting polyester or epoxy matrix with glass or carbon fibers; boat shells and custom covers. These are composites in the Wood & Composites material family. Prepreg layup uses reinforcement already containing resin and is a related but different route.
Tooling and quantity: relatively simple one-sided molds support small runs and large custom parts. Manual work and cure time limit production rate.
Geometry: good for broad shells. The mold gives one face its finish; the other depends on the layup. Tight corners, inaccessible cavities and precise thickness on both faces are difficult. Fiber direction affects strength, so layer arrangement is part of the design.
Supporting detail: Addendum 112 — Public process reference.
Use geometry, material, quantity and tooling cost to narrow the process choice, then estimate cost per part and production rate.
Check geometry and material before comparing prices; Checklist
Check geometry and material before comparing prices
A low quoted price is irrelevant if the process cannot make the required shape or use the required material. Start with Plastics as Materials and the capability cards in Plastic Forming Processes.
Describe the geometry: hollow container, open sheet-like shell, constant cross-section or discrete solid part.
Choose a material type and candidate grade that meet the load, temperature and environment.
State the quantity, expected repeat orders and required delivery rate.
Check how the part leaves the tool: draft, undercuts and access to internal spaces.
Compare tooling, per-part cost, achievable detail and likely defects for the remaining processes.
Use part shape to build a short list; Practice
Use part shape to build a short list
Starting candidates, not exclusive rules
Need
Start with
Then ask
Many thin-walled hollow containers
Blow molding
Can the hot tube or preform stretch into this shape with an adequate wall?
A large hollow shell in a modest quantity
Rotational molding
Are the longer cycle and achievable detail acceptable?
An open tray or sheet-like cover
Thermoforming
Will the sheet thin too much, and can it release from the tool?
A long constant cross-section
Extrusion
Which end features or side holes would need later operations?
Many detailed discrete parts
Injection molding
Can walls stay reasonably uniform, and does quantity justify the mold?
Repeated thermoset parts or composite panels
Compression molding
Can the charge fill the matched tools before curing?
A few detailed resin parts
Casting
Will mold life, trapped air and cure time meet the need?
A custom fiber-reinforced shell
Hand layup
Is the labor acceptable, and can the reinforcement reach every region?
“Solid” does not mean “make every region thick.” An injection-molded housing is a discrete part, yet hollowing out bulky sections often improves it. Several processes can make a tank; size, quantity, resin and detail determine the better candidate.
Spread tooling cost over the number of acceptable parts; Practice
Spread tooling cost over the number of acceptable parts
A simple comparison is average cost per part = tooling cost / quantity + variable cost per part. Variable cost includes the costs that grow with production, such as material and processing time. Tooling cost is paid even if only a few parts are made.
Illustrative estimates, not supplier prices: suppose two processes can both meet a cover's specification. Route A costs $900 for tooling and $14 per part. Route B costs $18,000 for tooling and $2 per part.
Average cost per acceptable part, assuming no scrap or extra charges
Quantity
Route A
Route B
100
$900 / 100 + $14 = $23.00
$18,000 / 100 + $2 = $182.00
5,000
$900 / 5,000 + $14 = $14.18
$18,000 / 5,000 + $2 = $5.60
Supporting detail: Addendum 113 — Find the quantity where the two estimates are equal.
Cycle time and cavity count set the ideal production rate; Practice
Cycle time and cavity count set the ideal production rate
A cavity makes one part per cycle. With cycle time in seconds, ideal parts per hour = 3600 / cycle time × cavities.
For a 30-second cycle and two identical cavities: 3600 / 30 × 2 = 240 parts/h. That assumes uninterrupted operation and every part acceptable. Use the complete repeating cycle time, including opening and ejection; do not add overlapping cooling time twice.
Actual useful output is lower when setup, stoppages or rejects occur. More cavities may increase tooling cost and require a larger machine, so a higher ideal rate does not by itself settle the process choice.
Explain the choice with both a benefit and a limitation
Explain the choice with both a benefit and a limitation
A useful selection sounds like this: “For 300 large hollow PE garden reservoirs, investigate rotational molding because the shape fits and tooling can be economical at modest quantities. Confirm wall control and cycle time before committing.”
The quantity alone does not prove that choice. A narrow neck, precision sealing face, delivery deadline or different resin could change it. State the assumptions, identify a credible alternative, and compare the features that matter.
Supporting detail: Addendum 114 — Further process-selection reading.
Materials and Manufacturing Processes/Plastics
Cutting and Machining Plastics
Choose a separating process for the plastic and the feature, then control heat, chips and edge damage.
Choose the cut from the material and the feature
Choose the cut from the material and the feature
Separating removes material. A saw makes a blank, a drill makes a round hole, and a router or mill can make an outline, pocket or slot. Identify the resin and grade before choosing the process: two clear sheets can be acrylic and polycarbonate, with very different cutting behavior.
Process
Useful for
What controls the result
Sawing
Straight cuts or curved blanks on a band saw
Use a blade intended for the plastic and thickness. Teeth must cut without grabbing or packing the cut with chips; the finest tooth spacing is not always best.
Drilling
Holes through sheet or solid stock
Use suitable drill geometry, support the exit surface and provide chip clearance. Brittle acrylic can crack when the drill grabs at breakthrough.
Milling and routing
Accurate edges, slots and pockets
Sharp cutting edges, room for chips to escape and a supported workpiece reduce melting and chatter.
Laser cutting
Sheet profiles in an approved material
The resin, additives, thickness and laser wavelength matter. A glossy edge alone does not prove dimensional accuracy.
Hot-wire cutting
Contours in suitable thermoplastic foam
A heated wire softens a narrow path. This is not a general cutting method for solid plastic sheet or every foam formulation.
Heat builds up near the cut because plastics generally conduct heat poorly. Softened chips can stick to the tool or weld back onto the edge. The symptoms are smeared surfaces, strings of softened material and chips packed into the cutter.
Slowing the feed alone can make melting worse. Feed is how quickly the tool advances through the work; spindle speed is how quickly it turns. Too little advance per tooth lets the edge rub instead of taking a useful chip. Start with cutting data for the resin and tool, keep the tool sharp, and maintain chip clearance. Reducing excessive spindle speed may help, but feed, speed and cut depth must be considered together.
Deep holes need a planned way to clear chips. Coolants and cleaners must be compatible with the plastic; an unsuitable liquid can cause fine cracks called crazing. Use Feeds and Speeds for the relationships, not its metal cutting values as plastic settings.
Supporting detail: Addendum 115 — Why a slower cut can produce more heat.
Acrylic, PVC and polycarbonate behave differently under a laser
Acrylic, PVC and polycarbonate behave differently under a laser
Acrylic (PMMA) absorbs the infrared energy of a CO₂ laser. Concentrated heating removes material along the cut and can leave a smooth, glossy edge. That result depends on the sheet grade, thickness and process settings; it is not a promise for every clear plastic or every laser.
PVC is not a laser-cutting substitute for acrylic. Heating PVC can release hydrogen chloride; with moisture it forms hydrochloric acid, creating an exposure and corrosion concern. This is a chemical incompatibility, not simply a poor-looking edge.
Polycarbonate is often a poor choice for a clean CO₂-laser-cut sheet edge. It can yellow, char and leave a degraded edge instead of acrylic's clear finish. Specialized processes can cut some polycarbonate, so “polycarbonate cannot be laser processed” is too broad. Routing or sawing is often the better starting choice for a clear polycarbonate profile. Do not assign PVC's chlorine chemistry to polycarbonate.
Supporting detail: Addendum 116 — Manufacturer references and the limits of a material list.
Trim the molding excess without cutting into the part; Practice
Trim the molding excess without cutting into the part
A gate is the entry from a molding flow channel into the part cavity. Degating separates the part from that feed connection. Flash is a thin unwanted fin, often at a mold joint; trimming removes it. A burr is a raised edge left by cutting. These are different defects, even when the same trimming tool can remove them.
Support the part near the cut and leave the required contour intact. Cutting into the wall creates a notch that may start a crack. For batches, tumbling with suitable media can remove small burrs, but it can also round wanted edges or damage thin features. Inspect the dimensions and surface after the trial.
Match solvent cement, adhesive, welding or mechanical joints to the plastic pair, load and need for disassembly.
Start with both plastics and what the joint must do; Checklist
Start with both plastics and what the joint must do
Fabricating joins pieces into a useful assembly. Name both materials, then state the load, service temperature, appearance and whether the assembly must come apart. A leak-tight seam, a removable cover and a clear display corner need different joints.
These routes identify candidates. The actual grade, joint shape and service conditions decide whether a candidate works.
Identify the two resins and any coating or surface contamination.
State the load direction, environment and need for disassembly or sealing.
Check the joining product or process guidance for that material pair.
Make a representative trial joint and inspect it after full cure or cooling.
Solvent cement softens the surfaces; adhesive adds a bond layer
Solvent cement softens the surfaces; adhesive adds a bond layer
Solvent cementing uses a compatible liquid to soften or dissolve the surfaces so polymer chains can mix across the joint. As solvent leaves, the joint develops strength. It is chemical softening, not heat melting. Acrylic-to-acrylic is a common application; PVC and ABS also have specific cement systems. The cement must match the resin and fit of the joint.
Adhesives bond through a separate layer. Epoxies, cyanoacrylates and other formulations have different gap, flexibility and temperature limits. “Plastic glue” does not mean it bonds every plastic. Allow the specified cure time before loading; a joint that holds itself together may not have reached service strength.
Polyethylene (PE) and polypropylene (PP) resist many ordinary adhesives. Their low surface energy makes it difficult for an adhesive to spread into intimate contact, called wetting. Specialized adhesives or a controlled surface treatment can help; sanding alone is not a universal fix. See Chemicals and Safety Data Sheets for chemical handling.
Supporting detail: Addendum 117 — Why a clean-looking bond can peel off.
Welding needs compatible thermoplastics and a designed joint
Welding needs compatible thermoplastics and a designed joint
Plastic welding heats the joint region so compatible thermoplastics can fuse. Cooling while the joint is held in position completes the connection. Cured thermosets do not remelt into a comparable fusion weld. Even two thermoplastics are not automatically weld-compatible.
Method
How the joint forms
Typical reason to choose it
Hot-gas welding
A controlled stream of heated gas softens the joint faces and compatible filler rod.
Accessible seams or repairs in weldable sheet.
Extrusion welding
A tool supplies molten compatible filler while the base surfaces are preheated.
Larger seams needing more deposited material than a small rod weld.
Hot-plate welding
A heated tool softens mating faces; the tool withdraws and the faces are pressed together.
Parts with accessible matching joint faces.
Hot-wire or resistance-element welding
Electrical resistance heats a wire or element at a designed joint region. Tool arrangements differ.
A localized joint designed for that heating arrangement; not the foam-cutting process.
Ultrasonic welding
A horn applies rapid mechanical vibration under force, generating heat at the joint.
Repeated assembly of compatible molded parts with a suitable joint geometry.
Heat sealing
Heat and pressure fuse compatible film surfaces or their sealant layers.
Bag and packaging seams; not every multilayer film seals to itself.
Supporting detail: Addendum 118 — Why heat alone does not guarantee a strong or sealed weld.
Hot-melt adhesive is not a fusion weld
Hot-melt adhesive is not a fusion weld
A hot-melt adhesive is applied molten and usually gains handling strength as it cools. The adhesive melts; the two parts do not have to melt together. Choose the formulation for both surfaces, the available assembly time and the service temperature. An ordinary hot-melt joint may soften or creep under sustained load in warmth. Fast setting is not the same as suitability for structural service.
Use mechanical joints when access and disassembly matter; Practice
Use mechanical joints when access and disassembly matter
A snap fit bends a feature during assembly so it catches behind another feature. It needs room to flex, rounded transitions and a resin that tolerates the required strain. Some snap fits release repeatedly; others are intentionally difficult to undo.
Thread-forming screws for plastics create their mating thread in a designed hole. Repeated removal can wear plastic threads. A threaded insert supplies a metal thread; a heat-set insert is installed by locally softening a thermoplastic around it. Hole size, surrounding wall thickness and installation conditions come from the insert supplier. A metal insert cannot rescue an undersized plastic wall.
Through-bolts and suitable washers can spread the clamping load. Excessive tightening can crack brittle plastic; sustained load can cause creep, a gradual change in shape, and reduce clamping force. Allow for movement and thermal expansion rather than trapping a sheet tightly at every hole.
Compare two cases: a clear permanent acrylic corner is a candidate for compatible solvent cement; a PP cover that must be removed regularly is a candidate for screws and a suitable thread arrangement. An adhesive that works on the first pair tells you little about the second.
Supporting detail: Addendum 119 — Insert dimensions come from the chosen insert system.
Read an FDM part as deposited roads and layers, then choose orientation, walls, infill and supports for its job.
A slicer turns a solid model into deposited layers
A slicer turns a solid model into deposited layers
Material extrusion is the standard family in which material is selectively dispensed through a nozzle. This page covers thermoplastic filament printing, often called fused filament fabrication (FFF). Fused deposition modeling (FDM) is a registered trademark of Stratasys for an implementation of this mechanism. The machine feeds filament into a heated nozzle and lays down narrow roads of softened material that bond as the part builds. Relative motion between the nozzle and build plate advances the layers; the nozzle itself does not have to move upward on every printer.
A slicer converts the model into tool paths, including walls, internal fill and any temporary supports. Preview those paths before printing. An enclosed shape on a CAD screen does not tell you how its underside will be supported.
A section through a partly printed part. Walls, infill and supports are different tool paths. The large lines are illustrative, not a scale drawing.
Supporting detail: Addendum 120 — Where additive manufacturing fits the five course categories.
Layer height, walls and infill do different jobs
Layer height, walls and infill do different jobs
Layer height is the vertical increment between layers. A smaller height makes steps on sloping surfaces finer and usually adds print time. It does not make all small horizontal features printable: nozzle size, road width and motion accuracy also matter.
Walls or perimeters trace the boundary. Top and bottom layers close the part. Infill is the pattern inside those boundaries. More infill generally adds material and time, but strength also depends on walls, orientation, bonding and load direction. A 20% infill setting does not mean the entire part uses 20% of its solid volume, because the walls and skins remain.
Simple layer-count example: for a 24 mm height with every layer 0.20 mm thick, 24 ÷ 0.20 = 120 layers. Real slicers may use a different first-layer height or variable layers. Halving layer height roughly doubles the layer count, not necessarily the total print time.
Orient for the load as well as for fewer supports; Checklist
Orient for the load as well as for fewer supports
FDM parts are anisotropic: properties depend on direction. A load that pulls layers apart can expose a weaker bond than a load carried along continuous deposited roads. Avoid placing the main tensile load across layer interfaces when an orientation can carry it along the layers. This is a design starting point, not a strength rating.
An overhang extends beyond the layer below. A short bridge spans between supported ends. A long unsupported underside may need temporary support material. Support contacts can leave marks, so keep them away from critical visible or mating surfaces where possible. There is no universal overhang angle that works for all materials and settings.
For a rectangular test bar pulled along its length, laying its length in the build plane usually gives a better starting orientation than standing it upright and pulling across stacked layers. A bracket may have several important load directions; choose a compromise or change the design, then test it.
Mark the main load direction and critical fit surfaces on the model.
Compare orientations for layer direction, build-plate contact and unsupported undersides.
Preview walls, infill and supports one layer at a time.
Check that support can actually be removed from each enclosed space.
Choose filament for service conditions and printer capability
Choose filament for service conditions and printer capability
Filament
Useful starting point
Check before choosing
PLA
Stiff models and easy-to-print prototypes
Heat exposure and impact requirements; a neat print is not automatically suitable for a warm enclosure.
PETG
Tougher functional parts with useful layer bonding
Stringing, moisture and support-removal behavior for the grade.
ABS / ASA
Applications needing greater heat resistance than ordinary PLA; ASA is often chosen for outdoor exposure
Warping control, equipment capability and processing requirements.
TPU
Flexible parts
Hardness grade and whether the feed system can handle flexible filament.
Nylon (polyamide)
Tough engineering parts
Moisture control, dimensional change and the required printing conditions.
PVA is used as a water-soluble support material in compatible multi-material systems; it is not a universal companion for every filament. Use the exact filament manufacturer's settings and the printer's limits. Consult Equipment Operating Procedure and Chemicals and Safety Data Sheets for process controls.
Supporting detail: Addendum 121 — Material guidance is grade-specific.
Estimate mass from deposited volume, not infill alone; Practice
Estimate mass from deposited volume, not infill alone
Mass = deposited volume × density. If a simplified model has 8 cm³ of solid walls and skins plus a 32 cm³ interior at 25% infill, its estimated deposited volume is 8 + (32 × 0.25) = 16 cm³. At an assumed density of 1.24 g/cm³, that is 19.84 g. Supports, brims and purge material add more.
This estimate treats infill percentage as a volume fraction of the interior. A slicer estimates the actual paths more closely. Time also includes travel, acceleration, heating and cooling constraints; volume alone does not give an exact printing duration.
Separate property changes from surface treatments, and match annealing, smoothing and coatings to the exact plastic.
Conditioning changes properties; finishing changes the surface
Conditioning changes properties; finishing changes the surface
Conditioning changes the material's state or properties: relieving internal stress, developing a thermoset cure, or controlling absorbed moisture. Finishing changes the surface for appearance, protection or function. A part can need both. Removing a support is Separating; sanding the resulting surface is Finishing.
Start with the resin, dimensions and service requirement. A glossy surface does not prove that a part is strong, properly cured or dimensionally correct.
Annealing relieves stress, but can change dimensions
Annealing relieves stress, but can change dimensions
Annealing uses a controlled heating, holding and cooling schedule. In acrylic it can reduce stress left by machining, bending or polishing. It is not a general instruction to heat near molding temperature. Use the resin supplier's schedule for the grade and thickness, including support of the part during treatment.
Printed PLA can also be annealed. Depending on its formulation and thermal history, heating can allow more crystalline order and improve heat resistance. Shrinkage, expansion in another direction or warping can spoil a fit. Measure before and after; do not assume every strength property improves.
Supporting detail: Addendum 122 — Stress relief and crystallinity are different changes.
Curing creates a network; drying removes moisture
Curing creates a network; drying removes moisture
A thermoset cure is a chemical reaction that builds links between polymer chains. Resin and hardener, heat or light may initiate the reaction, depending on the system. Correct proportions, time and temperature matter. A prescribed post-cure can develop properties further; an already cured thermoset will not simply remelt like a thermoplastic.
Drying moisture-sensitive filament addresses a different problem. Moisture can affect extrusion and part quality, but drying does not replace annealing or cure. Use a drying schedule intended for the material; excessive heat can deform filament or its spool.
Remove scratches progressively before adding gloss or paint
Remove scratches progressively before adding gloss or paint
Sanding replaces a coarse scratch pattern with progressively finer scratches. Start with the finest abrasive that will remove the defect efficiently. Within the same grit system, a larger number generally means a finer abrasive. A sequence such as P240 → P320 → P400 → P600 illustrates progression; it is not a required recipe for every plastic or coating.
Remove the previous scratch pattern before moving on and clean away abrasive residue between stages. Wet sanding with suitable waterproof abrasive can reduce loading and heat where the material and equipment permit it. Keep corners and fit surfaces from rounding over. Paint may need a controlled scuffed surface rather than a polished one; follow its preparation specification.
Tumbling can finish many parts together, but media and time affect edge rounding and small features. Buffing can improve gloss, but excessive heat or pressure can smear the surface. Check a representative sample rather than equating more polishing with a better part.
Flame and solvent smoothing are material-specific processes
Flame and solvent smoothing are material-specific processes
Flame polishing can smooth suitable acrylic edges by briefly softening the surface. It can also round edges and introduce stress. It is not a general treatment for clear plastics: polycarbonate is not interchangeable with acrylic, and a process must be validated for its exact grade. A clear edge is not necessarily an optically accurate or low-stress edge.
Solvent or vapor smoothing softens a compatible polymer's surface chemically. Acetone smoothing is associated with ABS and ASA; do not transfer that recipe to PLA or PETG. Smoothing can erase fine lettering, change dimensions and alter mechanical performance. It does not guarantee that weak layer bonds inside a print have been repaired.
Supporting detail: Addendum 124 — Why a clear surface can crack later.
Coatings need adhesion as well as the right appearance; Practice
Coatings need adhesion as well as the right appearance
For paint, remove contamination with a compatible cleaner, prepare the surface as specified and use a primer or adhesion promoter when the coating system calls for one. PE and PP often need special preparation or products because of low surface energy. A primer is not automatically compatible with every plastic. Trial the complete system, including cure, on a representative sample.
Dip coating deposits a liquid film as the part is withdrawn, followed by drying or curing as the formulation requires. Withdrawal rate and liquid properties affect thickness. Powder coating plastics requires a suitable way to attract or deposit the powder and a cure that the part can withstand; an insulating plastic does not become conductive merely because a grounding wire touches it.
Electroplating needs a conductive surface. Plastics therefore require preparation and a conductive layer before electroplating. Decorative options also include printing, decals, in-mold labels and dyes for receptive polymers. Choose them for the required abrasion, outdoor exposure and chemical resistance; decoration is not automatically protection.
Supporting detail: Addendum 125 — Powder coating needs a complete substrate and cure system.
Read tree structure, distinguish botanical groups, and choose species for their properties rather than their names.
Wood belongs to the Wood & Composites family
Wood belongs to the Wood & Composites family
Wood is a cellular material whose properties depend on direction. Long cells run mainly along the trunk; their arrangement helps explain why a board carries loads and splits differently along and across its grain.
In the material-family model, wood belongs to Wood & Composites. Engineered wood products combine veneers, strands, particles, or fibers with binders. These products are why composites share this family. See Engineered Wood Products for the product choices; the material families and manufacturing process categories are foundation topics.
Supporting detail: Addendum 126 — What makes the cell walls work together?.
Read a trunk from bark to heartwood
Read a trunk from bark to heartwood
Bark
Outer bark protects the tree. Inner bark carries sugars made by the leaves.
Cambium
A thin growing layer produces new wood toward the inside and new inner bark toward the outside.
Sapwood
The outer wood conducts water and contains living storage cells. Many of its conducting cells are already dead at maturity.
Heartwood
Older inner wood no longer conducts water. Deposits can change its color and decay resistance; heartwood is not automatically stronger or decay-resistant in every species.
Pith and rays
The pith marks the central stem tissue. Rays run radially across the wood and contribute to storage and transport across the trunk.
A growth ring records a growth cycle. In many temperate trees, earlywood develops earlier in the season and latewood later. Their cells differ in size and wall thickness, creating visible bands. Ring contrast varies by species; ring width alone is not a strength grade.
Hardwood and softwood describe the tree, not its hardness; Practice
Hardwood and softwood describe the tree, not its hardness
Hardwoods come from angiosperm trees; softwoods come from gymnosperm trees, commonly conifers. Leaf shedding is not the defining test: some hardwood trees are evergreen, and some conifers shed their needles.
Balsa is a very soft hardwood. Southern yellow pine is a softwood but can be much harder than balsa. Ask about the species and the property you need, rather than treating the category name as a test result.
Supporting detail: Addendum 127 — How the cell structure differs.
Connect grain orientation and moisture changes to board movement, defects, and design choices.
Follow the grain through the face, edge, and end
Follow the grain through the face, edge, and end
Grain describes the direction of wood cells. Figure is the visible pattern created by growth structure and the way the wood is cut. A board's broad surface is its face, its narrow long surface is its edge, and its cut end exposes end grain. Face and edge grain usually run generally along the board; they are not separate botanical structures.
Wood is generally stronger in tension along the grain than across it. A short projection with grain running across its narrow base can split off even if the rest of the part is thick. Knots divert nearby grain, and sloping or interlocked grain makes a board less predictable.
During machining, a cutting edge can lift fibers ahead of the cut and tear them out. Grain direction helps predict that result, but does not replace the machine's operating procedure. See Machine Hazards and Housekeeping and Equipment Operating Procedure for safety; wood separating and finishing are later topics.
Sawing orientation changes figure and movement
Sawing orientation changes figure and movement
Read the growth rings on the end of a board. Plain-sawn boards have rings more nearly parallel to the broad face and often show cathedral-shaped face figure. Quarter-sawn boards have rings more nearly perpendicular to the face; their width follows the radial direction more closely. Rift-sawn boards have an intermediate, oblique ring angle and commonly show straight face grain.
Quarter-sawn oak can expose conspicuous ray fleck. Rift-sawn oak is often selected for straight grain with less prominent fleck. Trade descriptions and angle boundaries vary, so inspect the end grain as well as the sales label. The diagram shows selected orientations, not a mill's complete cutting plan.
Moisture content uses oven-dry wood mass as its reference
Moisture content uses oven-dry wood mass as its reference
MC (%) = (wet mass − oven-dry mass) / oven-dry mass × 100. A sample weighing 150 g before drying and 100 g after oven drying has 50% MC. MC can exceed 100% because the reference is dry wood mass, not the original wet mass.
Water occupies cell cavities and is also held in cell walls. At the fiber saturation point, the walls are saturated while the cavities contain no free liquid water. Below this region, loss of water from the cell walls causes appreciable shrinkage. It is not one exact threshold for every species and condition.
Equilibrium moisture content (EMC) is the moisture content wood approaches in a particular surrounding humidity and temperature. A board can be dry today and absorb moisture later.
Green
Freshly cut or unseasoned; moisture varies greatly.
Air-dried
Dried by surrounding air; the achievable condition depends on the climate and storage.
Kiln-dried
Dried in a controlled chamber. This is a drying history, not a promise that the board will never move or that every kiln-dried product has the same MC.
Choose and acclimate material for its intended service environment. Use measurements to judge readiness; a fixed number of days cannot guarantee equilibrium for every thickness and starting condition.
Most movement is across the grain; Interactive
Most movement is across the grain
For normal straight-grained wood, shrinkage is usually greatest tangentially (along growth rings), smaller radially (across rings), and much smaller longitudinally (along the cells). Swelling reverses the moisture-loss trend. Actual amounts depend on species, grain orientation, and the moisture interval.
Do not apply a green-to-oven-dry shrinkage percentage directly to a small seasonal humidity change. A movement estimate needs a species-specific coefficient, board orientation, starting MC, and expected service MC. Reaction wood and juvenile wood can also depart from ordinary longitudinal behavior.
Estimate movement using starting dimension × coefficient × (final MC − starting MC), with both MC values within 6–14%. The attachment experiment below separates total width change from travel at a particular point.
Wood movement and attachment clearance — both moisture contents must be 6–14%.
Change = starting dimension × coefficient × (final MC − starting MC), with MC entered as a percentage (8, not 0.08). Negative means shrinkage; positive means swelling. Use the tangential coefficient CT for the width of a flat-sawn board or when the ring orientation is unknown, and the radial coefficient CR for the width of a quarter-sawn board or the thickness of a flat-sawn one.
Worked example: a flat-sawn white fir board 9.15 in wide at 8% MC, CT = 0.00245, reaching 11% MC: 9.15 × 0.00245 × (11 − 8) = 0.0672525 in wider, about 9.2173 in final width. The exact conversion starts at 232.41 mm and ends at about 234.118 mm. The Handbook's separately rounded 232 mm example ends at about 233.705 mm.
Predict: with one ideal fixed reference on a stationary support, does center fixing make the right edge move half as far, the same distance, or not at all, compared with fixing the left edge?
Same total width change, different edge travel: 8% to 11% MC
Fixed reference
Left edge travel
Right edge travel
Center
0.0336 in outward
0.0336 in outward
Left edge
0 (fixed)
0.0673 in outward
For uniform free strain, signed point displacement = (signed distance from the fixed reference ÷ installed width) × total width change. Center fixing halves the edge travel, not the total width change. A point closer to the reference travels less.
Compare available travel in each direction from the installed position. With 0.040 in outward travel, center-fixed edges remain inside the travel window, while the opposite edge of the left-edge-fixed board exceeds it. Drying reverses the movement: 8% to 6% MC gives 0.0224 in inward travel at each center-fixed edge, exceeding a separate 0.020 in inward allowance. Enough travel in one direction does not supply travel in the other.
Each estimate starts from the installed dimension and MC. Edge points are geometric tracking points, not a fastening layout. The support is stationary, with one ideal fixed reference and otherwise free uniform width change; friction, warp, strength, restraint stress and cracking are not calculated. Exceeding a travel window does not predict what the restrained board will do. A result within the window does not approve a joint.
Commercial lumber is rarely perfectly flat- or quarter-sawn, so this method can overestimate width shrinkage and underestimate thickness shrinkage. Board properties and ring angles vary. These are approximate estimates; no correction or safety factor is added. Outside 6–14% MC a different method applies.
Name the distortion before deciding what to do; Practice
Name the distortion before deciding what to do
Defects described by shape
Defect
What you see
Cup
Curvature across the width: the face resembles a shallow trough.
Bow
Curvature along the length, out of the broad face's plane.
Crook
Curvature along the length within the face's plane; the edge wanders sideways.
Twist
The corners no longer lie in a common plane.
Check / split
A separation along the grain. A check may be confined to a surface or end; a split extends through the piece.
Unequal shrinkage, uneven moisture, and irregular grain can contribute to warp. Drying stresses can open checks and splits. A stain is a color change, not automatically proof of lost strength; decay is a different concern.
Allow solid wood to change width; Checklist; Practice
Allow solid wood to change width
A solid-wood tabletop needs room to expand and contract across its grain. Suitable slotted attachments let it move relative to a supporting frame. A panel held in grooves needs clearance rather than rigid restraint across its full width. Details depend on the joint and expected movement.
Choose the fixed reference deliberately, then check travel from each attachment's installed position in both moisture directions. Slot length alone does not give clear travel: the fastener occupies space, and its starting position divides the available movement. The experiment above uses clear travel directly rather than inferring a hardware size.
Do not assume that a finish locks moisture out. It can slow moisture exchange, but does not eliminate seasonal movement. Plywood often solves a panel-stability problem better than simply making a solid board thicker.
Identify the grain direction and width that can move.
Check moisture against the intended service environment.
Inspect for warp, splits, and grain interruptions before laying out parts.
Check that attachments allow the expected movement.
Wood conditioning and fabricating cover drying and joint-making in more detail; Engineered Wood Products compares alternatives to solid lumber.
Separate sales size from measured size and calculate board footage using an explicit dimension convention.
Nominal size is a name; actual size is what fits; Practice
Nominal size is a name; actual size is what fits
A nominal lumber size identifies a product category. Dry, surfaced construction lumber sold as a 2 × 4 commonly measures 1-1/2 × 3-1/2 in in cross-section. Rough, green, specialty, and reclaimed stock can differ. Measure the piece when fit matters.
Drying and surfacing help explain the difference, but nominal names are not a universal subtraction rule. Do not assume that removing the same amount from every nominal size will give its actual dimensions.
Quarter thickness and surfacing describe different things
Quarter thickness and surfacing describe different things
Hardwood thickness is often named in quarter-inch increments before final surfacing: 4/4 means nominal one-inch stock and 8/4 means nominal two-inch stock. Neither guarantees that much finished thickness. Drying, flattening, and planing reduce the usable material.
Rough
Sawn surfaces remain; allow material for flattening and sizing.
S2S
Surfaced on two sides, normally the two broad faces. Do not assume the edges are straight or ready for a joint.
S4S
Surfaced on all four long sides: both faces and both edges. Ends are not included in the four.
Ask for the supplied thickness, width, length, moisture condition, grade, and surfacing. A thickness label alone is not a complete purchase specification.
A board foot is volume, not length
A board foot is volume, not length
One board foot (BF) is the volume of a piece 1 in × 12 in × 12 in: 144 cubic inches. With thickness and width in inches and length in feet:
If all three dimensions are in inches, divide by 144 instead. Multiply by the number of identical boards only after finding the volume of one.
Supporting detail: Addendum 130 — Why the mixed-unit formula divides by 12.
State the measuring convention. A physical-volume calculation uses actual dimensions. A sales tally may use nominal thickness or other trade rules and may round individual board measurements. Ask the seller; do not replace a quoted tally basis with finished dimensions without saying so. The examples here explicitly specify their basis and use unrounded arithmetic until the final answer.
Keep purchase tally and finished volume separate; Interactive; Practice
Keep purchase tally and finished volume separate
Suppose a seller specifies a tally using nominal 1 in thickness, measured 7 in width, and 9 ft length. The tally is 1 × 7 × 9 / 12 = 5.25 BF.
If that board finishes at 3/4 in thick with the same width and length, its physical volume is 0.75 × 7 × 9 / 12 = 3.9375 BF, or 3.94 BF to two decimals. These answers describe different quantities. The finished volume does not change the stated sales agreement.
A board tally is not a finished-parts yield. Allow for saw cuts, defects, flattening, trimming, and the layout of the parts. Appearance grades and structural grades answer different questions; an attractive board is not automatically suitable for a load-bearing member.
Build a list of boards below to compare the sales tally with actual volume, calculate cost, and estimate a material allowance.
Say which allowance you mean. This calculator treats the allowance as the share of the material you buy that will not end up in parts: BF to buy = needed BF ÷ (1 − allowance), so a 20% allowance means buying 1.25 times what you need. Many shop guides instead say “add 20%” to what you need (× 1.20), which is a different definition and buys less. Both are used; check which one a source or an instructor means before you compare numbers.
Compare veneers, strands, particles, fibers, and laminations to choose a wood product for its intended use.
Engineered wood changes the arrangement of the wood
Engineered wood changes the arrangement of the wood
Engineered products combine wood pieces with binders to make sheets or members that a single log could not supply as consistently. They belong to Wood & Composites: the wood supplies much of the structure, while the binder holds the selected arrangement together.
Engineering redistributes natural variability; it does not make all products equally strong, waterproof, or free of manufacturing defects. Select the product grade, thickness, orientation, exposure suitability, and fastening details for the job.
Plywood cross-laminates veneers to restrain movement
Plywood cross-laminates veneers to restrain movement
A veneer is a thin sheet of wood. In plywood, adjacent veneer layers commonly have grain at right angles. Each layer restrains the cross-grain movement of neighboring layers, making the panel more stable in its plane than a comparable wide solid-wood board.
Conventional plywood commonly has an odd number of plies in a balanced layup, with matching face-grain directions. Odd ply count is not a universal rule for every panel construction. The grain direction of the faces still matters to panel stiffness and strength; cross-lamination does not mean equal performance in every direction.
Plywood serves cabinet boxes, furniture panels, sheathing, and subfloors when the appropriate product is selected. Face appearance, core voids, bond durability, and panel rating vary. A decorative face veneer does not establish a structural rating.
Choose the sheet by its structure and service conditions; Practice
Choose the sheet by its structure and service conditions
Sheet goods: useful differences
Product
Structure and strengths
Limits and typical uses
OSB: oriented strand board
Wood strands bonded in layers with deliberate orientation. Structural grades provide useful panel strength and stiffness.
Common in wall, roof, and floor sheathing. Follow the marked strength direction and rating. Edges can swell when wetted; it is not a decorative substitute for every plywood face.
MDF: medium-density fiberboard
Fine wood fibers and resin produce a smooth surface without solid wood's visible grain pattern. Well suited to painted profiles.
Common in interior cabinet doors and trim. Heavy; ordinary grades swell with moisture. Edge fastening needs suitable hardware and preparation. Moisture-resistant grades are not automatically waterproof.
Particleboard
Small wood particles bonded into an economical, comparatively uniform panel; useful as a substrate under a decorative surface.
Common in interior furniture and laminate countertops. Ordinary grades are moisture-sensitive, edges are vulnerable, and fastener holding and shelf deflection need attention.
Painting a moisture-sensitive board does not turn it into a product rated for prolonged wet exposure. For wood dust and product-handling hazards, use Personal Protective Equipment and Chemicals and Safety Data Sheets rather than inferring precautions from a product's name.
Glulam bonds lumber laminations with their grain generally parallel to the member's length. It is used for structural beams and columns, including large members and curved forms.
LVL (laminated veneer lumber) bonds thin veneers with grain predominantly along the member. It is part of the structural composite lumber group and is commonly used for beams and headers over openings. It is not simply thick plywood: its layup favors lengthwise performance.
Use the manufacturer's design information for a particular structural product. Product names alone do not give allowable loads, spans, or permission to cut holes. Lamination and bending methods belong to the later wood forming and fabricating topics.
Match teeth to grain direction, leave room for chips, and include the saw's kerf in every cutting layout.
Teeth remove chips; the kerf is the wood they remove
Teeth remove chips; the kerf is the wood they remove
Sawing is a Separating process: each tooth removes a small chip, and successive teeth make a slot. The slot's width is the kerf. The space ahead of a tooth, called the gullet, carries chips out of the cut.
Many steel saw teeth have set: teeth bend slightly to alternating sides so the cut is wider than the blade body. Carbide-tipped circular blades commonly get that clearance from tips wider than the steel plate instead. Set and kerf are related, but they are not the same measurement.
A rip cut runs along the grain, usually to reduce a board's width. A crosscut runs across the grain, usually to reduce its length. Describe the cut relative to the grain, not just as a long or short cut.
Ripping teeth commonly have a flat, chisel-like cutting edge. Crosscut teeth commonly have alternating bevels that score and sever fibers at the sides of the cut. These are useful patterns, not universal rules: combination and specialty blades use other arrangements.
For circular blades of the same diameter, more teeth generally share the work into smaller bites at the same feed and rotational speed. That can improve a crosscut surface, but leaves less space for chips. Thick ripping cuts often benefit from fewer teeth and larger gullets. “Thicker wood needs more teeth” is not a general rule.
Band and reciprocating blades commonly specify teeth per inch (TPI). Tooth spacing must suit the thickness engaged in the cut. A coarse blade has more chip space; a finer blade can suit thinner stock and finer work. Blade width also matters on a band saw: a narrower blade can follow a tighter curve.
Hook angle describes the tooth face's lean relative to a radial line on a circular blade. More positive hook generally gives a more aggressive bite; low or negative hook is less aggressive. Machine type and the blade maker's intended application matter along with the desired finish. A ripping blade is not automatically appropriate on a miter saw.
See Feeds and Speeds for the relationship between tooth engagement, feed and cutting speed; metal-cutting settings do not transfer directly to wood.
Supporting detail: Addendum 134 — Blade terminology reference.
Count cuts before calculating strip yield; Practice
Count cuts before calculating strip yield
Start with the usable width after any edge preparation. Let W be usable board width, s the required strip width and k the kerf, all in the same units. These ideal layouts assume straight cuts, exact dimensions and no extra finishing allowance.
One cut per strip, leaving an offcut:used width = n(s + k). The maximum whole number is floor(W / (s + k)); “floor” means round down. For a 12 in board, 3 in strips and a 1/8 in kerf, floor(12 / 3.125) = 3 strips. Three cuts use 9.375 in, leaving 2.625 in. Four strips alone use 12 in, leaving no room for the cuts.
All final pieces use both original outside edges:W = ns + (n − 1)k for an exact partition. There are only n − 1 cuts between n pieces. If a layout leaves an extra offcut to separate, count that extra cut too. Draw the layout before choosing a formula.
Real layouts also allow for defects, edge trimming and later machining. Kerf is material removed, not useful strip width.
Start with the required cut, surface or hole, then match the machine and cutter to that result.
Choose the required geometry before choosing the machine; Checklist
Choose the required geometry before choosing the machine
A machine name does not describe a finished part. First state the result: a straight edge, a curved outline, a flat face, a hole or a round profile. Then consider the workpiece dimensions, accuracy, surface quality and available tooling. The machines below remove material and belong to Separating.
This is a selection guide, not an operating procedure. Machine-specific use belongs with Machine Hazards and Housekeeping and Equipment Operating Procedure. Grain and moisture are covered in the wood-as-a-material topic; the operation selected here depends on those properties.
Describe the surface or cut that must exist when the operation is complete.
Identify which existing face or edge can locate the workpiece.
Check machine capacity and whether the cutter can reach the feature.
Decide whether the cut is final size or leaves material for another operation.
Match the cut to a suitable starting machine; Practice
Match the cut to a suitable starting machine
Common choices; capacity and tooling can change the selection
Required result
Starting choice
What distinguishes it
Straight rip to width
Table saw
The fence locates a straight reference edge for a parallel cut.
Square crosscut or miter
Miter saw; table saw with crosscut sled or miter gauge
A miter is an angled cut across the width. Crosscut capacity limits the workpiece size.
Dado across a face
Router; table saw with compatible dado tooling
A dado is a flat-bottomed channel across the grain. Not every table saw accepts a dado set.
Curved outside outline
Band saw or jig saw
A band saw uses a continuous loop; a jig saw uses a short reciprocating blade.
Resaw into thinner boards
Band saw
The cut passes through the board's width to divide its thickness. Resaw capacity and blade selection matter.
Enclosed interior opening
Jig saw or scroll saw
A starter hole gives blade access without a cut from the outside edge. A scroll saw suits fine, intricate work; its blade can be threaded through the hole.
Router bits make profiles and channels; templates repeat shapes; Practice
Router bits make profiles and channels; templates repeat shapes
A router spins a router bit. Straight or spiral bits make channels and pockets; roundover and chamfer bits change an edge's profile. A bearing-guided bit or guide bushing can follow a template, which is a pattern used to reproduce an outline.
Routers may be handheld, mounted in a table or moved by a CNC machine. A shaper commonly carries profile cutters on a table-mounted spindle. Both shape wood, but their cutters and mounting systems are not interchangeable merely because the resulting profile looks similar.
Supporting detail: Addendum 135 — Why “router bit” is more useful than “end mill” here.
Spindle and faceplate turning put grain differently relative to the axis
Spindle and faceplate turning put grain differently relative to the axis
In typical spindle turning, grain runs mainly parallel to the rotation axis, as in a handle or table leg. In typical faceplate or bowl turning, grain runs mainly across the axis, as in a bowl blank. Faceplates and chucks are workholding methods; the name alone does not guarantee the grain orientation.
Turning removes material to make circular features. It does not bend the wood. Lathe Operations explains metal-lathe operations as a separate topic; wood turning has different tools and workholding practices.
Choose a drill bit for the hole's bottom, edge and diameter; Practice
Choose a drill bit for the hole's bottom, edge and diameter
Common wood-hole tools
Bit
Useful result
Limit to remember
Twist
General holes in a range of diameters
The usual point leaves a conical bottom in a blind hole.
Brad-point
Accurately located holes with clean entry edges in wood
The center point projects beyond the cutting lips.
Forstner
Clean-sided blind recess with a largely flat bottom
Most leave a small center-point mark; “flat” does not mean perfectly featureless.
Spade
Economical larger holes where finish is less critical
Usually leaves a center-point recess and a rougher result.
Hole saw
Large through-hole by cutting around a core
Leaves a plug; it does not clear a flat-bottomed pocket.
A drill press improves control of axis and depth; it does not make every bit suitable for every hole. Cutter geometry, workpiece support and setup still affect accuracy.
Establish one flat face and one square edge before making the opposite surfaces parallel and cutting to length.
A jointer establishes flatness; a planer establishes thickness
A jointer establishes flatness; a planer establishes thickness
Stock is the material a part starts from. Rough lumber may have uneven surfaces or warp. A jointer removes material to establish a flat face. With that face as a reference against a square fence, it can establish a straight edge at 90° to the face.
A thickness planer cuts the upper face relative to the face supported by its bed. With a flat reference face down, it makes the opposite face parallel and brings the board to thickness. Jointing both faces separately does not ensure they are parallel.
Supporting detail: Addendum 136 — Why a planer alone can preserve a bow.
Build reference surfaces in order: face, edge, thickness, width, length; Practice
Build reference surfaces in order: face, edge, thickness, width, length
This is the geometry sequence for preparing rough stock. It assumes enough material remains for the finished dimensions and that the stock fits the equipment. It is not a machine setup guide; use Equipment Operating Procedure and Machine Hazards and Housekeeping for operation.
Face-joint: establish a flat face and mark it as the reference.
Edge-joint: use the reference face to establish one straight edge square to it.
Plane: place the reference face against the planer bed and bring the opposite face parallel to it at the required thickness.
Rip: use the straight reference edge to locate the cut; make the opposite edge parallel at the required width.
Crosscut: establish a square end, then cut the other end to the required length.
Any preliminary breakdown into shorter, oversized blanks comes before final sizing. Leave allowance for the later cuts; an early rough crosscut is not the final crosscut in this sequence.
Try the order on a warped board: what each machine removes or copies; Interactive
Try the order on a warped board: what each machine removes or copies
Pick a board with cup, bow, twist or crook, as defined in Grain and Moisture Movement. Choose the next operation, predict the result, then check it with a straightedge, winding sticks and a square. Try the planer first, then the reference order, and compare. This is reference-surface geometry, not machine operation: see Jointer, Table Saw and Equipment Operating Procedure before using the machines.
Square a warped board. With JavaScript, this card is an interactive board you can machine one operation at a time: pick a cup, bow, twist or crook, predict what the jointer, planer or table saw will do, and check the result with a straightedge, winding sticks and a square. The figures below come from the same model.
The reference order on four warped boards
Each strip starts with a rough board (warp exaggerated to be visible) and applies face-joint, edge-joint, plane, rip and crosscut. Every later step uses a surface an earlier step made true.
Cup board, Joint face, Joint edge, Plane, Rip, Crosscut. Final: face A 0.0 mm out of flat, thickness 19.0 mm, edge A 0.0° off square.Bow board, Joint face, Joint edge, Plane, Rip, Crosscut. Final: face A 0.0 mm out of flat, thickness 19.0 mm, edge A 0.0° off square.Twist board, Joint face, Joint edge, Plane, Rip, Crosscut. Final: face A 0.0 mm out of flat, thickness 19.0 mm, edge A 0.0° off square.Crook board, Joint face, Joint edge, Plane, Rip, Crosscut. Final: face A 0.0 mm out of flat, thickness 19.0 mm, edge A 0.0° off square.
Planer first: thickness becomes even, the cup stays
Cup board, Plane, Joint face, Joint edge, Plane, Rip, Crosscut. Final: face A 0.0 mm out of flat, thickness 13.1–19.0 mm, edge A 0.0° off square.
Worked example (cupped board). The rough board’s face A is 6.2 mm out of flat. In the flexible-board example the planer presses it flat, cuts the top parallel to the pressed underside, and releases it: thickness becomes 19.0 mm, but face A is still 6.2 mm out of flat and face B now copies the cup (6.1 mm). Flattening face A afterwards leaves the board 13.1–19.0 mm thick, short of 19 mm. In the reference order the same board finishes at 19.0 × 110.0 × 520.0 mm with every check at zero within the model’s tolerance.
Cup board: what each step leaves (model mm). Planer: flexible board pressed flat by the rollers.
Order
After
Face A out of flat
Face B out of flat
Thickness
Edge A off square
Planer first
Rough board
6.2
6.1
36.0
6.9°
Planer: face A on the bed, plane to 19 mm
6.2
6.1
19.0
6.9°
Jointer: flatten face A
0.0
6.1
12.9–19.0
0.8°
Jointer: straighten edge A against the fence
0.0
6.1
12.9–19.0
0.0°
Planer: face A on the bed, plane to 19 mm
0.0
6.1
12.9–19.0
0.0°
Table saw: rip to 110 mm, edge A on the fence
0.0
3.4
13.1–19.0
0.0°
Crosscut: square both ends to 520 mm
0.0
3.4
13.1–19.0
0.0°
Reference order
Rough board
6.2
6.1
36.0
6.9°
Jointer: flatten face A
0.0
6.1
29.9–36.0
0.8°
Jointer: straighten edge A against the fence
0.0
6.0
29.9–36.0
0.0°
Planer: face A on the bed, plane to 19 mm
0.0
0.0
19.0
0.0°
Table saw: rip to 110 mm, edge A on the fence
0.0
0.0
19.0
0.0°
Crosscut: square both ends to 520 mm
0.0
0.0
19.0
0.0°
Edge before face. On the twisted board, jointing edge A first and face A second leaves edge A 1.9° out of square: where the twisted face touched the fence, its local angle set the edge angle. Flatten the face first, then use it against the fence.
What the model assumes
Geometry only, in millimetres. The board is a grid of points on its faces, edges and ends. Every cut is a plane or a surface built from straight lines, and a point outside the cut slides inward along the board until it reaches the cut, so no step can add material.
Jointer face: an ideal long, flat table. The board rests on its lowest points; the cut stays parallel to that resting plane and passes continue until the deepest hollow is reached. The pass count shown is an illustrative step, not a depth-of-cut recommendation.
Jointer edge and table-saw rip: the edge rests on its outermost points along a long table or fence, so the cut is straight along the length. The face touching the fence or table beside the cutter sets the edge angle, so a flat face gives a square edge and a twisted face does not.
Planer, flexible-board example: feed-roller pressure is assumed to bend the board until its overall curve lies on the bed; the top is cut parallel to that pressed underside and the warp returns on release. A stiffer board, or one shimmed on a flat sled, can instead keep its resting attitude; switch the planer to the rigid case to compare. Neither case is a rule for every board or planer.
Crosscut: each end is cut perpendicular to face A and edge A near that end, first end just to clean up, second end at the finished length.
Warp amounts (cup 6 mm, bow 14 mm, twist 12 mm, crook 16 mm on a 640 × 150 × 36 mm blank) are deliberately large illustrative values, not measured boards. Machine setup, feed, guards, snipe, tearout, kickback and moisture movement are outside this model.
Check geometry instead of counting machine passes; Checklist
Check geometry instead of counting machine passes
One pass is not proof that a surface is ready. The result of each stage is the reference for the next. Flatness means a surface lies in a plane; parallel faces maintain a constant separation; square surfaces meet at 90°.
Check the reference face for flatness with a straightedge and for twist with winding sticks, a matched pair of sighting bars.
Check the reference edge for straightness and squareness to the face.
Measure thickness at several positions after planing.
Check width, parallel edges, end squareness and final length.
Recheck dimensions and geometry if material removal releases stresses and the board moves.
Stop and reconsider the intended dimensions if flattening would make the board too thin or too narrow. No sequence can recover material already removed. Use How Saws Cut Wood to account for kerf in the width and length layout.
Materials and Manufacturing Processes/Wood
Bending and Laminating Wood
Compare steam bending, kerf bending, bent lamination and veneering by what changes shape and what holds the result.
Separate the bending step from the cutting and bonding steps
Separate the bending step from the cutting and bonding steps
Bending changes the shape of wood and belongs to Forming. A complete route can use several of the five process categories: cutting thin strips or kerfs is Separating; bonding layers is Fabricating. Veneering bonds a thin wood facing to a supporting base, so it is not automatically a bending operation.
Wood remains in the Wood & Composites material family. See Manufacturing Process Categories for the process model. Wood structure, moisture and engineered-wood products belong to the wood-as-a-material topic; here the question is how to obtain a shape.
What bends, and what retains the shape?
Route
What changes
Main trade-off
Steam bending
One piece is softened, bent over a form and restrained while it sets and dries.
Continuous grain can follow the curve, but stock quality and bend severity strongly affect success.
Kerf bending
Partial-depth slots let the remaining thin web bend; slots close on the inside.
Material removal reduces the intact section and leaves visible or concealed slots.
Bent lamination
Thin strips bend together over a form; cured adhesive holds the assembly.
Repeated curves are practical, but strip preparation, glue lines and springback matter.
Veneering
A thin facing bonds to a substrate, flat or curved.
The base supplies the shape and support; a face veneer alone is not a thick structural member.
Steam makes suitable wood more bendable; the form holds the curve
Steam makes suitable wood more bendable; the form holds the curve
Heat and moisture soften the wood's lignin-rich matrix, allowing the piece to deform more readily. The wood does not become a liquid. It is bent around a form, a shaped support, and held while it cools and dries. Clear, straight-grained white oak and ash are common candidates; species alone does not guarantee a successful bend.
The outside of a bend tends to stretch while the inside compresses. Too much stretching can split the outer fibers; too much compression can wrinkle the inner face. Grain deviations, drying history, moisture, thickness and bend radius all matter. A larger radius is a gentler bend. There is no single radius-to-thickness ratio that works for every piece.
Supporting detail: Addendum 137 — Why heat and moisture work together.
Bent lamination uses thin strips and adhesive to retain a curve; Practice
Bent lamination uses thin strips and adhesive to retain a curve
Thin strips bend more easily than one solid piece of the same total thickness. Bent lamination brings prepared strips together with adhesive over a form, then restrains them until the bond has developed as specified for that adhesive. The strips commonly run with their grain along the curve. Alternating grain direction is not a requirement of bent lamination.
Springback is the tendency for a bend to open when restraint is removed. It can occur in both steam-bent and laminated parts. Thinner laminations can reduce springback for a given total thickness and curve, but adhesive behavior, layer count and material also matter. A trial bend establishes any form compensation; there is no universal correction percentage.
Do not rank every “hot/wet” part above every “cold/dry” part in strength. Compare the actual grain path, remaining section, bond quality, loading and service conditions.
Kerf bending trades an intact section for easier curvature
Kerf bending trades an intact section for easier curvature
A series of partial-depth slots on the inside of the intended curve leaves a thin continuous web on the outside. The slots narrow as the piece bends. Slot depth and spacing, the remaining web and the desired radius determine how it deforms.
This method can suit curved coverings where the slotted side is concealed. It also removes load-carrying material. Filling or bonding the slots does not automatically restore the properties of the original uncut board. A backing or supporting structure may be part of the design; structural performance needs its own justification.
Veneer follows a prepared substrate; it does not replace it
Veneer follows a prepared substrate; it does not replace it
Veneer is a thin wood layer. A substrate is the base it is bonded to. Veneering puts a chosen grain appearance over that base and can cover a flat surface or an appropriate curved form. The substrate must have the intended shape and a sound, even bonding surface.
In book matching, adjacent veneer leaves are opened like book pages to make a mirrored pattern. In slip matching, leaves are placed beside one another in the same orientation for a repeated pattern. Neither arrangement is the same as alternating structural grain directions through a panel's thickness.
Unequal face and back construction can encourage a panel to warp. Veneer thickness, grain, adhesive and the balancing back layer belong in the layup design. Glue selection and detailed bonding methods belong to wood fabrication; engineered panels belong to the material topic.
Materials and Manufacturing Processes/Wood
Drying and Conditioning Wood
Compare drying methods, prepare stock for its service environment and calculate moisture content on an oven-dry basis.
Condition the wood for the environment where it will be used
Condition the wood for the environment where it will be used
Conditioning changes material properties. Drying removes moisture so wood can be prepared for a particular use. It does not permanently freeze the moisture content: dried wood still exchanges moisture with surrounding air. Review the wood-as-a-material topic for the underlying grain and movement behavior.
Not every use requires dried wood, but closely fitted indoor furniture generally does. Choose a target moisture content appropriate to the expected indoor temperature and humidity, then check the actual stock before final machining and assembly. A mill's drying target and a suitable in-service range are not necessarily identical. “Kiln-dried” describes a process; it is not a measurement of what the board contains today.
For indoor furniture in most of the United States, the USDA Wood Handbook recommends 8% average moisture content, with individual pieces at 6–10%, at installation. Regional guidance differs: the dry Southwest uses a 6% average (4–9% for individual pieces), while damp, warm coastal areas use an 11% average (8–13%). Use these as starting points and match the actual service environment. See Table 13–2 and Figure 13–1, page 13–5.
Supporting detail: Addendum 138 — Why the indoor moisture target depends on the building.
Air drying follows the weather; kiln drying controls the conditions
Air drying follows the weather; kiln drying controls the conditions
Two drying routes, often used in sequence
Route
How it works
What it can and cannot do
Air drying
Boards are stacked with spacers called stickers so air can reach their faces, with support and protection from direct rain.
Needs little purchased drying energy, but speed and final moisture depend on climate, species and thickness. Outdoor air drying may not reach the target for heated indoor furniture.
Kiln drying
A chamber controls temperature, humidity and airflow through a drying schedule.
Can reach lower, more controlled moisture levels. An unsuitable schedule can cause cracks, internal damage, distortion or residual stress.
Drying faster is not always drying better. The outside of a board may dry while the center remains wet. Suitable schedules manage this difference; elapsed time or a dry-feeling surface alone does not prove the board is ready.
Radio-frequency and microwave systems both use electromagnetic energy for dielectric heating, but the terms are not synonyms. Industrial systems control frequency, power and moisture removal; this is a process overview, not a household-microwave procedure.
Acclimate stock with airflow and repeated measurements; Checklist
Acclimate stock with airflow and repeated measurements
Acclimating means giving lumber time to approach the conditions in the intended working or service environment. There is no reliable fixed number of days for every board. Thickness, initial moisture, species and humidity all affect the time required.
Identify the intended service environment before choosing the moisture target.
Support boards flat with aligned stickers and space for airflow.
Check several boards and locations with a suitable moisture meter, using its species and temperature corrections where required.
Record repeat measurements and look for stability, not just one favorable reading.
Recheck after major material removal or a change of storage environment before final fitting.
Meter depth and measurement method matter: a surface reading can miss a wetter core. Keep stock in suitable conditions after drying. Joint design still needs to allow movement; see Wood Joinery and Fasteners.
Calculate moisture content using oven-dry mass as the denominator; Practice
Calculate moisture content using oven-dry mass as the denominator
On the oven-dry basis used for wood, MC (%) = (initial mass − oven-dry mass) / oven-dry mass × 100. Both masses must refer to the same sample and use the same units. “Initial” means the sample's mass before the moisture determination; it need not be freshly cut green wood.
For an illustrative sample with initial mass 230 g and oven-dry mass 200 g, the water removed is 230 − 200 = 30 g. Then MC = 30 / 200 × 100 = 15.0%.
Supporting detail: Addendum 139 — Why dividing by the initial mass answers a different question.
Distinguish temporary softening from permanent treatment
Distinguish temporary softening from permanent treatment
Heat and moisture in steaming can soften wood enough for bending. The softening is conditioning; changing the shape is Forming. The part must be restrained as it dries and sets, and some springback can occur. Species, grain quality, thickness and bend radius govern success; there is no universal bending radius for all wood.
Other treatments have specific purposes. Resin impregnation introduces resin into wood; impreg is resin-treated wood, while compreg also uses compression during manufacture. Increased dimensional stability or hardness can come with changes in other properties. Decorative color is not what defines compreg.
Pressure treatment is a delivery method, not a promise of every kind of resistance. Preservative treatment and fire-retardant treatment use different systems for different purposes. Neither the word “treated” nor “pressure-treated” alone establishes water exclusion, chemical resistance or suitability for an application. Use the treatment identification and product specification.
Wood–plastic composites made by combining wood particles or fibers with a polymer are a materials topic. Irradiation is not a universal requirement for making them. Finishing preparation is covered in Preparing and Finishing Wood; chemical handling belongs in Chemicals and Safety Data Sheets.
Materials and Manufacturing Processes/Wood
Wood Joinery and Fasteners
Choose joints and fasteners by the load, glue surfaces, assembly access and movement the connection must allow.
Choose the connection for the load and the grain direction
Choose the connection for the load and the grain direction
Joining separate parts is Fabricating. Start with the direction a load will push or pull, then choose the surfaces that carry it. A shelf needs support underneath; a frame must resist being pushed out of square. A joint that works well for one can be a poor choice for the other.
There is no single strongest joint. Wood species, dimensions, grain direction, fit, adhesive and loading all matter. A snug fit locates parts; it should not require enough force to split them. Most glued joinery is not an engineering interference fit.
Recognize the shoulders, sockets and mating surfaces
Recognize the shoulders, sockets and mating surfaces
Schematic exploded profiles, not cutting dimensions. The colored parts remain separate so the contact surfaces are visible.
Simple joints: geometry, use and limits
Joint
What it is and where it fits
Strength consideration
Butt
One unshaped end or edge meets another piece. Common in simple assemblies.
An end-to-face butt joint offers little resistance to opening without reinforcement. A long-grain edge-to-edge panel joint is a different, often effective glued connection.
Rabbet
A step cut along an edge or end receives another part; useful for cabinet backs and box corners.
The shoulder locates the part and carries load in one direction. Glue or fasteners resist separation.
Dado
A channel across the grain receives a shelf or divider.
The bottom and shoulders provide bearing and location. Too deep a cut weakens the remaining side panel.
Groove
A channel along the grain; useful for a panel edge or drawer bottom.
A groove can retain a panel while allowing it to move. Do not automatically glue a solid panel all around.
Lap
Parts overlap. In a half-lap, material is removed from each so the assembled faces are flush.
A fitted half-lap can give broad glue contact in frames; the cut also reduces each member's section.
Miter
Angled ends meet, often two 45° cuts for a 90° frame corner.
Hides end grain, but an unreinforced corner is vulnerable to opening. A spline, dowel or other reinforcement can help.
Add glue area, alignment or mechanical interlock where needed; Practice
Add glue area, alignment or mechanical interlock where needed
Reinforced and interlocking connections
Joint
Geometry and typical use
What to check
Mortise and tenon
A projecting tongue, the tenon, enters a matching socket, the mortise. Used in rails and legs.
Long-grain cheeks provide glue area; shoulders help resist racking (being pushed out of square). Keep enough wood around the socket.
Dowel
A separate round wooden pin enters matching holes in both parts; used in furniture frames and alignment.
Hole position, depth, dowel size and bonded embedment determine performance. A misaligned hole can prevent the shoulders from closing.
Biscuit
A thin oval insert enters matching slots; useful for aligning panel edges during assembly.
Do not assume an alignment biscuit gives the same reinforcement as a deep dowel or tenon.
Pocket screw
A screw driven through an angled recess joins one part to another; common in face frames.
Use the matching screw and jig setting. Clamp the parts against shifting; leave enough wood for the head and threads.
Box/finger
Alternating rectangular fingers mesh at a corner; common in boxes.
Many glue surfaces resist separation when properly bonded. Straight fingers do not lock against withdrawal as dovetails do. Here “finger” means a box corner, not an industrial end-splice.
Dovetail
Flared tails fit between matching pins; common at drawer corners.
The taper mechanically resists withdrawal in one direction. Thin pins, short grain or poor fit can still fail; orientation matters.
Give screw threads something to grip and the head something to pull
Give screw threads something to grip and the head something to pull
A pilot hole guides the screw and reduces splitting in the receiving piece. A clearance hole lets the screw pass freely through the near piece so its head can pull that piece against the far one. A countersink is a tapered seat for a matching flat head. These holes do different jobs.
Choose pilot diameter from the screw maker's guidance for the wood and screw. A hole that is too small risks splitting; one that is too large removes thread engagement. Threads gripping both pieces before the gap closes can hold the pieces apart.
Use wood screws intended for the application. Drywall screws are intended to attach gypsum board; their head geometry and often brittle behavior make them a poor default for furniture or load-bearing wood joints. Purpose-designed structural screws also differ from ordinary wood screws. Match corrosion protection to the environment and any wood treatment.
Nails are quick to install and many tolerate bending better than hardened screws, but withdrawal resistance depends on shank form and grain direction. Brads are slender finish nails with small heads: useful for light trim and positioning, not a substitute for a designed load-carrying joint.
For repeated disassembly, consider bolts with nuts, cross-dowels, threaded inserts or cam connectors. These knock-down fittings use reusable mating hardware. Capacity still depends on the wood bearing around the fitting, edge distance and the specific hardware, not merely on having metal threads.
Let a wide solid-wood part move across its grain; Checklist; Practice
Let a wide solid-wood part move across its grain
A tabletop fastened rigidly across its width can split or distort as moisture changes. Use a connection designed to permit movement, such as tabletop clips or correctly oriented slotted screw holes. Locate the part while leaving travel in the direction it needs; a screw tightened so hard that nothing can slide defeats the slot.
A frame-and-panel assembly can hold a solid panel in grooves without gluing the panel's perimeter. A manufactured panel may need a different detail: do not assume every wood product moves like solid wood.
Identify the grain direction and the expected load in each part.
Dry-fit the joint and confirm that shoulders close without splitting or distortion.
Check fastener access, edge distance and the intended disassembly method.
Confirm that the attachment leaves room for cross-grain movement.
Match the adhesive to the fit and exposure, then prepare the surfaces and hold the assembly through the specified cure.
Build the joint around sound, closely fitted glue surfaces
Build the joint around sound, closely fitted glue surfaces
Glue needs clean, sound surfaces and a joint designed for the load. For ordinary PVA wood glue, prepare mating surfaces that contact closely without being forced into shape. Paint, finish, dust and old adhesive can prevent a reliable bond.
Long grain is a surface running along the wood fibers; end grain exposes their cut ends. A long-grain edge joint can provide broad, continuous contact. End grain can absorb liquid adhesive rapidly and leave too little at the interface; a plain end-grain butt joint also has limited bonded area and unfavorable loading. End grain can bond, but adding more glue does not automatically make that joint equivalent to a fitted tenon or lap.
Fiber direction and adhesive coverage both matter. The diagram is a simplified comparison, not a strength ranking of every possible joint.
Supporting detail: Addendum 140 — What “stronger than the wood” actually demonstrates.
Choose the adhesive for fit, exposure and repair needs; Practice
Choose the adhesive for fit, exposure and repair needs
Adhesive families: starting points, not product specifications
Adhesive
Useful for
Fit and exposure limits
PVA, including yellow wood glue
Closely fitted wood-to-wood joints in furniture and cabinetry.
Not a structural gap filler. Water resistance varies from interior formulations to products rated for specified wet exposure; color does not establish the rating.
Polyurethane wood glue
Moisture-curing bonds where the product lists the materials and exposure.
Expanding foam is not sound replacement wood in a loose joint. Clamp to control expansion. Do not transfer one product's water rating to the whole family.
Epoxy
Some repairs, mixed-material joints and gaps using a suitable resin, hardener and structural filler.
Mix the specified ratio. A fairing filler meant for easy sanding is not necessarily a structural adhesive filler. Water and temperature performance depend on the system and cure.
Hide glue
Traditional furniture and repairs where future disassembly matters.
Hot hide glue and liquid hide glue have different working times. Close fit is important; heat and moisture can weaken the bond as well as aid repair.
CA (cyanoacrylate)
Small parts, small repairs and rapid positioning.
Thin and gel grades suit different gaps. Short working time and often brittle bonds limit its use for large assemblies or impact loads; check the exact grade.
Construction adhesive
Building assemblies and dissimilar materials listed on the cartridge.
A broad product category, not one chemistry. Bead size, gap limits, compatibility, support time and water resistance are product-specific. It is not automatically suitable for precision furniture joints.
Hot-melt adhesive sets quickly as it cools and is useful for temporary positioning or packaging. Do not assume that quick set gives a durable furniture bond.
Open time is the period after spreading adhesive during which the surfaces may remain apart. Assembly time includes getting the joint together and into clamps; manufacturers may define open and total assembly time separately. Clamp time is how long the assembly must be restrained. Full cure is when the adhesive reaches its specified cured properties under the stated conditions.
These are not interchangeable. A joint that can leave the clamps may still be unready for machining or service loads. Check the exact product's instructions for temperature, moisture, timing and exposure. A fixed “30 minutes for all yellow glue” rule is unreliable.
PVA requires time for water loss and bond development; one-part polyurethane depends on moisture; epoxy working time depends on its resin/hardener system and temperature. Hot hide glue has a short working window as it cools. CA can fix parts very quickly, so trial assembly is especially important. Construction adhesive often needs continued support after initial grab.
Supporting detail: Addendum 141 — Where to find product-specific instructions.
Use clamps to close the joint, not to repair a bad fit; Checklist
Use clamps to close the joint, not to repair a bad fit
Apply enough pressure to seat the surfaces and maintain alignment, following the adhesive instructions. Excess force can dent the wood, bow a panel or force out too much adhesive. A gap that closes only under severe force is a fitting problem.
Bar and pipe clamps span large assemblies; C-clamps apply local pressure; spring clamps suit light holding jobs. Cauls are straight blocks or beams used to distribute pressure and help keep faces aligned. Protect visible surfaces and prevent the cauls from becoming glued to the assembly.
A small, reasonably even bead of squeeze-out can indicate coverage, but it does not prove the entire bond is sound. A dry spot may be hidden inside. Excess glue can seal the surrounding pores and leave a pale patch under stain. Remove it by a method appropriate to the adhesive and surface; do not smear it into a wider area. Inspect again before finishing.
Dry-fit all parts and place the clamps and cauls within reach.
Read the product's assembly, clamp and cure requirements.
Spread adhesive as directed, assemble within its working time and close the joint.
Check alignment, flatness and diagonals where a rectangular assembly must be square.
Inspect squeeze-out and clean surrounding surfaces appropriately.
Keep the joint restrained and unloaded for the specified intervals.
Prepare a uniform surface, distinguish color from protection and choose a finish for appearance, wear and repair.
Remove each grit's scratches before moving to a finer abrasive; Practice
Remove each grit's scratches before moving to a finer abrasive
Start with the least coarse abrasive that removes the actual defects efficiently. Higher grit numbers generally mean finer particles within the same grading system. A possible bare-wood sequence is 80 → 120 → 150 → 180, but sound, smooth stock may start later. Stop at the grit recommended for the chosen stain or finish; 220 is not a universal destination.
Each step removes the previous step's scratches. Jumping straight from a coarse grit to a very fine grit leaves deep scratches that the fine abrasive removes slowly. Inspect under light across the surface, remove dust between steps and replace clogged abrasive. Finish hand sanding along the grain where practical; machine sanding also requires control of pressure and motion.
Do not use prolonged sanding to hide a poorly fitted joint. It can round edges, dish a surface or sand through a thin veneer. Remove glue residue before coloring; a smooth glue patch may still reject stain.
Treat raised fibers, defects and open pores as different problems
Treat raised fibers, defects and open pores as different problems
Water can raise loose fibers and make a previously smooth surface feel rough. When the finishing system calls for it, lightly dampen bare wood, let it dry, then sand the raised fibers lightly with the final preparation grit. This grain raising step reduces roughness under later water-based coats. Heavy sanding can expose fresh fibers and restart the problem.
Preparation products do different jobs
Product or step
Purpose
Check before using it
Defect filler or putty
Fill a small hole or surface defect.
Some products harden and sand; others remain softer and belong after finishing. Color and stain uptake may differ from wood. Sawdust mixed with glue does not reliably stain like the surrounding wood.
Grain/pore filler
Fill open pores for a level surface, especially under a glossy film.
Choose compatible filler and test whether it goes before or after coloring. Filling pores is optional when visible texture is wanted.
Pre-stain conditioner
Reduce uneven stain absorption on blotch-prone wood.
It can lighten or alter the result; it does not guarantee uniform color. Follow the compatible stain system and its timing.
Sanding sealer
Provide a readily sanded initial coating in a compatible system.
It is not required under every finish. The wrong sealer can reduce adhesion or durability.
Bleaching changes wood color chemically; it is not the same as staining. Product chemistry determines the sequence, drying and any required follow-up preparation. Do not use a universal “bleach immediately after final sanding” rule. Consult Chemicals and Safety Data Sheets and Personal Protective Equipment for chemical handling and protection.
Use stain or dye for color, then decide what protection is needed
Use stain or dye for color, then decide what protection is needed
Pigment stain contains fine solid particles that lodge in pores and surface texture. It can emphasize grain and partly obscure it. Dye dissolves in its carrier and can give transparent color; it can still absorb unevenly. Some commercial stains contain both pigment and dye. A gel stain has a thicker consistency and often gives more surface color control on vertical or blotch-prone work.
Coloring alone is not normally the protective finish. Follow the product's application and wipe-off interval: leaving ordinary wiping stain on indefinitely is not a dependable way to make it darker. Test the complete stain-and-topcoat sequence because the clear coat changes the appearance too.
Compare a low-build oil finish with a protective surface film
Compare a low-build oil finish with a protective surface film
Idealized finish families. Real products overlap: an oil–varnish blend can build some film, and film finishes also penetrate surface pores.
Choose by the service conditions and exact formulation
Finish
Appearance and use
Tradeoff
Drying oils, such as linseed or tung oil
Usually applied thinly for a low-build, grain-enhancing surface.
Easy to renew in many applications, but thin oil treatments usually give less wear and spill protection than a suitable film. Drying oil cures; mineral oil does not cure the same way.
Shellac
A resin coating available in different colors; useful for furniture and compatible sealing applications.
Repairable, but vulnerable to alcohol and heat. Check wax content and compatibility before applying another finish over it.
Lacquer
A family of film coatings often used for furniture and sprayed production work.
Many dry quickly; conventional solvent lacquers can be repaired by re-dissolving the surface. Catalyzed products cure differently and are not equally repairable.
Varnish/polyurethane
Film-forming resin systems often selected for wear and spill resistance.
Repair and recoating need preparation. Modern varnishes commonly use synthetic resins. Exterior protection requires an exterior formulation; “varnish” alone does not promise UV resistance.
Water-based clear coatings
Often chosen to retain a lighter color; may use acrylic, polyurethane or blends.
Water-based identifies the carrier, not a separate guarantee of durability. Grain raising and intercoat adhesion need attention. Color change depends on both coating and wood.
Wax or paint
Wax offers a low-build, easily refreshed surface. Paint supplies opaque color in a film.
Wax alone offers limited protection. Paint hides grain and needs compatible preparation, primer where specified, and a suitable topcoat system.
Names such as “Danish oil” or “tung oil finish” may describe blends rather than pure oil. Read the product description. No ordinary finish makes wood completely moisture-proof or eliminates the movement allowance in Wood Joinery and Fasteners.
Match application method and recoat timing to the product
Match application method and recoat timing to the product
Brushing suits many small assemblies; use a compatible brush and maintain a wet edge without repeatedly working a coating that has begun to set. Wiping gives thin, controllable applications when the product is designed for it. Spraying can coat complex shapes evenly but needs suitable equipment, setup and the safety controls in Chemicals and Safety Data Sheets.
Roller coating suits suitable products on broad surfaces. Industrial curtain coating passes panels through a flowing sheet of finish; dip coating immerses parts. Electrostatic spraying requires a suitable coating and process setup to attract charged droplets to the work; ordinary dry wood does not automatically provide that setup.
Build the recommended coats and observe the recoat window. Sand between coats only as directed, with the specified abrasive and after sufficient drying. A fixed 320-grit rule does not fit every coating. Dry-to-touch is not full cure; allow the specified cure before service or final rubbing to adjust sheen.
Choose with a sample board and the expected wear in mind; Checklist; Practice
Choose with a sample board and the expected wear in mind
A frequently wiped surface needs a finish rated for that use; a lightly handled decorative object may favor appearance and easy renewal. Compare resistance to water, cleaning products, abrasion and heat, then consider color, sheen, repairability and available application equipment. A durable film is useful only if it adheres and cures properly.
Prepare a sample of the same wood with the intended sanding sequence.
Test any conditioner, filler and colorant together with the topcoat.
Record products, grits, application method and drying intervals.
Inspect color, texture and adhesion after the specified cure.
Choose the complete system before coating the finished assembly.
Supporting detail: Addendum 142 — Further product-specific preparation guidance.
How bonding, grains and alloy condition affect the properties used to choose a metal.
Metal selection starts with the job the part must do
Metal selection starts with the job the part must do
A metal can carry a load, conduct current, transfer heat or resist wear. Those are different jobs. Start with the required behavior, then compare a particular alloy in a particular condition. An alloy combines a base metal with other elements to change its behavior.
Metallic bonding helps explain conduction and forming
Metallic bonding helps explain conduction and forming
In a metal, some electrons are shared throughout the structure rather than tied to one bond between two atoms. Their mobility helps metals conduct electricity and heat. Metallic bonding can remain intact while atoms rearrange during permanent deformation, which helps explain why many metals can be rolled or drawn.
Most engineering metals contain many tiny crystals called grains. Atoms have an ordered arrangement inside each grain; adjacent grains have different orientations. Grain size, alloy chemistry and processing history all influence properties.
Supporting detail: Addendum 143 — Why two pieces of the same alloy can behave differently.
Strength, hardness, ductility and toughness answer different questions
Strength, hardness, ductility and toughness answer different questions
Mechanical properties used when comparing metals
Property
Question it answers
Selection example
Strength
How much stress can the material withstand? Yield strength concerns the start of permanent deformation; tensile strength concerns the maximum stress in a tensile test.
A loaded bracket must resist permanent bending.
Hardness
How strongly does the surface resist local indentation?
A wear surface may need hardness, but hardness alone does not predict every kind of wear.
Ductility
How much permanent deformation can occur before fracture?
A formed part needs enough ductility to survive bending.
Toughness
How much energy can the material absorb before fracture?
A part struck repeatedly needs resistance to fracture, not simply a hard surface.
Strong does not mean stiff. Stiffness describes elastic deflection. Hardening a steel can raise its strength substantially without a comparable change in its elastic stiffness. Geometry also affects how far a part bends.
Pull a tensile specimen: strength, stiffness, ductility and toughness on one curve; Interactive
Pull a tensile specimen: strength, stiffness, ductility and toughness on one curve
A tension test pulls a specimen of known size until it breaks and records force against stretch. Dividing by the original area and gauge length turns that record into an engineering stress–strain curve, and one curve answers four different questions: how stiff, how strong, how far it stretches and how much energy it absorbs.
The curves below are synthetic teaching curves, shaped to resemble common behaviour. Read the method from them, not the numbers for any real alloy.
Tensile test: one curve, four different properties. This fallback shows the same synthetic curves and calculations as the live lab.
A round specimen with a chosen gauge length L0 = 50 mm and diameter 12.5 mm (original area A0 = 122.7 mm²) is pulled by a moving crosshead. Engineering stress σ = F/A0 (N/mm² = MPa). Engineering strain ε = ΔL/L0 (mm/mm, shown here in %). Both use the original dimensions, so engineering stress falls after the neck forms even though the force is concentrated on a shrinking section.
Synthetic specimen A (ductile, low-carbon-steel-like; illustrative, not a grade). Shaded: area under the curve to fracture. Dashed red line: unloading from 10% strain.
Yield strength (0.2% offset): draw a line with slope E starting at 0.2% strain; where it meets the curve, σy ≈ 250 MPa (at 0.325% strain). Specimen A then stretches along a level yield plateau (stress constant at 250 MPa up to 1.5% strain) before strain hardening makes the curve rise again.
Ultimate tensile strength (UTS): the highest engineering stress, 400 MPa at 20% strain. A neck begins to form after this peak.
Toughness (tensile): the area under the curve to fracture, ∫σ dε ≈ 107 MJ/m³ (1 MPa × 1 = 1 MJ/m³ = 1 J/cm³) of work per original volume. For this gauge volume that is about 659 J. This is not fracture toughness KIC, which is measured on a cracked specimen.
Worked example: unloading leaves permanent set. Stop at ε = 10.0%, where σ = 371 MPa. Removing the load follows a straight line parallel to the elastic slope, so the elastic part σ/E = 371/200 000 = 0.185% springs back. Permanent set = 10.0% − 0.185% = 9.815%, or 4.91 mm on the 50 mm gauge length. Below the yield point the same rule gives zero set: at 0.1% strain and 200 MPa, 0.1% − 200/200 000 = 0.
The same specimen at four moments. Length to scale; the neck shape is illustrative only.
Before loading. Gauge length 50.0 mm (original L₀ = 50.0 mm). Drawn to scale.
At the peak (UTS): stretched uniformly, no neck yet. Gauge length 60.0 mm (original L₀ = 50.0 mm). Drawn to scale.
After the peak: deformation concentrates in a neck. Gauge length 63.5 mm (original L₀ = 50.0 mm). Drawn to scale; neck shape illustrative.
Fractured; pieces fitted together. Broken pieces fitted back together: gauge length 64.9 mm (original L₀ = 50.0 mm). Drawn to scale; neck shape illustrative.
Compare the four synthetic specimens. Each ranks differently on each property: the stiffest is not always the strongest, and the most ductile is not the toughest.
All four synthetic curves on one set of axes; the right panel magnifies the first 1% of strain, where the elastic slopes differ.
A Ductile, low-carbon-steel-like
B Aluminium-alloy-like
C Brittle, gray-iron-like
D Polymer-like (cold drawing)
Read from the four synthetic curves (illustrative; not material data)
Specimen
Stiffness E (GPa)
0.2% offset yield (MPa)
UTS (MPa)
Elongation after fracture (%)
Area to fracture (MJ/m³)
A: Ductile, low-carbon-steel-like
200
250
400
29.8
107
B: Aluminium-alloy-like
70
266
310
12.6
38
C: Brittle, gray-iron-like
100
none: fractures first
215
0.1
0.42
D: Polymer-like (cold drawing)
2.5
36.7
48.0
53.2
21
Specimen C fractures before the 0.2% offset line reaches its curve, so it has no offset yield strength in this test: the value is undefined, not zero. Specimen D (polymer-like) reaches its peak stress early and then draws a neck along the specimen; its offset value is shown only for comparison.
Model, assumptions and sources
The four curves are synthetic: piecewise cubic curves through chosen points, shaped to resemble common behaviour. They are not measurements, grades, certification values or design allowables. Real results depend on composition, processing, specimen geometry, test speed and temperature, none of which are modelled.
Unloading and reloading follow a straight line with the initial elastic slope E (an ideal elastic approximation, no hysteresis). The load never goes below zero: once the unload line reaches zero load the specimen is slack. Permanent set = ε − σ/E, never negative. Elongation after fracture uses the same rule at the fracture point.
The specimen length is drawn to scale. Its thinning before the peak keeps volume constant; the neck and the fracture are drawn only to show where deformation concentrates, not calculated from a necking or fracture law. True stress, strain rate, temperature and hardness are outside this lab.
The area under the curve is work per original volume in this tension test (MPa = MJ/m³). Impact and fracture-toughness tests measure related but different behaviour.
Sources: ASTM E8/E8M, Standard Test Methods for Tension Testing of Metallic Materials (the test method and its definitions; consult the current edition). W. D. Callister Jr. and D. G. Rethwisch, Materials Science and Engineering: An Introduction, chapter “Mechanical Properties of Metals” (engineering stress and strain, modulus, 0.2% offset yield, tensile strength and necking, ductility, toughness as area under the curve, elastic recovery on unloading).
Density, conductivity and corrosion can decide the choice
Density, conductivity and corrosion can decide the choice
Density is mass per volume. Compare equal volumes when comparing densities; a large aluminum part can still weigh more than a small steel part. Use Geometry, Mass, and Force and Dimensional Analysis for mass, weight and unit calculations.
Conductivity describes how readily heat or current travels through a material. Metals vary widely: choosing a good conductor is different from choosing a high-strength alloy.
Corrosion resistance depends on the metal and its surroundings. Stainless steel and aluminum can corrode. Water, salts, trapped moisture and contact with other metals can change performance. A protective surface film helps only while the environment allows it to remain effective.
Supporting detail: Addendum 144 — Why connecting two different metals can change corrosion.
Ferrous means iron-based; a magnet does not identify the grade; Practice
Ferrous means iron-based; a magnet does not identify the grade
Ferrous metals have iron as their base: steels and cast irons belong here. Nonferrous metals have another base, such as aluminum, copper or titanium. Nonferrous does not mean that no trace of iron can be present.
Magnetic response is a clue, not a material certificate. Some stainless steels are weakly magnetic or effectively nonmagnetic in certain conditions. Appearance and a magnet cannot establish an alloy, its temper or its strength.
Carbon, alloy, stainless and tool steels, plus the difference between a steel family and a complete material specification.
Steel is iron-based, with carbon and other elements controlling behavior
Steel is iron-based, with carbon and other elements controlling behavior
Steel contains iron and carbon, often with additional alloying elements. Both composition and processing matter. The same grade can arrive softened for machining or hardened for service.
Use four practical groups: carbon steel, alloy steel, stainless steel and tool steel. These are useful buying categories, not four mutually exclusive chemical definitions: stainless and tool steels also contain alloying elements.
The four steel groups are a selection map. They do not replace grade and condition.
Carbon steel spans easy forming through hardenable cutting edges
Carbon steel spans easy forming through hardenable cutting edges
Relative carbon levels; actual grade limits come from the specification
Group
Typical behavior
Typical uses
Low carbon
Generally readily formed and welded; limited response to ordinary through-hardening.
Sheet parts, brackets and general fabrication.
Medium carbon
More potential for heat-treated strength; forming and welding require more consideration.
Shafts, axles and machinery parts.
High carbon
Can develop high hardness after suitable treatment; less forgiving of forming and impact.
Springs and some cutting tools.
These are trends, not a strength ranking of every item on a shelf. Compare the delivery condition and required properties before substituting one grade for another.
Alloy, stainless and tool steels solve different service problems
Alloy, stainless and tool steels solve different service problems
Choose a family, then qualify a specific grade
Family
Composition idea and purpose
Uses and limits
Alloy steel
Intentional additions such as chromium, nickel or molybdenum adjust properties and heat-treatment response.
Loaded shafts and gears. Alloy steel is not automatically corrosion resistant.
Stainless steel
Chromium supports a protective surface film; other elements adjust performance.
Food equipment, fittings and exposed hardware. Grade, cleaning and environment still matter.
Tool steel
Carbon and alloy additions support hardness, wear resistance or performance at elevated temperature.
Dies, punches and cutting tools. Heat treatment must balance wear resistance against chipping.
Use Heat Treating Metals to distinguish hardening from tempering. Hardenability means the ability to harden to depth under given cooling conditions; it is not the same as a measured surface hardness.
Grade labels identify a material; they are not a heat-treatment recipe
Grade labels identify a material; they are not a heat-treatment recipe
Common labels include 1018 and 1045 for carbon steels, 4140 for alloy steel, 304 and 316 for stainless steels, and O1, A2 and D2 for tool steels. Different designation systems have different rules. Do not apply a four-digit carbon-steel decoding rule to stainless or tool-steel labels.
On an order, identify the governing material specification, grade, delivery condition, form and dimensions. A short grade name alone does not specify strength, hardness, surface finish or dimensional tolerance. Ask for the required certification when traceability matters.
Use the current governing specification or the producer's grade sheet for composition limits and treatment requirements.
Decode carbon and alloy steel numbers; read stainless and tool grades separately
Decode carbon and alloy steel numbers; read stainless and tool grades separately
In the common AISI/SAE four-digit carbon and alloy steel system, the first two digits identify the steel series: 10 is plain carbon steel and 41 is chromium-molybdenum steel. The last two digits give nominal carbon content in hundredths of a percent.
Reading the series and nominal carbon content
Grade
Series
Nominal carbon
1018
10: plain carbon
18 → 0.18%
1045
10: plain carbon
45 → 0.45%
4140
41: chromium-molybdenum
40 → 0.40%
304 and 316 stainless: their chemistries are similar, but 316 has an added alloying element, molybdenum. This improves resistance to chloride exposure and urban or industrial pollution compared with 304.
Tool-steel groups: O1 is an oil-hardening grade, A2 is an air-hardening grade, and D2 is a high-carbon, high-chromium grade. These labels describe different tool-steel groups; they are not carbon-percentage codes.
Supporting detail: Addendum 145 — Sources and quoted designation meanings.
Cast iron is a separate iron-based material, and it can be machined
Cast iron is a separate iron-based material, and it can be machined
Cast irons generally contain more carbon than steels. Their properties depend strongly on how carbon appears in the structure. Gray iron contains graphite flakes and is useful for machine bases and housings where vibration damping matters; it is relatively brittle in tension. Ductile iron contains graphite nodules and can provide much greater ductility.
Casting creates the initial shape. Machining can then finish bores, faces and other accurate features. “Cast” and “machined” are not competing material identities. White cast iron contains substantial hard carbide and behaves differently from graphite-containing irons.
Watch the steel-family series at its original publisher; Practice
Watch the steel-family series at its original publisher
Aluminum, copper alloys, titanium, zinc and magnesium as choices for weight, conductivity, corrosion and manufacturing needs.
Choose the useful property, then check the tradeoff
Choose the useful property, then check the tradeoff
Nonferrous metals have a base other than iron. They are not all lightweight, corrosion-proof or easy to machine. A useful first comparison names both the benefit and the constraint.
Starting points for material selection, not design allowables
Metal
Why choose it?
Typical use and tradeoff
Aluminum
Low density, useful corrosion resistance and ready availability in extruded shapes.
Frames and housings. Lower elastic stiffness than steel; alloy and temper strongly affect strength.
Copper
High electrical and thermal conductivity.
Conductors and heat-transfer parts. Relatively high density and cost; alloying usually reduces conductivity.
Titanium
Useful strength relative to weight and corrosion resistance.
Aerospace and chemical-service parts. Material and processing costs can outweigh the weight saving.
Zinc
Useful casting behavior and ability to protect steel as a coating.
Die-cast hardware and galvanized products. Temperature and load requirements limit use.
Magnesium
Very low density among structural metals.
Light housings. Corrosion protection and suitable manufacturing procedures matter.
Aluminum needs both an alloy label and a condition
Aluminum needs both an alloy label and a condition
Aluminum is sold in many alloys and conditions. Wrought products are shaped by processes such as rolling or extrusion. Their familiar four-digit labels are organized into series, including 1xxx through 7xxx. A series is a family, not a hardness scale: a higher first digit does not guarantee a harder or better part.
6061 and 7075 are common alloy labels to look for in supplier literature. Compare data for the actual product form and temper rather than treating either number as a complete specification. Cast aluminum uses a different designation system; do not transfer wrought-number rules to cast products.
A suffix such as -O or -T6 identifies a condition as part of an alloy-temper designation. It must stay attached to the alloy on an order. See Heat Treating Metals for why processing history matters.
-O: “Annealed” — “Thermally treated to obtain the lowest strength temper.”
-T6: “Solution heat-treated and artificially aged.”
Use the governing product specification for an actual purchase.
Aluminum series 1xxx–7xxx identify purity or the main alloying additions
Aluminum series 1xxx–7xxx identify purity or the main alloying additions
Wrought aluminum series
Series
Principal alloying element or purity
1xxx
Commercially pure aluminum: at least 99% aluminum.
2xxx
Copper.
3xxx
Manganese.
4xxx
Silicon.
5xxx
Magnesium.
6xxx
Magnesium and silicon.
7xxx
Zinc.
Supporting detail: Addendum 146 — Source for the series table.
6061 favors fabrication; 7075 offers higher strength in the T6 condition
6061 favors fabrication; 7075 offers higher strength in the T6 condition
Compare like conditions: 7075-T6 has higher tensile strength than 6061-T6. The alloy number alone does not establish the strength of the material in hand.
6061 and 7075 at selection level
Alloy
Typical uses
Fabrication considerations
6061
Truck and marine frames; tanks.
Weldable and readily machined. Welding can change the temper in the weld area.
7075
Aircraft components, molds and industrial tooling.
Good machinability, but generally considered unsuitable for welding because of cracking susceptibility.
Supporting detail: Addendum 147 — Sources and comparison limits.
Brass and bronze trade some of copper's conductivity for other properties; Practice
Brass and bronze trade some of copper's conductivity for other properties
Brass is principally a copper-zinc alloy. Depending on grade, it can offer useful forming or machining behavior for fittings, hardware and decorative parts. Do not assume every brass has the same machinability or suitability for contact with drinking water.
Bronze traditionally means copper-tin alloy, but commercial names also include aluminum bronze and silicon bronze. Bronzes serve in bearings, bushings, gears and corrosion-resistant hardware, depending on grade. The word “bronze” alone is not enough to buy a bearing material.
For a conductor, begin with conductivity requirements. For a bearing, begin with load, speed, lubrication and wear. The same copper-based family will not automatically win both comparisons.
Recognize stock shapes, distinguish size conventions, and specify enough information to receive the metal a design requires.
Stock is the material shape you buy before making the part
Stock is the material shape you buy before making the part
Stock is material supplied in a usable starting form. Choose a shape that leaves enough material for the finished part and any cutting or machining allowance. Buying the smallest possible shape can fail if saw cuts, surface cleanup or distortion consume the allowance.
Cross-sections show shape only. Dimensions and wall thickness still belong on the order.
Sheet, plate, bar and structural shapes use different size descriptions
Sheet, plate, bar and structural shapes use different size descriptions
What to specify for common forms
Form
Description
Size information
Sheet and plate
Flat products; plate is the thicker category under the applicable product convention.
Thickness, width and length. There is no single sheet/plate boundary for every metal and specification.
Bar
Solid round, flat, square or hexagonal cross-section.
Diameter, width and thickness, square side, or hex size across flats, plus length.
Structural shapes
Angle, channel and I-shaped sections place material where the structure needs it.
Section designation and dimensions, thicknesses and length under the relevant product system.
A gauge number is a sizing convention, not a universal thickness. Specify actual thickness and units when ambiguity would affect the part. Check the applicable material's gauge table if a drawing uses gauge.
Tube dimensions and nominal pipe sizes are not interchangeable
Tube dimensions and nominal pipe sizes are not interchangeable
Tube is commonly ordered by outside dimensions and wall thickness: outside diameter for round tube, or outside width and height for rectangular tube. State the length too.
Pipe commonly uses a nominal pipe size and a wall schedule. A nominal size is a label; it need not equal the measured outside or inside diameter. Use the applicable pipe dimensions table before calculating a fit or flow area. Structural tubing is not automatically suitable for pressure service.
Measure the right boundary. For round hollow stock, inside diameter equals outside diameter minus twice the wall thickness. The wall occurs on both sides of the opening.
Hot-rolled and cold-finished describe processing, not alloy identity
Hot-rolled and cold-finished describe processing, not alloy identity
Hot-rolled steel is shaped at high temperature and commonly arrives with mill scale and comparatively broad dimensional tolerances. Cold rolling or other cold-finishing operations can improve surface finish and dimensional control. Cold-finished bar may be drawn rather than rolled.
Cold work can increase strength and leave residual stresses. Removing material can release those stresses and move the part. Cold-finished does not automatically mean precision ground, and neither term guarantees a particular tolerance without a product specification.
Supporting detail: Addendum 148 — Why an attractive surface can still be the wrong purchase.
A purchase description must preserve alloy, condition, form and size; Checklist
A purchase description must preserve alloy, condition, form and size
An illustrative request is: 6061-T6 aluminum round bar, 25 mm nominal diameter × 500 mm cut length, quantity 2. Before purchasing, add the governing product specification, diameter and cut-length tolerances, finish and certification requirements that the design needs. This example is not a complete engineering specification.
Identify the alloy and required delivery condition from the design.
State the stock form and every necessary dimension with units.
Allow for saw kerf (material lost in the cut), cleanup and final machining.
State tolerances, quantity and any required material certificate.
Compare availability, cut charges, shipping and minimum orders as well as material price.
Confirm that the delivered label and documents match the order before using the stock.
Drops or remnants are leftover pieces that may reduce cost. Their identification and usable dimensions still need checking.
Estimate mass from cross-sectional area, length and density; Practice
Estimate mass from cross-sectional area, length and density
For uniform stock, mass = cross-sectional area × length × density. For a solid round bar, area = πd²/4. For round tube, area = π(D² − d²)/4, where D is outside diameter and d is inside diameter. Subtract the opening before multiplying by length.
Use the density for the actual alloy from a material data sheet and keep units consistent. A result in kilograms is mass; weight as a force also requires gravitational acceleration. See Geometry, Mass, and Force and Dimensional Analysis.
Choose a conditioning process by its goal: soften, refine structure, harden, improve toughness or reduce residual stress.
Heat treatment is conditioning: change structure to change properties
Heat treatment is conditioning: change structure to change properties
Heat treatment uses controlled heating, holding and cooling to change a metal's internal structure. It belongs to Conditioning in Manufacturing Process Categories. It can change properties without intentionally changing the overall shape, although distortion can occur.
The result depends on alloy, starting condition, section thickness and the complete cycle. Heating more or cooling faster is not automatically better. A treatment that strengthens one alloy can soften another.
Supporting detail: Addendum 149 — Steel microstructures are not the four steel families.
Anneal to soften; normalize suitable steels to refine structure
Anneal to soften; normalize suitable steels to refine structure
Annealing is a family of treatments used to soften material, restore ductility or adjust its structure. Full annealing of suitable steels includes slow cooling; annealing cold-worked metal can form new grains and restore formability. Not every anneal uses the same temperature or cycle.
Normalizing heats suitable steel into its austenitic range and then cools it in air. It can refine and make the structure more uniform after earlier processing. Air cooling and slow furnace cooling produce different results.
Choose the process for the desired condition. Do not apply one universal temperature offset to all steels.
Quench hardening usually needs tempering afterward; Practice
Quench hardening usually needs tempering afterward
Quench hardening heats suitable steel to form austenite, holds as required, then cools fast enough to obtain the intended hardened structure. It commonly raises hardness and strength but can reduce ductility and toughness. Cracking and distortion are possible.
Tempering reheats hardened steel below the temperature at which austenite begins to form. It adjusts the balance of hardness and toughness and reduces some quenching stresses. It is not simply heating “just below” one critical temperature; the required cycle depends on grade and target properties.
Separate illustrative cycles, not a furnace program. Peak temperatures, holds and cooling rates are grade-specific.
These concepts explain specifications; they are not operating instructions. Use the approved process for the identified material, equipment and quench medium.
Surface hardening puts wear resistance near the outside
Surface hardening puts wear resistance near the outside
A part may need a hard wear surface and a tougher interior. Carburizing adds carbon near the surface of suitable steel before hardening. Nitriding introduces nitrogen to develop a hard surface layer. These change surface chemistry.
Induction hardening heats a surface region electrically and then quenches it. It uses the steel's existing composition rather than adding carbon. It therefore needs a suitable starting steel. Case depth, surface hardness and core properties must be specified together.
Cold work strengthens; stress relief addresses locked-in stresses; Practice
Cold work strengthens; stress relief addresses locked-in stresses
Work hardening, also called strain hardening, occurs as metal is permanently deformed during cold working. It commonly raises strength and hardness while reducing remaining ductility. “Cold” here means below the relevant recrystallization range, not necessarily cold to the touch.
Stress relief reduces residual stresses left by processing. These are stresses that remain without an external load. The goal is often dimensional stability during later machining or service. Stress relief is not automatically a full softening anneal and does not guarantee zero distortion.
Aluminum strengthening does not use steel's martensite route
Aluminum strengthening does not use steel's martensite route
Some aluminum alloys can be strengthened by solution treatment, quenching and aging. Solution treatment puts selected elements into solid solution; subsequent aging develops small particles that obstruct deformation. Aging can occur naturally or through controlled heating, depending on the alloy and required condition.
Solid-solution strengthening and precipitation strengthening are different mechanisms. Dissolved atoms provide the first; particles of another phase provide the second. Other aluminum alloys obtain much of their strength through cold work. Annealing can soften cold-worked material.
An aluminum temper describes its processing condition. It is not synonymous with the steel process called tempering. Preserve suffixes such as -O and -T6 when reading or writing a material description; consult the relevant alloy-temper specification for their exact meanings.
Supporting detail: Addendum 150 — Further reading on conditioning processes.
Materials and Manufacturing Processes/Metals
Forming Metal
Compare casting, bulk deformation, sheet forming and powder metallurgy by shape, material, tooling and production quantity.
Choose the shape-making route before comparing production cost; Checklist
Choose the shape-making route before comparing production cost
Metal parts can begin as liquid poured into a mold, solid stock plastically deformed into a new shape, or powder pressed into a compact. Plastic deformation means a permanent shape change after the force is removed. Each route limits the shapes it can make and the tools it needs. A die is a tool that controls shape; a mold contains material while it takes shape.
These shape-making routes sit under Forming in the classification used by Manufacturing Process Categories. In metalworking references, forming often means solid-metal deformation specifically, with casting listed separately. Cutting is Separating; joining is Fabricating; property-changing treatment is Conditioning; surface protection or appearance is Finishing. Metals are one of the four families in Material Families, alongside Plastics, Wood & Composites, and Ceramics & Glass. Metal properties and heat treatment are separate topics.
Identify the alloy, overall shape, holes and thin regions.
State the quantity and whether the design will change.
Check tool access and how the part will leave the mold or die.
Compare tooling cost, repeatability and production rate.
Allow for trimming, machining, joining and finishing afterward.
Casting makes a shape by solidifying metal inside a mold
Casting makes a shape by solidifying metal inside a mold
Three casting routes and their trade-offs
Route
How it works
Typical products and cost trade-off
Sand casting
A pattern makes a cavity in bonded sand. Remove the pattern, assemble the mold, pour metal, then break away the mold after solidification.
Pump housings and large machine bases. Relatively flexible tooling can suit small batches; making a new mold for every part adds work.
Investment casting
A disposable pattern, often wax, receives a ceramic shell. Remove the pattern and fire the shell before pouring metal. Break away the shell afterward.
Detailed brackets, valve parts and turbine components. Fine detail can reduce later machining, but pattern and shell preparation add time and cost.
Pressure die casting
Inject molten metal into a reusable metal die, let it solidify, then open the die and eject the part.
Repeated aluminum or zinc housings. Expensive dies and equipment can pay off over long runs; alloy, size and geometry must suit the process.
There is no universal quantity at which die casting becomes cheapest. Obtain estimates for the actual geometry, alloy, tool life and required secondary operations.
Supporting detail: Addendum 151 — Sources for the casting routes.
A casting needs room to release, shrink and feed
A casting needs room to release, shrink and feed
The cope is the upper mold half; the drag is the lower half. The sprue leads downward from the pouring opening, and a runner and gate lead into the cavity. A riser supplies liquid metal as the casting solidifies and contracts. A core occupies space that must remain hollow.
Draft is a slight taper that helps a pattern or casting leave its tooling. A shrinkage allowance changes tooling dimensions to account for contraction. Neither is a universal number: alloy, geometry and process matter. Critical faces or holes may need machining afterward.
Supporting detail: Addendum 152 — Why a larger pattern does not replace a riser.
Rolling squeezes, forging compresses and extrusion pushes through a die
Rolling squeezes, forging compresses and extrusion pushes through a die
Solid-metal forming routes
Route
Shape and examples
Tooling and quantity
Rolling
Rotating rolls reduce thickness or produce a section. Sheet, plate and structural shapes are common products.
Large equipment investment suits substantial throughput; a designer can often buy standard rolled stock.
Open-die forging
Dies compress a solid workpiece without enclosing its whole outline. Examples include large shafts and rings.
Relatively simple dies accommodate varied sizes; repeated positioning and later machining may be needed.
Closed-die forging
Shaped die cavities guide metal flow into repeated parts such as connecting rods and wrenches.
Dedicated tooling favors repeated production. Excess metal may form flash that is trimmed away.
Extrusion
A ram pushes a billet through a die opening. Long channels, rails and heat-sink profiles have a substantially constant cross-section.
A dedicated profile die can serve many lengths. Cut ends, cross holes and local pockets require later operations.
Wire drawing
Pull wire through a reducing die to make it thinner and longer. This is different from pushing stock through an extrusion die.
Die sets and handling equipment suit repeated lengths; several reductions may be needed.
Hot working occurs at temperatures and deformation rates that allow recrystallization, the formation of new grains, during deformation. Cold working occurs where that process does not remove the work hardening as deformation proceeds. The boundary depends on the metal and processing conditions; it is not one temperature for every alloy. Hot rolling permits large shape changes, while cold rolling commonly improves dimensional control and surface quality and can increase strength through work hardening.
Supporting detail: Addendum 153 — Cold forming does not guarantee an unchanged dimension.
Supporting detail: Addendum 154 — Sources for solid-metal deformation.
Sheet forming changes shape; blanking and shearing separate material; Practice
Sheet forming changes shape; blanking and shearing separate material
Bending changes the angle of sheet, as in a bracket or enclosure. A press brake uses a punch and die to make bends; adaptable tooling suits prototypes and short runs. Roll forming progressively bends strip through roll stations into a long profile, such as a channel. Its dedicated roll tooling favors repeated lengths. It is different from rolling sheet thinner.
Deep drawing pulls sheet from a flat blank into a die cavity to make a cup or shell. Tooling must control material flow to limit tearing and wrinkling. Dedicated tools suit repeat production. This is different from pulling wire through a reducing die.
Stamping names a press-based production route that can combine several operations. Bending and drawing are Forming; shearing and blanking are Separating. In blanking, the cut-out piece is the wanted blank; in punching a hole, the removed slug is usually scrap. A stamping line can therefore perform more than one process category.
Bend allowance accounts for the material length within a bend when developing a flat pattern. The sheet stretches on the outside and compresses on the inside. Use a validated bend table or supplier data for the alloy, thickness, radius and tooling; adding outside leg dimensions alone does not give the correct blank length.
Supporting detail: Addendum 155 — Sources for sheet forming and flat patterns.
Powder metallurgy presses particles, then bonds them by sintering
Powder metallurgy presses particles, then bonds them by sintering
In conventional press-and-sinter powder metallurgy, powder fills a die and is compressed into a green compact: a shaped part that is not yet fully bonded. Heating then bonds the particles during sintering, generally without melting the main metal throughout. Some systems include a liquid phase.
Small gears and porous bearings are typical products. Dedicated dies and presses favor repeat quantities and can produce a near-net shape, close to the finished dimensions. Tool access, ejection and density variation limit geometry; critical features may still require sizing or machining.
Supporting detail: Addendum 156 — Porosity can be useful or unwanted.
Compare welding, brazing, soldering and mechanical assembly by joint access, heat input, production needs and service requirements.
Choose a joint around its load, access and need for disassembly
Choose a joint around its load, access and need for disassembly
Joining parts is Fabricating. First identify the metals, thicknesses, loading, service environment and whether the assembly must come apart. Then check access for the joining equipment and for inspection.
A welded frame can avoid a large casting tool, but fit-up, fixtures and inspection still cost money. A bolt-on cover allows service access, but needs clearance for the fasteners and tools. See Fasteners and Galvanic Corrosion for mechanical assembly.
Welding joins the base metal; melting is not required in every process
Welding joins the base metal; melting is not required in every process
Fusion welding melts base metal at the joint, with or without added filler metal. The pool solidifies to form the joint. The common arc, oxy-fuel and resistance spot processes below are fusion processes.
Solid-state welding forms a bond without bulk melting of the base metals. Friction welding is one example. A solid-state process can still heat and alter nearby metal; “not melted” does not mean “unchanged.”
The heat-affected zone is nearby base metal whose structure or properties change because of the thermal cycle, without itself becoming weld metal. Selecting a process includes checking those changes and distortion, not merely whether a bead looks smooth.
Supporting detail: Addendum 157 — Sources for fusion welding, solid-state welding and the heat-affected zone.
Compare the heat source, filler and access of five welding processes; Practice
Compare the heat source, filler and access of five welding processes
Starting candidates for process selection
Process
How it works and where it fits
Trade-off
Oxy-fuel welding
A fuel-and-oxygen flame heats the joint; a separate filler rod may be added. Oxyacetylene can suit selected thin-steel work and repair.
Flexible equipment, but slower and with more broadly distributed heating than many production arc processes.
SMAW / stick
An arc melts a flux-coated consumable rod. The coating supplies protection for the weld pool. Common for steel repair and construction work.
Portable equipment and flexibility; rods need replacement and slag needs removal between appropriate stages.
GMAW (MIG/MAG)
An arc melts continuously fed wire under external shielding gas. Common for repeated steel or aluminum fabrication with suitable wire, gas and settings.
Continuous wire supports production and automation; shielding and equipment access must suit the job.
GTAW / TIG
An arc from a non-consumable tungsten electrode heats the joint under inert gas. Filler, when needed, is supplied separately. Useful for controlled joints in thin stainless steel and aluminum.
Good control of heat and filler, but often slower than wire-fed production welding.
Resistance spot welding
Opposed electrodes press overlapping sheets together and pass current through them, forming a local fused nugget. Common in repeated sheet assemblies.
Rapid repeat joints with suitable equipment and fixtures; conventional arrangements require access to both sides. Separate spots do not make a sealed seam.
Supporting detail: Addendum 158 — Why MIG is a familiar name but GMAW is the broader term.
Supporting detail: Addendum 159 — Sources for the five process mechanisms.
Brazing and soldering melt filler while the base parts stay solid
Brazing and soldering melt filler while the base parts stay solid
In brazing and soldering, a molten filler wets the solid base parts. In a suitable close-fitting joint, capillary action draws filler into the gap. The usual dividing temperature is 450°C: the American Welding Society describes brazing fillers as having a liquidus above 450°C and soldering fillers below it. Liquidus is the temperature above which the filler is fully liquid. This distinction concerns the filler, not the flame temperature or the machine's setting. In both processes the base parts remain solid. Neither is simply a cooler version of fusion welding.
Brazing can join suitable dissimilar metals or attach a carbide tip to a steel tool body. Soldering is common in electrical connections. Choose filler and joint design for compatibility, temperature and loads; a soldered electrical connection is not automatically suitable for a structural load.
Joint clearance, surface condition and heating method matter. Brazing can be manual or performed in production equipment such as a furnace. Mechanization changes throughput and tooling costs; the process name alone does not identify the cheapest route.
Supporting detail: Addendum 160 — Sources for the filler-temperature distinction and capillary joint.
Specify the required joint, not just the name of the machine; Checklist
Specify the required joint, not just the name of the machine
Identify both base materials, thicknesses and any coatings.
Describe the joint location, overlap or preparation and equipment access.
State load, leak-tightness and appearance requirements.
Allow for distortion, inspection and any later machining.
Coordinate the finish and any assembly sequence constraints.
A drawing and its referenced specification communicate the required weld and acceptance criteria. A process abbreviation alone does not specify weld size, extent or quality. Likewise, a visually neat joint does not establish internal soundness. Heat-treatment selection is a separate topic.
Materials and Manufacturing Processes/Metals
Fasteners and Galvanic Corrosion
Choose mechanical joints for service access, thread compatibility and exposure to moisture and dissimilar metals.
Match the fastener to the assembly and its service access
Match the fastener to the assembly and its service access
Common mechanical joining components
Component
Purpose
Design check
Bolt and nut
Provide a removable threaded connection that can clamp parts together.
Provide tool access, suitable thread engagement and a compatible strength and material specification.
Washer
Provides a bearing surface or distributes load where the design requires it.
A plain washer does not by itself prevent loosening or electrically isolate an entire joint.
Rivet
Forms a retaining head through permanent deformation.
Suitable for repeated sheet assembly; removal normally destroys the rivet. Blind rivets permit installation from one side.
Threaded insert
Provides an internal thread in a host part.
Select an insert designed for the host material and thickness. Check installation access, pull-out and resistance to rotation.
Standard fasteners often reduce dedicated tooling for short runs, but every fastener adds parts and assembly time. Riveting or automated fastening may suit long runs. Removability, inspection and repair can justify a threaded joint even when another method is faster.
A thread size alone does not specify a complete fastener; Practice
A thread size alone does not specify a complete fastener
The mating threads must agree in diameter, spacing and thread system. Similar-looking inch and metric parts are not interchangeable. Pitch describes axial spacing between adjacent thread forms; threads per inch describes a count over a unit length.
A purchase or drawing specification also needs the relevant length, head style, material or strength grade, coating and thread-fit requirements. The wrench size is not the thread diameter. Use the applicable thread reference and supplier drawing to decode a designation before choosing mating parts.
Read diameter and thread spacing separately
Example
Diameter
Spacing and system
1/4-20 UNC
Nominal thread diameter: 1/4 inch.
20 threads per inch; UNC is the Unified coarse series. The pitch is 1/20 inch, not 20 inches.
M6 × 1
Nominal metric thread diameter: 6 mm.
Pitch: 1 mm between corresponding points on adjacent threads. The 1 is not a count of threads per inch.
These are thread-size examples, not complete fastener specifications. Nominal diameter identifies the size; tolerances govern the actual mating dimensions. A 1/4-20 thread and an M6 × 1 thread differ in both diameter and spacing.
Supporting detail: Addendum 161 — Sources for thread names and size examples.
Galvanic corrosion needs a metal pair, electrical contact and an electrolyte
Galvanic corrosion needs a metal pair, electrical contact and an electrolyte
Dissimilar metals can form a corrosion cell when they are electrically connected and share a conductive liquid, called an electrolyte. Moisture containing salts can provide that liquid. The more active member of the pair acts as the anode and may corrode faster; the other acts as the cathode.
A galvanic series ranks metals by their behavior in a specified environment. It helps screen combinations; it does not predict a service life. Alloy condition, surface films, wetting and exposed areas matter. A dry pair is not automatically a working galvanic cell.
Supporting detail: Addendum 162 — Why the wetted areas matter.
Supporting detail: Addendum 163 — Sources for galvanic contact, coatings and area effects.
Review the complete joint before calling a fastener compatible; Checklist; Practice
Review the complete joint before calling a fastener compatible
“Stainless” does not mean compatible with every metal, and a coating is not a permanent guarantee of isolation. Consider material pairing, durable electrical separation, drainage and a suitable protective finish together. An insulating washer under a head does not isolate a shank that still touches the hole wall.
Identify the base metal, fastener, washer and their coatings.
Identify where electrical contact and moisture can occur.
Check the material pairing for the actual service environment.
Review sleeves, washers or gaskets for complete isolation and mechanical suitability.
Provide drainage and an inspectable, maintainable finish.
Compatibility review does not replace structural sizing or joint design.
Materials and Manufacturing Processes/Manufacturing Documentation
Critical Dimensions for the Shop
Choose dimensions from fit, function and interfaces, then give the maker and inspector the same references and limits.
A critical dimension controls fit, function or an interface
A critical dimension controls fit, function or an interface
A critical dimension is one whose variation can stop the part doing its job. Start with what touches another part, what must move or clear, and what locates the part. A hole's diameter may control whether a pin enters; its position may control whether two parts line up.
Critical does not mean “make every tolerance tight.” A tolerance is the permitted variation in a dimension. Choose it from the function, then check that the process and inspection method can achieve it. See Tolerances and Fits for limits and fits, Measurement Language for units and measurement language, and Surface Texture and Finish for surface requirements.
Give hole locations from named reference edges
Give hole locations from named reference edges
The original DL-01 display plate below illustrates a shop drawing. Its two suspension holes must stay at the intended locations; length and width mainly establish the display area. These are invented teaching limits, not a general specification for plywood or hanging hardware.
All dimensions in mm. Not to scale for measurement. L and B are plain-language reference labels, not formal geometric-tolerancing datum symbols. C marks the dimensions selected as critical for this example.
Display area and thickness. Measure with calipers; check adjacent edges with a try square for no visible gap.
C — two through holes
Each diameter 4.5 ±0.2 mm.
Openings for the loops; use suitable plug gauges for 4.3–4.7 mm limits.
C — center positions
From L: x = 15 ±0.5 and 85 ±0.5 mm. From B: y = 20 ±0.5 mm for each.
Consistent suspension locations. Check each coordinate from the stated edge.
Surface and edges
No coating; no loose fibers, splits or separated plywood layers.
Visual inspection after sanding; retain the dimensional limits.
All features have requirements, including those not marked C. See Operation Method Sheets for the manufacturing sequence and Bills of Materials for the matching parts list.
Worked record: correct horizontal separation, wrong locations
For this classroom comparison with DL-01 revision A, treat the following readings as exact mm values. The near-edge readings run horizontally right from L and vertically up from B to the nearest edge of each hole. Calculate each center using that hole's measured diameter.
Left hole: diameter 4.6; near edges 13.3 from L and 17.2 from B. Center x = 13.3 + 4.6/2 = 15.6 mm; y = 17.2 + 4.6/2 = 19.5 mm.
Right hole: diameter 4.4; near edges 83.4 from L and 18.3 from B. Center x = 83.4 + 4.4/2 = 85.6 mm; y = 18.3 + 4.4/2 = 20.5 mm.
Record the comparisons: both diameters meet 4.3–4.7 mm. Left x = 15.6 exceeds 15.5; right x = 85.6 exceeds 85.5, so both x locations fail. Both y locations meet 19.5–20.5 mm, including its endpoints. The horizontal separation is 85.6 − 15.6 = 70.0 mm, the nominal x-coordinate difference, but the pair is shifted right. These hole readings do not meet the drawing's separate location limits; correct horizontal separation alone does not locate the pair. This record compares only the stated hole readings, not the outline, thickness or surface requirements.
Supporting detail: Addendum 164 — How to check a center when a caliper touches the hole edge.
Dimension the part so it can be made without measuring the picture; Checklist; Practice
Dimension the part so it can be made without measuring the picture
Include the part identity, revision, material, units, overall dimensions, feature sizes and locations, thickness, and required finish. Supply enough views to remove ambiguity. Call a hole “through” when it passes through the material; otherwise specify depth.
Locate related features from a common reference where that matches their function. Do not give multiple independent dimensions for the same feature unless their relationship is clear. A redundant dimension can contradict the dimensions used to make the part.
Identify every mating surface, clearance and locating feature.
Choose references the maker can establish and the inspector can reach.
Check that each feature has a size, location and acceptance limit.
Remove conflicting or missing dimensions; do not rely on drawing scale.
Match the drawing revision to the method sheet and BOM.
Materials and Manufacturing Processes/Manufacturing Documentation
Bills of Materials
List the parts in an assembly and estimate each part's material share without confusing stock purchases with per-part consumption.
A bill of materials says what goes into one assembly
A bill of materials says what goes into one assembly
A bill of materials (BOM) lists the parts needed for a product. Give each part a stable number, a clear name, a quantity per assembly, a material and a make-or-buy designation. Identify the stock for made parts and the purchasing description for bought parts.
Made means the part needs a drawing and a route such as an operation method sheet. Bought means it arrives as a component; it still needs a size and specification so the buyer can obtain the correct item. Match the BOM revision to the assembly drawing. State whether quantities are per assembly or for the whole batch.
Material cost per part is its allocated stock share times stock price
Material cost per part is its allocated stock share times stock price
Estimated material cost per part = stock share allocated to that part × price of that stock unit. Keep both amounts on the same basis: length for constant-section bar, area for sheet of the same thickness, or mass when purchased by mass.
Allow for the saw cut's width (kerf), trimming and unusable stock. Finished-part volume alone can understate what making the part consumes. State how you allocate waste and reusable leftovers so two estimates can be compared.
Supporting detail: Addendum 165 — Consumption, purchase cost and batch yield answer different questions.
Worked BOM: one display label assembly costs $1.20 in allocated materials
Worked BOM: one display label assembly costs $1.20 in allocated materials
This original example matches DL-01 in Operation Method Sheets and Critical Dimensions for the Shop. All prices are invented teaching values, not quotations. Assembly DL-A, revision A, contains one made plywood plate and two purchased closed cord loops.
The 110 × 50 × 6 mm starting blank is allocated a 120 × 60 mm area of a 1200 × 120 × 6 mm birch plywood strip costing $18. The larger allocation includes room for cutting and trimming. Allocation share = (120 × 60) / (1200 × 120) = 0.05. Plate material estimate = 0.05 × $18 = $0.90.
DL-A revision A — quantities and material estimate per assembly
Part number / name
Make / buy; material and stock
Quantity
Cost each
Extended cost
DL-01 / display label plate
Make; birch plywood, blank 110 × 50 × 6 mm; allocated stock area 120 × 60 mm as above.
1
$0.90
$0.90
DL-02 / closed cord loop
Buy; waxed cotton cord, 1 mm diameter, 100 mm closed-loop circumference; example pack of 20 for $3.
2
$0.15
$0.30
Total allocated material and purchased-component cost per assembly
$1.20
Extended cost is quantity × cost each. The $1.20 excludes labor, machine time, tooling, consumables, taxes and delivery. It is not a complete manufacturing cost or a selling price. Broader cost roll-up and design-for-manufacturing decisions belong with manufacturing economics.
Buying one strip and one pack costs $21, even for one assembly. Unused material remains inventory; do not confuse that purchase total with $1.20 of allocated consumption.
Check quantities, units and waste before totaling the BOM; Checklist; Practice
Check quantities, units and waste before totaling the BOM
Match every drawing part number to a BOM row.
State the quantity per assembly and multiply once for the batch quantity.
Specify stock dimensions and material for made parts, and purchasing details for bought parts.
Use the same units in the stock-share numerator and denominator.
Document the cutting allowance and treatment of leftovers.
Multiply each quantity by its unit cost and sum the extended costs.
Keep unrounded intermediate calculations; round money to cents at the stated reporting step.
Materials and Manufacturing Processes/Manufacturing Documentation
Operation Method Sheets
Turn a drawing into an ordered plan with equipment, setup, process settings and a check that proves each operation is complete.
A method sheet tells another person how to make and check the part
A method sheet tells another person how to make and check the part
A drawing describes the required part. An operation method sheet describes how to make it. A process plan or routing sheet serves the same planning purpose, although the amount of detail varies. Write one row for each operation, in the order it will be performed.
Start with the part number and name, drawing revision, date, material and raw stock size: the starting piece before machining or cutting. Use actual dimensions and units. A material family alone is not a purchasing specification; identify the material needed for this part.
What belongs in each operation row
Field
What the next person needs
Operation
An action and its intended result, such as drill two through holes.
Equipment and setup/tooling
The equipment, cutting tool, support, holding method and reference face or edge.
Process parameters
Settings with units, or an identified approved setup instruction. Do not write an unexplained number for speed or feed.
Setup and cycle time
Time to prepare the operation, separate from time to repeat it on one part.
Pass/fail criteria and inspection tools
The required result, permitted limits and how to measure or compare it.
Keep quality checkpoints, failed-part decisions, actual times and improvement notes with the sheet. Equipment permission and operating procedures still come from Equipment Operating Procedure; a method sheet is not machine training.
Establish reference surfaces before locating features
Establish reference surfaces before locating features
Choose the order around what each later step needs. Make a straight, square reference edge before measuring hole locations from it. Make features while there is enough material to support and hold the work. Inspect a feature before the next step hides it.
This is a planning pattern, not a mandatory route for every part.
Holes may be easier to make before small parts are cut free from a larger piece. Final finishing usually follows cutting and drilling, so those operations do not damage the finished surface. Inspect afterward too: finishing can change dimensions.
Supporting detail: Addendum 166 — Why there is no universal operation order.
Worked method sheet: a hanging display label
Worked method sheet: a hanging display label
Original teaching example, not a production release. Part DL-01, display label plate, revision A. Material: birch plywood, starting blank 110 × 50 × 6 mm. Finished dimensions and acceptance limits are on the example drawing. Two purchased cord loops complete the assembly in Bills of Materials. No coating is specified.
This hand-tool route uses a supported blank, a fine-tooth handsaw, a drill press and sanding blocks. An actual shop must qualify its tooling and record machine settings before releasing the plan. The times below are invented planning estimates, not measured performance.
DL-01 revision A — route and inspection
Operation
Equipment, setup and parameters
Pass/fail check and tool
10 — Establish edges and trim
Bench, clamps, handsaw and sanding block. Support the blank; establish straight bottom edge B and left edge L square to it. Mark the final outline from B and L, saw outside it, then sand to the lines.
Calipers: length 99–101 mm; width 39–41 mm; thickness 5.5–6.5 mm. Try square: no visible gap along the checked edges against the blade. Reject split or separated plywood layers.
20 — Locate two hole centers
Rule, square and marking tool. From L mark x = 15 and 85 mm; from B mark y = 20 mm for both. Keep the same references for both holes.
Rule and square: confirm both marks against the drawing before drilling; this layout check does not replace finished-hole measurement.
30 — Drill through
Drill press, 4.5 mm wood-cutting bit, backing board and clamped work. Record the qualified spindle speed in rpm and the approved drilling setup before use.
Hole diameter 4.3–4.7 mm using suitable plug gauges; hole-center x and y coordinates within ±0.5 mm of the drawing using calipers and measured hole diameter. No splits at the holes.
40 — Finish and inspect
Sanding block, example sequence 120 then 180 grit. Remove loose fibers at edges and hole mouths without enlarging holes beyond their limits.
Visual inspection: no loose fibers, splits or separated layers. Recheck dimensions and hole limits using the tools above.
50 — Add two cord loops
Hand assembly. Thread one purchased closed loop through each hole, then pass the rest of that loop through its emerging end to form a hitch. Seat both hitches alike.
Visual comparison: two closed loops present, one through each hole, each hitched around the plate edge with no loose cut end. This is a display example, not a load-rated hanger.
Planning time per operation, minutes
Operation
Setup per batch
Cycle per assembly
10
3
5
20
1
2
30
4
2
40
1
3
50
1
1
Total
10
13
For three assemblies, the serial estimate is 10 + (3 × 13) = 49 minutes, assuming each setup is done once and all operations run one after another. Record waiting, interruptions and repeated setups separately when comparing with actual elapsed time.
Replace “make it right” with an action and an acceptance test; Checklist; Practice
Replace “make it right” with an action and an acceptance test
“Drill the holes neatly” leaves the next person guessing. “Drill two through holes at the drawing coordinates; check diameter and location against revision A” gives an action and a result, but still needs the equipment, support, tooling and settings in the row.
Pass means every stated criterion is met. Fail means identify and hold the part for a decision; do not quietly send it to the next operation. Rework is a specified additional operation that can bring the part into conformance. Removing more material cannot restore an undersize outside dimension or shrink an oversize hole.
Match the part, drawing and method-sheet revisions.
Check that every operation names equipment, tooling, holding and references.
Fill required settings with units before releasing the plan.
Give every quality checkpoint a measurable limit or an explicit comparison and an inspection method.
Define who decides rework or rejection when a check fails.
Record what changed so the next batch can repeat the improvement
Record what changed so the next batch can repeat the improvement
Record setup time once per setup and cycle time per piece. State when each timer starts and stops; include inspection consistently. Keep quantity attempted, quantity accepted, scrap count and rework count. A reworked part may later pass, so these counts are not all separate groups to add together.
For each trial, record material identity, tool, setting and units, holding arrangement, actual measurements and the problem observed. A useful photo shows the reference edge, stop or tool position; caption it with the operation and revision. Use photos you have permission to share, with no personal information.
Example improvement record — a proposed trial, not a claimed result
Observation
Change to test
Evidence to keep
Hole locations vary between pieces.
Use the same reference edges and a verified locating stop instead of re-marking from different edges.
Record each hole location before and after the change, batch size, setup time and rejects. Keep the acceptance limits unchanged.
Change one factor at a time where practical. Verify the first piece after a setup change before repeating it through a batch. If the change helps, update the method-sheet revision and keep the evidence. A faster operation that produces more rejects is not automatically an improvement.
Materials and Manufacturing Processes/Manufacturing Documentation
Making Silicone Molds from a Printed Pattern
Plan a one-part mold, document the product-specific mixing and curing conditions, and inspect a repeatable batch of castings.
A printed pattern defines the cavity in the silicone mold; Interactive; Practice
A printed pattern defines the cavity in the silicone mold
A pattern is the original shape copied by a mold. For a simple one-part, open-face mold, use a shape with a flat back and features that can be withdrawn through the opening. An original example is a small decorative relief tile with a flat back, gently sloping sides and no hooked details.
For a small batch of resin replicas, this is a casting task: liquid resin fills the mold cavity and cures. A fiber-reinforced shell made by wet hand layup builds layers of reinforcing fabric or mat with resin against a mold. Compare these routes in Plastic Forming Processes, then use Choosing a Plastic Forming Process to weigh material, geometry, quantity and tooling. Try the detailed-replica and reinforced-shell practice choices.
Draft is a slight taper that helps a part leave the mold. Let the shape widen toward the opening. A flat parting face, where the pattern meets the mold-box base, defines the open back of this mold. Avoid undercuts that hook behind the silicone; flexibility does not make every trapped shape removable.
A wide mouth does not rule out an interior hook. This illustrative model uses an exact-fit, centered, symmetric rigid 2D pattern and rigid cavity. Opening depth is 0; positive depth points down into the mold. The only permitted motion is outward translation upward at fixed orientation, into unobstructed space. Units are arbitrary consistent diagram units.
Hypothetical local-shoulder pose at outward pull 5. The original depth-25 section moves to cavity depth 20: pattern half-width 26 meets cavity half-width 22, a geometric overlap of 4 per side. Outlined bands and × marks locate interference; this is not physical passage through rigid material.
Exact piecewise-linear sections: stations are (depth, half-width)
Profile
Stations
Trial pull 5
Whole path
Taper
(0,30), (40,20)
1.25 side separation
No positive interference
Parallel
(0,25), (40,25)
Side contact
No positive interference; contact persists
Reverse taper
(0,20), (40,30)
1.25 interference per side
Blocked
Local shoulder
(0,30), (20,22), (25,26), (40,15)
Maximum 4 interference per side at depth 20
Blocked despite widest mouth
At cavity depth d, an outward pull t places pattern half-width w(d+t) against cavity half-width w(d). Positive Δ(d) = w(d+t) − w(d) means overlap. For the local shoulder at t = 5, the positive interval is (50/3, 520/23), approximately (16.6667, 22.6087); endpoints are zero-contact boundaries.
The continuous path requires width to be nonincreasing with depth. A deeper section wider than a shallower section provides an obstruction. For each pose, Δ is linear between original and translated knots; checking these knots and solving zero crossings is analytical, not an animation-frame test. At t = 0 every profile is in initial contact. At t = 40 there is no interior overlap, but the reverse taper and local shoulder still have blocked paths: a clear endpoint does not prove a reachable endpoint.
Comparisons use a numerical threshold of 64 × machine epsilon × maximum half-width, separate from physical clearance and manufacturing tolerance. Values within that floating-point threshold are treated as contact. This is geometric interference only: it omits friction, adhesion, shrinkage, forces, damage, cure, rotation, lateral motion, deformation and unshown 3D features. No-interference does not establish practical release; a rigid obstruction does not establish flexible-silicone failure.
The mold copies the pattern's surface. Smooth and inspect the print before making the mold.
Remove unwanted layer ridges and support marks without losing important dimensions. Choose pattern preparation, any sealer and any release agent for the specific print, silicone and casting material. Follow the manufacturers' compatibility instructions and test a small prepared sample before committing the full mold.
Read the technical data sheet before choosing a mix or cure schedule; Checklist
Read the technical data sheet before choosing a mix or cure schedule
The technical data sheet (TDS) supplies processing instructions. The safety data sheet (SDS) supplies handling information; use Chemicals and Safety Data Sheets for that guidance. Neither a generic lesson nor a familiar-looking container replaces the instructions for the actual product.
Record the silicone product, batch identification and technical-sheet revision.
Record the A:B ratio and whether it is by mass (weight) or by volume.
Record working time, mixing procedure, bubble-removal requirements and cure conditions.
Check compatibility with the printed pattern, coatings, release agent and intended casting material.
Complete a small compatibility trial and inspect its cure before the full pour.
Working time is the available time to mix and place the material under stated conditions. It is not the demolding time. Cure instructions may distinguish demolding from full properties or further treatment. Record the actual temperature and times; do not substitute a universal overnight wait.
Supporting detail: Addendum 167 — Where to find product-specific instructions.
A ratio by weight is not automatically a ratio by volume; Interactive; Practice
A ratio by weight is not automatically a ratio by volume
Read what the given mass represents. These invented A/B examples teach arithmetic for two-component materials; they are not silicone or resin recipes. For A:B = a:b by mass and target total material mass M, mA = M a/(a+b) and mB = M b/(a+b). If A is already measured, mB = mA b/a.
Same 10:1 mass specification, different meaning of 220 g
Given
A
B
Material total
220 g target total
200 g
20 g
220 g
220 g of A alone
220 g
22 g
242 g
Density connects mass and each component’s own volume: VA = mA/ρA and VB = mB/ρB. For a:b by volume, divide target total mass using weights aρA:bρB. For given A mass, VA = mA/ρA, VB = VA b/a, then mB = VBρB.
Use illustrative densities ρA = 1.2 g/mL and ρB = 0.8 g/mL with a 300 g target total:
Changing the basis while keeping 2:1 changes the specification
A:B specification
A mass / volume
B mass / volume
2:1 by mass
200 g / 500/3 mL (≈166.6667 mL)
100 g / 125 mL
2:1 by volume
225 g / 187.5 mL
75 g / 93.75 mL
The first row has a 4:3 component-volume ratio; the second has a 3:1 mass ratio. Those are equivalent descriptions of their respective batches. Converting 300 g to 0.3 kg keeps the same physical batch. Switching 2:1 from mass to volume does not. Individual component volumes do not establish mixed/cured volume, yield or cavity fill.
Ideal cumulative scale example: for 200 g A + 20 g B in a 35 g container, readings with no tare are 35 g empty → 235 g after A → 255 g after B. Tare once with the empty container on the scale and the readings are 0 g → 200 g → 220 g. The final reading includes A and B; B alone is 20 g. Container mass changes the gross reading, not the material ratio. This comparison does not re-tare after A.
Weigh with a scale suitable for the actual quantities and follow the product’s specified ratio basis, measurement and mixing procedure. The arithmetic assumes no material loss; it predicts no cure, exotherm, working time, compatibility or actual mixed/cured volume. The actual product’s TDS/SDS remain authoritative.
Document pattern preparation, pouring and cure as separate operations
Document pattern preparation, pouring and cure as separate operations
Prepare the pattern and box. Inspect the print, complete the qualified surface treatment, secure its flat back to the box base, and check that the box contains the liquid. Set wall and backing thickness from the mold material and geometry requirements.
Measure and mix. Record actual A and B quantities, the ratio basis and the start time. Follow the product's mixing instructions, including its directions for reaching material at the container walls and bottom.
Reduce trapped air. Follow the product's bubble-removal and pouring instructions. A controlled pour into a low point can let the material rise around the pattern instead of repeatedly trapping air over its details. Vacuum degassing is product- and equipment-dependent; do not assume every silicone requires it or has enough working time for it.
Cure and remove the pattern. Record temperature, elapsed time and the specified demolding condition. Inspect the mold surface and details after removal before using the cavity.
Make a first casting. Follow the casting material's own mixing, release and cure instructions. Its ratio and timing need not match the silicone's. Inspect the first piece before repeating the batch.
Use Operation Method Sheets to give each operation equipment, settings, timing and a pass/fail check. Record what actually happened, including a changed pour method or a delayed demold, rather than copying the planned values into the result column.
Inspect each casting for voids, dimensions and consistency
Inspect each casting for voids, dimensions and consistency
A void is an unintended empty region. Inspect visible faces, edges and small details for pits, missing material and incomplete filling. A good exterior does not prove that the interior has no voids; choose further inspection according to the part's function.
Define batch checks before casting
Check
What to document
Shape and dimensions
Drawing limits, measurement method and actual readings for critical features.
Visible surface
Which faces matter and what counts as a reject. For a teaching relief tile, an example criterion is no visible pits or missing raised detail on the display face.
Cure and release
Product-specific acceptance condition; any tacky region, tearing or distortion observed on removal.
Batch consistency
Casting number, material batch, measured charge, mixing and cure times, appearance, dimensions, rejects and rework.
If a defect repeats at the same position, inspect the corresponding mold feature. If it varies between pours, compare the recorded process conditions. These are starting points for investigation, not proof of a cause. Change one factor, make a trial, and retain the results before revising the approved method.
Materials and Manufacturing Processes/Foundations
Manufacturing Cost and Volume
Estimate unit cost and find where two production methods cost the same.
Count material, processing, quality and overhead costs once
Count material, processing, quality and overhead costs once
Material, labor, machine time, tooling and scrap all affect the cost of an acceptable part. Setup prepares an operation; cycle time is the time for a repeating operation.
Material: stock purchase, delivery and material lost during production.
Processing: labor, machine time, tools, consumables and energy.
Quality: prevention, inspection, rework, rejects and returns.
Overhead: shared support such as facilities and indirect labor.
Check what a machine rate already includes before adding labor, energy or depreciation. Scrap belongs in the estimate once, even if it appears under both material and quality headings.
Spread fixed cost over the quantity actually needed; Practice
Spread fixed cost over the quantity actually needed
For a simple batch model, C = F + vQ and u = C/Q = F/Q + v. C is total cost, F is fixed batch cost, v is variable cost per part, Q is the number of acceptable parts, and u is average unit cost. Use Q greater than zero.
Fixed cost stays constant within the stated production range; variable cost grows with quantity. Setup and dedicated tooling may be fixed for a batch. Material and processing per part often contribute to v. State the period and cost boundary before classifying a cost.
Illustrative process A costs $120 + $8Q. At 60 parts, total cost is $600 and unit cost is $10.00/part. Producing unwanted parts to spread fixed cost creates inventory; it does not create demand.
Supporting detail: Addendum 168 — Why a shorter cycle does not reduce every cost equally.
Set total costs equal to find process break-even; Practice
Set total costs equal to find process break-even
Compare routes that meet the same requirements at the same quantity. From F_A + v_A Q = F_B + v_B Q, obtain Q* = (F_B − F_A)/(v_A − v_B).
Let A cost $120 + $8Q and B cost $720 + $3Q. Then Q* = ($720 − $120)/($8 − $3) = 120 parts. Both cost $1,080 total or $9/part. A costs less below 120; B costs less above 120.
Supporting detail: Addendum 169 — When there is no positive crossing.
Move the volume slider and predict which process wins; Interactive
Move the volume slider and predict which process wins
Start with the original A/B costs and predict the cheaper process at 60 and 240 parts. Then change a setup cost or variable cost and compare at the same demanded quantity. The case selector also includes fractional crossings, parallel lines, an everywhere tie, and a crossing beyond the chart.
Process-cost explorer. Compare C = F + vQ and u = F/Q + v for two routes supplying the same demanded quantity of equivalent acceptable parts in one batch. Use the same included costs and period for each route, count each cost once, and assume the entered rates stay constant. The exercise does not establish equivalent quality, capacity or demand, or recommend a purchase.
Predict, calculate total cost for each route, then divide by the demanded quantity. With A = $120 + $8Q and B = $720 + $3Q:
Original comparison at three demanded quantities
Parts
A total / per part
B total / per part
Lower cost
60
$600 / $10.00
$900 / $15.00
A
120
$1,080 / $9.00
$1,080 / $9.00
Equal
240
$2,040 / $8.50
$1,440 / $6.00
B
Between whole parts: let A = $90 + $6Q and B = $245 + $2Q. Q* = 155/4 = 38.75 parts. At 38 parts A totals $318 and B $321; at 39 parts A totals $324 and B $323. No whole-part quantity ties.
Try the other cases: A = $60 + $4Q and B = $210 + $4Q never cross because their slopes match; A stays $150 lower. If both F and v match, costs tie at every positive quantity. With A = $80 + $2Q and B = $200 + $5Q, A is lower for every positive Q. With A = $100 + $2.50Q and B = $900 + $2Q, the positive crossing is at 1,600 parts, beyond the live graph's 0–300 interval.
The editable explorer accepts fixed cost $0–$100,000, variable cost $0–$1,000/part and whole demand 1–10,000. Dollar entries have at most two decimal places; exact cent totals determine equality. Displayed average unit costs are approximate. A graph ending before a crossing does not prove there is no crossing. Zero on a total-cost graph shows fixed cost; unit cost at zero parts is undefined.
Static comparison: at 60 parts A is $10.00/part and B is $15.00/part; at 240 parts A is $8.50/part and B is $6.00/part. Use Dimensional Analysis to check units and Outsourcing to consider more than cost.
Materials and Manufacturing Processes/Foundations
Material Utilization and Cost
Check a stock layout, account for cutting loss and roll up material costs.
Prove the parts fit before dividing areas; Practice
Prove the parts fit before dividing areas
Stock is material purchased for further work. Nesting arranges part outlines on stock to reduce waste. An area ratio cannot prove a layout fits. Check dimensions, orientation, grain direction where relevant, edge margins and spacing.
Kerf is the width removed by a cut. An offcut is leftover stock; a usable offcut may be saved. Include trim cuts and holding allowances before promising a part count.
Illustrative layout: a 1,000 mm bar supplies 98 mm blanks. Each blank requires one 2 mm separating cut, including the last blank, with no end trim. Ten blanks consume 10 × (98 + 2) = 1,000 mm. A different last-cut arrangement would need a different cut count.
Test the next-blank threshold; Interactive; Practice
Test the next-blank threshold
Predict first: can the same 1,000 mm stock still supply ten 98 mm blanks if separating kerf increases from 2 to 3 mm? What happens to stock cost per blank when the stock price stays $48?
This one-dimensional lab reserves a full separating kerf after every blank, including the last. Left and right excluded trim lengths already include their own cut losses. The layout does not use the far stock edge as a finished blank edge; it is a count under this policy, not a claim of globally maximum yield.
Usable interval U = stock length L − left excluded trim − right excluded trim Blank count n = floor[U / (blank length b + separating kerf k)]. Round down to a whole number. There are n separating cuts, plus any preparation already accounted for in excluded trim.
Each outlined block is an actual 98 mm blank; the narrow filled band after each is its full 2 mm kerf. Ten blanks plus ten kerfs fill this stock exactly. On narrow screens, scroll sideways to inspect the full bar.
Material balance: 1,000 mm = 0 excluded trim + 980 acceptable blanks + 20 separating kerfs + 0 offcut. Utilization = 980 / 1,000 × 100 = 98.0%.
Change the kerf to 3 mm: ten blanks would need 10 × (98 + 3) = 1,010 mm, so only nine fit. The new balance is 1,000 = 0 + 882 + 27 + 91 mm. The 91 mm offcut is 10 mm short of another 101 mm blank-and-kerf interval.
Allocate the whole stock charge: $48 / 10 = $4.80 per acceptable blank in the original layout; $48 / 9 ≈ $5.33 after the kerf change. All equal-cross-section blanks are assumed acceptable. No remnant credit or processing cost is included. If zero blanks fit, cost per blank is undefined.
Another threshold: at 2 mm kerf, 999.99 mm stock fits nine blanks, while 1,000.00 mm fits ten. This lab uses hundredths of a millimeter and currency cents; its bounded illustrative values are not machine settings. It is not a two-dimensional nesting tool.
Use a consistent physical basis for utilization; Practice
Use a consistent physical basis for utilization
Utilization = material in acceptable parts / material purchased × 100%. Compare length for the same cross-section, area for the same thickness, or mass on a consistent basis.
The bar example gives 980/1,000 × 100 = 98.0%. The remaining 2% is kerf. Distinguish reusable offcuts from material discarded.
Supporting detail: Addendum 170 — Why 20% loss means a 25% increase per useful amount.
Charge each part its share of stock and waste; Practice
Charge each part its share of stock and waste
Part material cost = share of stock charged to the part × stock price. A $48 sheet yielding eight identical acceptable blanks gives $48 × 1/8 = $6.00 per blank when the whole sheet is charged to those blanks. This includes their share of kerf and unusable offcuts.
Finished-part area divided by stock area can understate cost by leaving waste unassigned. State any credit for reusable remnants. Add delivery only if it is not already in the stock price.
A bill of materials (BOM) lists the components and quantities needed for one product. Add quantity × unit cost for every line.
Illustrative material-only BOM
Item
Quantity
Unit cost
Line cost
Blank
2
$6.00
$12.00
Standard fastener
4
$0.25
$1.00
Material total
$13.00
This is not finished product cost. Add processing, assembly and other applicable costs using Manufacturing Cost and Volume.
Materials and Manufacturing Processes/Foundations
Outsourcing
Decide which activities to keep in-house or place with suppliers, weighing relevant costs and capabilities alongside quality, capacity and delivery.
Compare equivalent acceptable parts over the same period
Compare equivalent acceptable parts over the same period
Outsourcing means arranging for an outside supplier to carry out work for the business rather than doing it internally. The work may be making a component or providing a service. A make-or-buy comparison is one application of that broader decision.
A core competence is a capability central to what the business does particularly well. Outsourcing may free resources to focus on those strengths, but it also makes the business depend on suppliers for the work they perform. Compare costs alongside capacity, quality, delivery and capabilities worth retaining. See OpenStax: Outsourcing and core strengths.
Make means produce internally; buy means purchase from a supplier. Define quantity, specifications and delivery date before comparing options. Use Manufacturing Cost and Volume for an initial cost comparison.
Include avoidable setup, tooling, material and processing for make; purchase price, freight, incoming checks and expected rework for buy. Compare costs that change with the decision. Shared rent that remains after outsourcing is not automatically a cash saving.
Start here: decide which future costs change between the two routes, then compare their totals. A relevant cost changes with the choice. An avoidable cost is removed by choosing the other route; a sunk cost has already been incurred and cannot be recovered. Fixed, direct and allocated describe costs, but those labels alone do not establish relevance.
Supporting detail: Addendum 171 — Why the cost boundary matters.
Worked case: which costs change for 100 parts?; Practice
Worked case: which costs change for 100 parts?
This original hypothetical order needs 100 acceptable brackets delivered within one month. All amounts below are illustrative dollars, not supplier prices or facts about a particular shop. For the numeric comparison, assume both routes supply the same specification and acceptable quantity by that deadline.
Making needs a new $300 setup and $9 per acceptable part ($6 material plus $3 additional processing). Buying needs a $10 per-part quote, a separate $0.50 incoming check per part, and $100 freight for the order. The quote excludes those checks and freight. These are future payments incurred only for their respective routes.
The $600 shared rent for the month is paid unchanged either way. A $200 study was paid for last month and is irrecoverable. Assume spare internal capacity, no displaced work or alternative income, and no other route-dependent costs or credits. These are case assumptions; spare time alone does not establish that opportunity cost is zero in a real decision.
Predict before reading the totals: does making's lower per-part charge outweigh its new setup at this quantity? Which two amounts should be excluded from the relevant-cost totals?
Relevant-cost ledger — the same 100 acceptable parts and one-month boundary
Cost and treatment
Make
Buy
New setup: avoidable if buying
$300
$0
Material + additional processing: $9 × 100
$900
$0
Supplier quote: $10 × 100
$0
$1,000
Separate incoming checks: $0.50 × 100
$0
$50
Freight: once per order
$0
$100
Shared rent: $600 either way, excluded
—
—
Past study: $200 irrecoverable, excluded
—
—
Total relevant cost
$1,200
$1,150
Here “—” means excluded from this comparison, not a zero expense. Make = $300 + $900 = $1,200; buy = $1,000 + $50 + $100 = $1,150. Buying is $50 lower under the stated assumptions. The new setup matters even though it is fixed for this order: buying avoids it. Adding the unchanged rent to both sides would leave the $50 difference unchanged; adding it only to make would invent a saving.
For a quantity sensitivity check, use the existing Manufacturing Cost and Volume explorer with A as make ($300 setup, $9/part) and B as buy ($100 order freight, $10.50/part). Identify relevant costs first; the explorer cannot decide which costs belong. Do not add freight or checks again after including them in those inputs.
A cheaper quote can still be the wrong choice; Practice
A cheaper quote can still be the wrong choice
Factor
Question
Capacity
Is machine and staff time available? What other useful work would be displaced?
Quality
Can each route meet the specification consistently, and how will it be verified?
Lead time
Can the route deliver when needed, including queues and transport?
Core competence
Is this capability central to what the organization does well and needs to retain?
Risk
What happens if demand changes, a supplier fails or the design changes?
Standard parts often favor buying; distinctive capabilities may favor making. Neither is a rule based on volume alone.
The worked case establishes a conditional cost difference. It does not verify a supplier's quality, available capacity or delivery promise. Before committing, obtain evidence that each route can meet the requirement. If making displaces another useful job, include the benefit given up; if buying adds rework, expediting or other costs, revise the ledger. See OpenStax: Make or buy a component for avoidable fixed costs and the qualitative checks alongside the numeric analysis.
Make the required function easier to produce, assemble, inspect and maintain.
Keep the function and simplify how it is made
Keep the function and simplify how it is made
Design for manufacturing (DFM) considers production while a design can still change. Preserve required strength, fit and service performance; remove complexity that serves no requirement.
Reduce separate parts when this simplifies production and service.
Use standard components and available stock sizes.
Match geometry to the process and provide tool and inspection access.
Make assembly easy to orient, reach and verify.
Fewer parts can reduce joining work, but one complex part may need costly tooling or be hard to repair. Compare the whole route.
Specify only the precision the function needs
Specify only the precision the function needs
A tolerance is the allowed variation in a dimension or other feature. Tight tolerances may require careful setups, slower processing and more capable inspection. Keep tight control where fit or function needs it; do not apply it everywhere by habit.
No machine name guarantees a tolerance or price. Geometry, material, tooling, setup and measurement all matter. Confirm capability for the actual feature.
Supporting detail: Addendum 172 — Why the loosest tolerance is not automatically cheapest.
Reduce material loss without shortening useful life; Checklist
Reduce material loss without shortening useful life
Use Material Utilization and Cost to compare layouts. Also consider energy, durability, repair, disassembly and practical material recovery at end of life. A lighter part that fails early may consume more resources over its service life.
Identify each part's function and critical features.
Check standard components and stock sizes.
Sketch manufacturing, assembly and inspection access.
Check tolerances against function and process capability.
Compare material use, service life and repair or recycling options.
Lean and Quality/Continuous Improvement
Lean Value and Flow
Define customer value and improve the whole path from request to delivery.
Start with what the customer needs
Start with what the customer needs
Lean thinking improves how work creates value while reducing waste and respecting the people doing it. Value is judged from the customer's need: the right function and quality, in the needed quantity, at the needed time.
A busy machine is not proof of useful output. Making something early that nobody needs can increase storage and delay the work that is needed.
Separate value creation from necessary support and avoidable waste
Separate value creation from necessary support and avoidable waste
Value-added work changes the product or service toward the customer's requirement and is done correctly. Cutting a needed feature may add value; searching for a misplaced tool does not.
Some non-value-added work is currently necessary: required checks, safety measures and records protect customers and workers. Improve how that work is done; do not delete a safeguard because it does not physically change the product.
Supporting detail: Addendum 173 — Process time is not automatically value-added time.
5S Workplace Organization supports visible, repeatable work. It is one supporting method, not the whole of lean.
Lean and Quality/Continuous Improvement
Eight Wastes: TIMWOODS
Recognize eight patterns of wasted effort in manufacturing and daily life.
Use TIMWOODS to name what you observe
Use TIMWOODS to name what you observe
Transportation, Inventory, Motion, Waiting, Overproduction, Over-processing, Defects and Skills form TIMWOODS. Describe the observed problem before choosing a remedy.
Compare shop examples with everyday examples
Compare shop examples with everyday examples
These are illustrative examples, not descriptions of a particular shop.
Transportation: unnecessary material movement
Shop: A part travels to a distant holding area and back. Daily life: Moving stored boxes between rooms without using them.
Inventory: excess material or work
Shop: Unneeded blanks fill a rack. Daily life: Buying food that expires before use.
Motion: unnecessary movement by people
Shop: An operator searches several drawers for a tool. Daily life: Searching for misplaced keys.
Waiting: idle time before work can proceed
Shop: A prepared job waits for missing information. Daily life: A completed form sits awaiting approval.
Overproduction: too much or too early
Shop: Extra parts are made without demand. Daily life: Printing copies nobody requested.
Over-processing: work beyond requirements
Shop: A hidden face receives an unnecessary cosmetic finish. Daily life: Entering the same information into duplicate lists.
Defects: work that fails requirements
Shop: An incorrect hole pattern requires a replacement part. Daily life: Retyping a form because of incorrect entries.
Skills: unused talent
Shop: An experienced operator's improvement idea is never considered. Daily life: Ignoring a team member's relevant skill when dividing work.
Distinguish similar wastes before proposing a change; Practice
Distinguish similar wastes before proposing a change
Transportation follows material; motion follows people. Overproduction creates unwanted output; inventory is the resulting excess stock. Several wastes can occur together.
Inspection is not automatically a defect, and every machine cycle is not automatically wasted time. Check Lean Value and Flow. Buffers may be needed for supply variation; removing them without understanding demand and reliability can interrupt delivery.
Show material and information flow, then distinguish process time from elapsed lead time.
Map one product family from request to delivery
Map one product family from request to delivery
A value stream map (VSM) shows the steps and information that move a product or service toward the customer. Define the boundary and select work following a similar route. Walk the current process and record what happens, including queues and handoffs.
Show who requests work, how instructions reach production, where material moves and where it waits. An operations-only map misses the information controlling those operations.
Read process boxes, inventory triangles and flow arrows
Read process boxes, inventory triangles and flow arrows
This original sketch uses common conventions: a rectangle for a process, a triangle marked I for inventory, attached data boxes for measurements and arrows for flow. The legend distinguishes material movement from information. This is a teaching sketch, not a complete symbol standard.
Measure elapsed lead time separately from process time; Interactive; Practice
Measure elapsed lead time separately from process time
Lead time is elapsed time through the stated boundary, including waits. Process time is time actively spent doing the work within that boundary. Not all processing adds customer value.
Transfer size changes when jobs finish
10 jobs; A = 4 min/job, B = 6 min/job. Compare transfer-all with transfer-one.
Transfer all 10 jobs
First item 46 minFull order 100 minProcessing / job 10 min
Transfer 1 at a time
First item 10 minFull order 64 minProcessing / job 10 min
A is upper blue, B lower gold; bars are jobs, dashed lines completed-batch transfers. Minutes from order release 0; both plots share a scale.
Job 10 with transfer-one: 36 min waiting before A + 0 held for batch + 18 waiting at B = 54 min waiting. Add 10 min processing: 64 min elapsed from order release 0.
Ideal schedule: all equal jobs arrive at 0; serial single-job A then B, first come first served. A never blocks; waiting space is unlimited. Completed batches transfer immediately; the last may be smaller. Constant times; no setup, transport, failure, rework or variation. Finite-order illustration, not a factory forecast or a universal best batch.
Supporting detail: Addendum 175 — Bounded model reference: scheduling equations and limits.
The transfer-batch experiment above schedules a whole order. The earlier map sketch uses a fixed queue for one item:
For one item in this simplified sequential example: cutting = 4 min, queue = 120 min, assembly = 6 min. Process time is 10 min; lead time is 130 min. No other delays or overlapping steps are included. Removing half the queue saves more elapsed time here than cutting one minute of processing.
Supporting detail: Addendum 176 — A queue suggests a question, not a proven cause.
A future-state map describes an improved flow to work toward. Choose a measurable change, assign responsibility and check the effect using Kaizen and Standard Work. Compare delivery, quality and workload across the whole stream.
Lean and Quality/Continuous Improvement
Kaizen and Standard Work
Use small measured experiments to improve work and preserve what the team learns.
Improve a specific problem with the people doing the work
Improve a specific problem with the people doing the work
Kaizen means continuous improvement. Start with an observed problem and a small change whose effect can be checked. Invite the people performing the task to explain what makes it difficult.
For example, repeated searching for a shared measuring tool may suggest a labeled location. Measure search time and check whether the location also works for the next user. This is an illustrative experiment, not a promised productivity gain.
Use Plan–Do–Check–Act to learn from a change
Use Plan–Do–Check–Act to learn from a change
Plan: define the problem, measure the starting condition and predict the effect of a proposed change.
Do: try an authorized change on a manageable scale and record what happens.
Check: compare results with the prediction, including quality and unintended effects.
Act: adopt and document an improvement, revise an uncertain idea or undo an unsuccessful change; begin the next cycle.
A useful result may be that the idea did not help. Keep that evidence rather than declaring success because something changed.
Use standard work as a baseline that can improve; Checklist
Use standard work as a baseline that can improve
Standard work records the current agreed method so people can repeat it and recognize departures. State the sequence, relevant timing, checks and materials needed. In repetitive production, standardized work also relates the sequence and required in-process stock to the pace of customer demand.
When an improvement is demonstrated, update the method and help everyone learn it. Do not bypass safety requirements or change controlled specifications as an informal experiment.
Record the problem and starting measure.
Describe one change and the expected result.
Test within applicable authorization and safety requirements.
Compare results and effects on other people or steps.
Update the agreed method if the evidence supports the change.
Sort machine tools by how they remove material, then follow the process that fits the feature.
Start with what removes the material
Start with what removes the material
A machine tool controls motion between a tool and the workpiece, the part being made. In material removal, the final shape is what remains after unwanted material is taken away.
This is a teaching map of removal mechanisms. Abrasives also make small chips; the branches distinguish the kind of tool or energy doing the work.
CNC is a control method, not a removal family. Computer numerical control can guide a mill, lathe, grinder, EDM machine or cutting jet. See G-code and Toolpaths. Forming moves material without removing it; see Manufacturing Process Categories for the wider manufacturing map.
Conventional cutting uses defined cutting edges
Conventional cutting uses defined cutting edges
Turning rotates the work past a cutting tool; milling rotates the cutter and feeds it relative to the work.
Drilling makes holes; sawing separates stock, the starting material, with successive teeth.
Broaching uses a sequence of teeth to progressively cut a profile, such as a keyway. Dedicated tooling often suits repeated production, but broaching is not limited to large runs.
Shaping and planing use a back-and-forth straight cutting stroke. A shaper normally moves the tool; a planer normally moves the work.
A process name describes the action, not every possible shape. Milling can make curved contours as well as flat faces.
Abrasive processes use many small cutting grains
Abrasive processes use many small cutting grains
Grinding wheels hold abrasive grains that remove material. Precision grinding controls size and surface texture, often on hardened parts. Grinding can also remove substantial stock; it is not restricted to light finishing.
Honing commonly uses abrasive stones with combined motions to refine a bore's size, form and surface. Lapping uses fine abrasive between a lap and the work to refine a surface. Neither is simply another name for grinding.
Nontraditional processes change the removal mechanism
Nontraditional processes change the removal mechanism
Thermal:EDM, laser and plasma remove material with concentrated heat. EDM's energy supply is electrical, but its removal mechanism is thermal.
Electrochemical:ECM uses electric current to dissolve metal.
Match the tool to the feature, the allowed size range, and the measurement you need to trust.
Choose from the tolerance and the shape of the feature
Choose from the tolerance and the shape of the feature
Start with what must be measured: an outside size, an opening, a depth, a height, or a small change from a reference.
As a rule of thumb, choose a tool that reads about ten times finer than the total tolerance. This is a starting point, not a standard or a guarantee that the measurement is good enough. Check its specified accuracy, condition, measuring range, and the way its contacts reach the part.
For a size of 0.625 ± 0.001 in, the total tolerance is 0.002 in. A starting resolution target is 0.002 / 10 = 0.0002 in. An outside micrometer reading 0.0001 in is a candidate for an accessible outside diameter. A 0.001 in caliper is too coarse for that rule of thumb.
Resolution is the increment; accuracy is agreement with a reference
Resolution is the increment; accuracy is agreement with a reference
Resolution
The smallest indicated change or scale increment. A display that changes by 0.0005 in has that resolution; its last digit is not an accuracy certificate.
Accuracy
How closely a measurement agrees with the reference value. Use the instrument's error specification and checks against suitable standards to judge its capability.
Precision
How closely repeated measurements agree under stated conditions. A dirty measuring face can give repeatable readings that are all wrong.
Extra digits cannot remove jaw wear, a tilted contact, dirt, or heat. Record the instrument and units along with the result when the measurement matters.
Use a steel rule for layout and quick size checks
Use a steel rule for layout and quick size checks
A steel rule is useful for stock lengths, approximate sizes, and setting a divider. Read the graduation pattern on the edge you are using: fractional edges may divide an inch into 8, 16, 32, or 64 parts; decimal edges may use 0.1, 0.05, 0.02, or 0.01 in increments. A decimal rule does not ordinarily have 0.001 in graduations.
Place the rule along the distance being measured and look straight at the marks. A damaged end is a poor zero. If you start at the 1 in line instead, subtract 1 in from the far-end reading. Do not use a rule to accept a feature with a tight size tolerance.
Calipers cover outside, inside, depth, and step measurements
Calipers cover outside, inside, depth, and step measurements
Dial, digital, and vernier calipers use a sliding jaw. The larger jaws measure outside sizes; the smaller jaws measure openings. A depth rod reaches down from the end of the beam. On tools with step faces, the back shoulders measure a step.
The readout changes how you read the tool, not how carefully you must position it.
Readout
Use and reading
Watch for
Dial
Quick mechanical reading: beam scale plus dial remainder.
Check the marked value per revolution. Dirt in the rack can disturb the reading.
Digital
Direct numerical display; often offers inch/mm and relative zero.
Confirm units and zero mode. Resolution varies by model; a common display increment is 0.0005 in / 0.01 mm.
Vernier
Main scale plus the aligned vernier division; no battery or dial mechanism.
Read the correct scale and its least count. Inch 0.001 in tools can use different main-scale spacings.
Use light contact and keep the jaws square. Measure near the beam where access allows. Long jaws can flex; small inside jaws may not reach the true diameter of a small hole. A caliper's versatility does not make it the best tool for every tolerance.
Micrometers specialize in outside sizes, inside sizes, or depths
Micrometers specialize in outside sizes, inside sizes, or depths
An outside micrometer measures between a fixed anvil and a moving spindle. Choose a range that contains the dimension: a 1–2 in instrument does not start from zero like a 0–1 in instrument. A conventional inch scale reads 0.001 in; a sleeve vernier can add 0.0001 in readings. A conventional metric scale reads 0.01 mm. Digital models differ.
The sleeve supplies the coarse reading; turning the thimble moves the spindle. The ratchet or friction device helps control contact force.
An inside micrometer spans an opening using internal contacts. Rod and two-point types require careful alignment; three-point types have a different contact arrangement. Check the reference and any extension length for the actual tool.
A depth micrometer rests its flat base on the reference face and extends a rod to the lower surface. Keep the base seated. Check the installed rod's range and the scale direction: many depth scales run opposite to an outside micrometer. Do not add a rod length without checking how that instrument is marked.
Indicators show change from a reference
Indicators show change from a reference
A dial indicator commonly has a plunger moving along its axis. A test indicator has a pivoting lever stylus and usually a shorter measuring range. Both are useful for alignment, comparing heights, and observing runout as a part turns.
Read the marked graduation and count revolutions where needed. Zeroing the bezel sets a reference; it does not turn the indicator into an absolute diameter tool. Total indicator reading, or TIR, is the maximum indication minus the minimum during a sweep. From −0.001 to +0.002 in, TIR is 0.003 in.
Use a rigid stand. A magnetic base needs a suitable magnetic support; it will not attach magnetically to granite. For plunger indicators, align motion with the plunger. For lever test indicators, follow the maker's stylus-angle instructions; the lever is normally close to parallel with the surface. These are different geometries.
Supporting detail: Addendum 177 — What a sweep can and cannot establish.
Gauge blocks supply a reference; transfer gauges carry a size; Practice
Gauge blocks supply a reference; transfer gauges carry a size
Gauge blocks have accurately finished opposing faces and a known length. Use suitable blocks to set a height, compare a measurement, or check an instrument. Clean and inspect the faces before wringing blocks together; follow their care instructions. A zero check alone is not a full calibration.
Build stacks from sizes actually present in the set. For example, 1.0000 + 0.1340 + 0.1005 = 1.2345 in uses three blocks if those sizes are available. Do not assume a set contains separate 0.0040 or 0.0005 in blocks.
A telescoping gauge transfers a bore size to an outside micrometer. With light locking friction, set the contacts slightly across the bore at an angle and sweep gently through the diameter; withdraw without changing the setting, then measure across the contacts. Follow the tool's instructions for locking and repeat until the technique is consistent.
A small-hole gauge expands rounded contacts inside a smaller opening. Adjust for light drag, withdraw as its design permits, and measure across the contacts with a micrometer. Neither transfer tool has its own numerical readout. Take readings at several depths and directions; keep them separate to reveal taper or out-of-roundness rather than averaging the shape away.
Read rules, micrometers, calipers, and verniers by separating the coarse scale from the remainder.
Read the unit and the graduation before the number
Read the unit and the graduation before the number
The same-looking line can mean 0.025 in, 0.5 mm, or something else. Identify the instrument and its scale before adding anything.
On a fractional rule, count spaces from the last whole inch using that edge's denominator. Seven 1/16 in spaces beyond 2 in gives 2 + 7/16 = 2.4375 in. That exact fraction-to-decimal conversion does not make the rule accurate to four decimal places.
On a decimal rule with 0.01 in spaces, eight spaces beyond 1.20 in gives 1.28 in. On a digital caliper, read the displayed unit and confirm whether the tool shows an absolute size or a deviation from a stored zero.
In inch shop speech, a thou is 0.001 in and a tenth often means 0.0001 in, one tenth of a thousandth. Write units and decimals to avoid confusing a shop tenth with 0.1 in.
An inch micrometer adds sleeve plus thimble
An inch micrometer adds sleeve plus thimble
For the conventional 0.001 in micrometer, one turn advances the spindle 0.025 in. The sleeve has a line every 0.025 in; each fourth line marks another 0.100 in. The thimble divides one turn into 25 spaces of 0.001 in.
Read the last sleeve line reached by the thimble edge. Count the 0.100 in intervals and the extra 0.025 in lines.
Read the thimble line at the sleeve's horizontal datum line.
Add the two. Include the range offset for a larger micrometer according to its markings.
Example: sleeve 0.300 in plus two 0.025 in lines, with thimble 18 at the datum:
0.300 + 0.050 + 0.018 = 0.368 in
Watch the rollover. Sleeve 0.375 and thimble 24 gives 0.399 in. The next 0.001 in step gives sleeve 0.400 and thimble 0: 0.400 in. Do not add the old 0.025 in interval again.
A vernier micrometer adds the fourth decimal place
A vernier micrometer adds the fourth decimal place
The sleeve vernier divides a thimble space into ten parts. Read the sleeve and the whole 0.001 in thimble amount first, using the thimble graduation just passed when the datum falls between lines. Then find the sleeve vernier line that aligns with a thimble line.
Example: the last sleeve line is 0.450 in, the datum is between thimble 12 and 13, and sleeve vernier line 7 aligns:
0.4500 + 0.0120 + 7 × 0.0001 = 0.4627 in
The matching vernier line adds 0.0007 in, not 0.007 in. Do not round the thimble to 13 and then add the vernier. If the zero line aligns, add zero; the end line represents the same alignment at the next interval.
A metric micrometer includes the exposed half millimeter
A metric micrometer includes the exposed half millimeter
On a conventional 0.01 mm micrometer, one turn moves the spindle 0.5 mm. The sleeve shows whole millimeters and half-millimeter marks; 50 thimble spaces divide the turn into 0.01 mm increments.
If 8 mm and the following 0.5 mm mark are exposed, and thimble 23 aligns, the reading is 8 + 0.5 + 0.23 = 8.73 mm. If that half-millimeter mark is still covered, the same thimble position gives 8.23 mm.
At the rollover, 8.49 mm is sleeve 8.0 plus thimble 49; 8.50 mm is sleeve 8.5 plus thimble 0. Use the marked unit; these increments are not the inch micrometer's increments converted by eye.
A 0.001 in vernier caliper adds the aligned division
A 0.001 in vernier caliper adds the aligned division
For the 25-division inch vernier used here, each main-scale space is 0.025 in. Twenty-five vernier spaces occupy the length of 24 main-scale spaces, so each vernier space is 0.024 in. Their 0.001 in difference makes the fine reading possible.
The shortened diagram shows the first few lines of a 25-division scale. The mismatch accumulates by 0.001 in per division.
Read the last main-scale line at or before the vernier zero.
Find the vernier division that lines up with a main-scale line.
Add its division number × 0.001 in.
Vernier zero just beyond 1.325 in, with division 17 aligned, gives 1.325 + 0.017 = 1.342 in. It is the vernier zero, not the right end of the slider, that locates the coarse reading.
Supporting detail: Addendum 179 — Other 0.001 in verniers can have different spacing.
A dial caliper adds the beam reading and the dial remainder
A dial caliper adds the beam reading and the dial remainder
On an inch dial caliper marked 0.100 in per revolution, the dial's 100 divisions each represent 0.001 in. Read whole inches and completed 0.100 in intervals on the beam, then add the dial reading.
Beam 1.200 in and dial 47 gives 1.200 + 0.047 = 1.247 in. Beam 1.200 plus dial 99 is 1.299 in. At the next thousandth the beam reaches 1.300 and the dial returns to zero.
Some dial calipers use a different travel per revolution. Check the dial markings rather than assuming this example applies. Clean the jaws, close gently, check zero, and confirm the reading again after measuring.
Practice reading a new micrometer or vernier scale; Interactive; Practice
Practice reading a new micrometer or vernier scale
The trainer draws ideal scales with zero error. It teaches reading, not instrument accuracy. Micrometer examples stay within 0–1 in; caliper examples stay below 2 in. Enter the exact indicated reading in inches.
Read these scale positions before uncovering the answers. These examples also serve as the print version of the trainer.
Inch micrometer: sleeve 0.275 in, thimble 24 at the datum.
Vernier micrometer: sleeve 0.275 in, datum between thimble 24 and 0, vernier line 9 aligned.
25-division vernier caliper: zero past main line 1.150 in, division 8 aligned.
Readings as sums
1. 0.275 + 0.024 = 0.299 in. 2. 0.2750 + 0.0240 + 0.0009 = 0.2999 in. 3. 1.150 + 0.008 = 1.158 in.
Control zero, contact force, alignment, cleanliness, and temperature before trusting the last digit.
Clean, check, measure, and check again; Checklist
Clean, check, measure, and check again
A good reading starts before the scale is read. Use this sequence with the instrument's own instructions.
Identify the feature, its limits, and its reference surfaces. Choose a suitable measuring tool.
Clean the contact faces and the part. Look for chips, dirt, raised burrs, and damage that would hold the contacts apart.
Let the part and instrument settle to the measuring environment. Avoid a freshly cut hot part or a tool warmed by long handling.
Check zero or the correct setting reference. Close a 0–1 in outside micrometer gently; use the appropriate setting standard for larger ranges or inside tools.
For a critical size, check a suitable known reference near the working size as well. Confirm the instrument is within its required calibration status.
Measure with the intended contact force and alignment. Release and repeat to check that you can reproduce the reading.
Record the result with units, location, and enough method information to repeat it. Check zero again afterward; investigate any change.
Zero adjustment removes an offset at one position. It cannot repair worn jaws, a damaged screw, or an error that changes along the range. If a tool fails its checks, have it evaluated rather than hiding the error with a new zero.
Use consistent light contact instead of squeezing out a number
Use consistent light contact instead of squeezing out a number
With a micrometer, bring the faces close, then use the ratchet or friction thimble as its maker directs. These devices help repeat the measuring force. They do not make dirt, tilt, or a flexible part disappear.
Use a smooth, slow approach. The required clicks or turns depend on the mechanism; a friction thimble may slip without clicking. Do not force the main thimble after the force-limiting device operates. The spindle lock holds a setting; it is not a clamp for tightening the measurement.
With a caliper or transfer gauge, feel means consistent light contact or drag, not a hard squeeze. Too much force bends jaws and compresses thin parts. Repeated readings should agree because the setup is repeatable, not because the tool has been forced to the expected number.
Keep contacts square and look straight at the scale
Keep contacts square and look straight at the scale
A tilted instrument can span a diagonal rather than the intended distance. For an outside diameter, keep the measuring direction perpendicular to the cylinder's axis. For a two-point inside measurement, the contacts must pass through the bore center in the cross-section while staying square along its length. A single instruction to “always find the largest” or “always find the smallest” does not cover both alignment directions.
Parallax is a reading error from looking at separated scales at an angle: the marks appear to shift against each other. Put your eye square to the reading line. Good lighting helps distinguish a line from a reflection.
For an indicator, keep its intended motion and contact geometry aligned. Preload enough to maintain contact throughout the expected movement, while staying within its usable travel. Do not apply a universal number of needle turns to both plunger and lever instruments.
Abbe error grows when tilt acts through an offset
Abbe error grows when tilt acts through an offset
The scale on a caliper runs along the beam, while the part often touches farther down the jaws. If the moving jaw tilts a little, its tip moves more than the scale location does. The scale misses that extra motion. This is Abbe error.
Picture a door: a small rotation moves the handle much farther than a point near the hinge. Greater distance between the measurement line and the scale line gives tilt more room to create error.
Keep the part near the beam when access permits, use light contact, and avoid loose or worn sliders. An ordinary outside micrometer puts its measurement and screw axes in line, reducing this particular source of error. Alignment still matters.
Supporting detail: Addendum 181 — The offset-and-angle relationship.
Temperature and surface condition can move the result; Practice
Temperature and surface condition can move the result
Parts and instruments change size with temperature. Let them approach the same stable measuring conditions; follow the reference temperature and corrections required by the inspection procedure. Avoid direct sun, drafts, and prolonged hand contact with precision tools.
Clean contact faces matter because the instrument measures what touches them. A chip can enlarge an apparent outside size; a raised edge can hold a depth-micrometer base above its reference. Surface peaks can affect contact too. See Surface Texture and Finish for surface condition rather than treating every last-digit change as a size change.
Measure at several positions when taper or out-of-roundness matters. Keep the individual values. An average can hide an oversize region and does not prove the whole feature meets its limits.
In this invented classroom example, each value is a local diameter reading in a 20 mm-deep bore. Near, middle, and far name axial stations 2, 10, and 18 mm from the entry face. X and Y are two marked perpendicular diametral directions at each station.
Invented classroom local-diameter readings; treat the stated values as exact
Axial station from entry face
Diametral direction
Local diameter (mm)
Near — 2 mm
X
20.000
Near — 2 mm
Y
20.002
Middle — 10 mm
X
20.001
Middle — 10 mm
Y
20.003
Far — 18 mm
X
20.004
Far — 18 mm
Y
20.026
For stated limits of 19.980 to 20.020 mm, the six-reading mean is 120.036 / 6 = 20.006 mm, inside the limits. The far-depth Y reading is 20.026 mm, above the stated upper limit. Keep that location with the value: the in-limit average does not make the sampled high reading disappear. These six local readings do not establish the size or form of the unsampled bore.
Carry dimensions from a reference onto the work with clear lines, checked centers, and correctly read angles.
Start layout from a reference you can return to
Start layout from a reference you can return to
Layout places lines, arcs, and points on a part to guide cutting or locate features. A neat line is useful only when it is in the right place.
Identify the reference surfaces from which dimensions are taken. Keep using those references rather than measuring each new line from the last one. A layout mark guides the work; it does not prove the finished part is within tolerance.
A surface plate supplies a reference plane for layout and inspection. Clean the plate, the part's supporting face, and the tool base. Support the part so it cannot rock. Use an appropriate angle plate or V-block when the shape needs support.
Protect the plate from impact and abrasive work. Its flatness depends on its size, grade, condition, and calibration; “a surface plate” does not imply one universal accuracy. Follow its specified support arrangement. Level and flat are different: leveling a plate does not repair a worn surface.
Dye makes a fine scribed line easier to see
Dye makes a fine scribed line easier to see
Layout dye adds contrast. Prepare the surface, apply a thin coating as directed, and let it dry before marking. Use Chemicals and Safety Data Sheets for chemical handling guidance.
A scriber scratches a narrow line through the coating. Hold the guide firmly and draw the point along it with light, consistent pressure. Repeated passes can make a wide, ambiguous mark. Scribe only where the drawing and process allow a permanent scratch.
A surface gage carries an adjustable scriber at a fixed height above its base. Set it from a separate height reference, then move the base along the plate to scribe a line parallel to that plane. A surface gage ordinarily has no direct height scale.
A height gage adds a scale or readout. Set its reference correctly, seat the base flat, set and lock the height as intended, and make the line. With a suitable probe it can compare or measure heights. It is not simply another name for a depth gage.
Supporting detail: Addendum 182 — Finding the middle of two heights.
Dividers and trammels carry a distance into an arc
Dividers and trammels carry a distance into an arc
Dividers have two pointed legs. Set their spacing from a suitable scale, hold one point at the center, and swing the other to mark a circle or arc. They can also transfer or step off equal distances.
Trammels put adjustable points on a beam for radii too large for ordinary dividers. Lock the points after setting, support the beam, and check the spacing again before marking.
The point spacing is the radius, not the diameter. For a 3.00 in diameter circle, set 1.50 in between points. Recheck transferred dimensions against the original reference; repeated stepping can accumulate error.
Prick-punch the location; center-punch after checking it
Prick-punch the location; center-punch after checking it
A prick punch has a sharper point for a small, precise location mark at intersecting layout lines. A center punch makes a wider depression to help start a drilling operation. Point angles vary by tool; the important distinction here is the fine locating mark versus the wider starting mark.
Locate the point carefully, bring the punch upright, and make a light mark. Check the location before enlarging it. A heavy first mark is difficult to correct. Support the work on a suitable punching support, away from the precision surface plate.
A punch mark is not a substitute for the machine setup or spotting method needed to locate a hole accurately. Check the finished feature with a suitable measuring method. Use Personal Protective Equipment and Equipment Operating Procedure for the applicable shop rules.
Supporting detail: Addendum 183 — Punch types and their uses.
A combination set uses one blade with three different heads
A combination set uses one blade with three different heads
Square head
Provides 90° and 45° reference faces. With the blade it can lay out right angles, check squareness, or establish an offset or depth. Seat the reference face fully before reading or scribing.
Center head
Its two faces seat on round stock, positioning the blade along a diameter. Scribe one line, rotate the work or head, and scribe another; their intersection locates the center on the end face.
Protractor head
Sets the blade to an angle on a graduated head. Read the scale in the correct direction, lock the setting, and recheck contact with the reference.
Clean the mating faces and blade groove so the head seats properly. Pick the tool's accuracy for the task: a combination set is useful for layout, but it does not automatically replace a precision square or a finer angle instrument.
A universal bevel transfers an angle; a vernier protractor reads it; Practice
A universal bevel transfers an angle; a vernier protractor reads it
A universal bevel has an adjustable blade and stock that can fit against two surfaces. Lock it to transfer or compare an angle. A plain bevel has no numerical scale; obtain the angle from a separate reference.
A vernier bevel protractor combines the adjustable blade with degree and vernier scales. On a 5-minute instrument, each matching vernier division adds 5 arcminutes. 60 minutes = 1 degree, so 5 minutes is 1/12 degree. This is the reading increment, not a universal accuracy claim.
Seat the stock and blade against the intended surfaces. Identify the angle being measured.
Read the whole degrees between the main zero and the vernier zero.
Use the vernier on the same side and in the same reading direction as those degrees. Find the matching division.
Add the matching division number × 5 minutes to the whole degrees.
Example: 32 whole degrees and the seventh matching vernier division give 32° + 7 × 5′ = 32°35′. That is 32 + 35/60 = 32.5833…°, not 32.35°.
Check the contact geometry before reporting an obtuse angle. If the instrument has measured the acute supplement, a reading of 32°35′ corresponds to 180° − 32°35′ = 147°25′ for the required obtuse angle. Do not automatically subtract every reading from 180°.
Drawing views and dimensioning conventions belong in the Engineering Graphics collection. Layout follows those requirements; it does not redefine them.
Machining/Cutting Fluids
Cutting Fluids and Application Methods
Cutting fluids cool, lubricate, carry chips away and protect surfaces; match the fluid and its delivery to the tool, material and operation.
Cool the cut, reduce friction and carry chips away
Cool the cut, reduce friction and carry chips away
Coolant does more than cool. A cutting fluid removes heat from the cutting zone, lubricates contact between the tool, chip and workpiece, flushes loose chips away, and helps protect the machine and work against corrosion.
Lubrication can reduce material sticking to the cutting edge, called built-up edge. Together with cooling and chip removal, that can improve surface finish and dimensional control. Fluid cannot make up for a dull tool, poor workholding or unsuitable feeds and speeds.
The fluid must reach the cutting zone to do its job. A full tank with a blocked filter or a nozzle aimed away from the cut is not effective delivery.
Choose a fluid family for the operation
Choose a fluid family for the operation
Use a product approved for the machine, work material and tooling. These are general tendencies, not a product selection chart for a particular shop. Check compatibility with seals, coatings and the metals being cut.
Family
Strength and typical use
Tradeoff
Straight oil (neat oil)
Used without water dilution. Strong lubrication suits operations where sliding contact dominates, such as some tapping, broaching and slow cutting.
Less cooling than water-based fluids; oil mist, smoke and fire risk depend on the product and process. Not suitable for every machine.
Soluble oil (emulsion)
Concentrate disperses oil droplets in water. Combines lubrication with water's cooling for many general machining operations.
Needs concentration and contamination control. Water quality affects stability; residue and foam can develop.
Semi-synthetic
A water-diluted formulation with less mineral oil than a conventional soluble oil. Often balances cooling, lubrication and cleanliness in general machining.
Still needs water-quality and sump maintenance. Foam, residue and compatibility depend on the formulation.
Synthetic
A water-diluted formulation without mineral oil. Cooling and visibility can suit grinding and suitable machining operations.
Lubrication depends on its additives; do not assume all synthetics suit heavy cutting. Concentration, corrosion protection and contamination still need attention.
Concentrate and working fluid are different. A supplier's oil-content figure for the concentrate is not the percentage to put in the tank. The working concentration comes from that product's technical data sheet.
Supporting detail: Addendum 185 — Why the family name does not settle performance.
Run dry, mist or flood according to the cutting setup
Run dry, mist or flood according to the cutting setup
Dry: use when the tool supplier's guidance for that material and operation calls for it. Some carbide milling benefits from avoiding repeated heating and sudden cooling of the edge. Dry does not mean chips or dust need no control.
Mist or minimum-quantity lubrication: a designed system meters a small amount of fluid toward the cut when lubrication and access matter more than bulk cooling. It does not provide flood-level heat removal or washing. Use the specified enclosure and mist control.
Flood: a continuous flow can remove heat and wash chips from the cut when the setup calls for wet machining. Supply enough flow to reach the edge consistently; a weak, intermittent splash is not the same thing.
Oil mist is liquid droplets carried by air, not a residue-free gas. Neither “all carbide runs dry” nor “more coolant is always better” is a useful rule. Follow the tool and machine guidance for the actual cut.
Supporting detail: Addendum 186 — Why some milling runs dry while other milling needs fluid.
Read Brix, apply the product factor, and balance concentrate and water when mixing a fresh charge or correcting a partly full tank.
Zero the refractometer, then multiply Brix by the product factor
Zero the refractometer, then multiply Brix by the product factor
A refractometer measures how a sample bends light. On an analog Brix instrument, read where the light and dark areas meet. Brix is a scale reading; it is not automatically coolant percent.
Find the product's refractometer factor and working concentration range in its technical data sheet. Use the specified method for that product.
Clean the prism. Calibrate to zero with water, using the water and temperature procedure specified for the instrument and fluid. Fluid suppliers commonly specify the water used for mixing.
Remove the calibration water. Apply a representative, well-mixed coolant sample, close the cover and read the light/dark boundary. Avoid sampling a floating oil layer.
Calculate concentration (%) = Brix reading × product factor. Record the result and compare it with the product's range for the operation.
Clean the prism after use. Recheck a doubtful reading; contamination can blur the boundary or bias the result. Use the supplier's alternative test if the sample cannot be read reliably.
Read the boundary: 3.2 Brix. With an invented teaching factor of 1.5, concentration is 3.2 × 1.5 = 4.8%. That factor is not a shop recommendation.
There is no universal factor or target range. The SDS explains hazards and handling; the product's technical data sheet supplies the mixing and measurement information. See Chemicals and Safety Data Sheets.
Add concentrate to water, and state what the ratio means
Add concentrate to water, and state what the ratio means
Water first; add concentrate while mixing. Follow the product's mixing instructions in a clean container or approved mixing system. For emulsions, this lets the emulsifier disperse oil into the water. Adding water to a body of concentrate can form an unstable or inverted mixture that does not disperse properly.
Write the order of a ratio. 24 parts water to 1 part concentrate contains 25 total parts, so its concentrate percentage is 100 × 1 ÷ (24 + 1) = 4.00%. It is not 100 ÷ 24. For water:concentrate = W:1, use C = 100 ÷ (W + 1).
To make 12 L of that 4.00% premix, measure 0.48 L concentrate and 11.52 L water. Put the water in first. This is a volume-based teaching example with additive volumes, not a product recommendation.
Supporting detail: Addendum 188 — Why mixing order matters.
A falling level does not tell you how strong the coolant is
A falling level does not tell you how strong the coolant is
Measure both level and concentration before topping up. Evaporation mainly removes water, raising concentration. Coolant carried out on parts and chips removes both water and concentrate. Adding plain water lowers concentration.
A tank below the target is lean; one above it is rich. Compare with the actual permitted range before deciding it needs adjustment. A tank can be low in volume and rich in concentrate at the same time.
Top up fluid that is still serviceable. Persistent odor, separation, sludge or contamination calls for the evaluation and cleaning decisions in Coolant Condition and Tank Maintenance. New premix does not make spoiled fluid sound.
Calculate the premix needed to reach both target level and concentration; Interactive
Calculate the premix needed to reach both target level and concentration
Use the same volume unit throughout. Let V be the current tank volume, C its measured concentration, F the intended final volume, and T the target concentration. Concentrations below are entered as percent numbers, such as 6 for 6%.
Premix volume A = F − V
Premix concentration P = (F × T − V × C) ÷ A
Concentrate to measure = A × P ÷ 100. Water to measure = A − concentrate volume.
Example: a hypothetical tank has 36 L at 4.0%. Bring it to 48 L at an assumed target of 5.5%. Add A = 48 − 36 = 12 L. The premix must be (48 × 5.5 − 36 × 4.0) ÷ 12 = 10.0%: 1.2 L concentrate added to 10.8 L water.
Check the balance: the tank contains 1.44 L concentrate, the addition supplies 1.20 L, and 2.64 ÷ 48 × 100 = 5.5%. These assumed values teach the calculation; the product must permit the proposed makeup mix.
Stop when the result cannot be made. A must be positive. A negative P means even plain water cannot achieve the target at that final level; P above 100% asks for more concentrate than the addition can contain. A full tank has no top-up space. Seek an approved partial replacement or other correction instead of overfilling. Even a mathematical result between 0 and 100% may be outside the product's permitted mixing method.
Mix the approved addition separately, add it, circulate as specified, then measure again. The calculation assumes accurate volumes, uniform mixing and no losses during the adjustment.
5.00% concentrate 5 parts concentrate in 100 total parts. 95:5 = 19:1 water : concentrate.
Brix needs the product factor
6 Brix × an invented teaching factor of 1.0 = 6.00%. Use the actual product data sheet factor.
Correct a lean sump: account for the added volume
Teaching example: 100 L at 3%, target 5%, capacity 120 L. With x litres of neat concentrate, the balance is 3 × 100 + 100x = 5(100 + x).
x = 100(5 − 3) ÷ (100 − 5) = 2.1053 L. Final volume = 102.1053 L, within capacity. Check: (3 + 2.105263…) ÷ 102.105263… × 100 = 5.00%.
This is a concentrate balance, not an instruction to pour neat concentrate into a sump. Use the product-approved makeup method described on this page.
Predict what water replaces
Start with 100 L at 5%. Losing 20 L of well-mixed coolant leaves 80 L at 5%. Replace it with water: 4 L concentrate ÷ 100 L = 4%. Replace it with 5% premix: (4 + 1) ÷ 100 × 100 = 5%.
If instead only 20 L of water evaporates, all 5 L of concentrate remains: 5 ÷ 80 × 100 = 6.25%. Replacing that water restores 5%; adding 5% premix raises it to 6%. The loss mechanism matters.
Supporting detail: Addendum 189 — Derive the balance, or solve for an unknown addition volume.
Practice the reading, the ratio and the top-up balance; Practice
Practice the reading, the ratio and the top-up balance
Use fresh hypothetical values to check the method. Every question states its rounding and assumptions; none supplies a shop concentration recommendation.
The practice catalog contains the full Coolant Concentration and Mixing bank.
Machining/Cutting Fluids
Coolant Condition and Tank Maintenance
Recognize concentration drift and contamination, decide whether to top up or replace, and work through a general tank-cleaning sequence.
Look for oil, odor, solids and foam—not just a low level
Look for oil, odor, solids and foam—not just a low level
The sump is the reservoir that collects coolant for reuse. It also collects material that does not belong in the cutting fluid.
Tramp oil: unwanted lubricant leaking into the coolant, such as hydraulic oil or oil from sliding machine surfaces. Skim the floating layer and investigate its source; it can interfere with fluid condition and concentration readings.
Bacteria and odor: water-mixed fluids can support microbial growth. New or persistent bad odor is a reason to investigate, not a test that identifies the organism. Lack of odor does not prove the fluid is healthy.
Concentration drift: evaporation tends to make the tank richer; repeated water additions can make it lean. Measure using Brix and the product factor.
Chips and fines: chips settle and fine particles collect as sludge. They occupy tank space and can obstruct screens, filters and flow paths.
Foam: check concentration, water quality, contamination and air entering the delivery system. Foam is not a reliable concentration measurement.
Skin irritation: an overly strong mix can irritate skin; an overly weak mix can lose protection against microbial growth. Irritation is a reason to report exposure and investigate, not to guess a dilution.
Top up a serviceable tank; replace fluid that cannot be restored
Top up a serviceable tank; replace fluid that cannot be restored
Use a top-up when the existing coolant is fit for continued use and the problem is level or a correctable concentration. Choose the addition from the measured condition, not from the fresh-fill recipe. A rich tank may need a weaker makeup mix; a lean tank may need a stronger one.
Arrange a cleanout and replacement when contamination, unstable mixing or persistent odor cannot be brought under control by the approved maintenance process, or when the machine/fluid maintenance instructions require it. Investigate leaks and other causes so the fresh charge does not immediately inherit the problem.
Straining removes larger solids; it does not remove dissolved contamination or establish that drained fluid is reusable. Do not return rejected fluid just because it looks cleaner. Do not add household disinfectant or an unapproved chemical to mask odor.
Use the machine and fluid suppliers' maintenance intervals and condition checks. There is no universal calendar changeout interval or guaranteed sump life.
Clean the tank and its return path before refilling; Checklist
Clean the tank and its return path before refilling
Use this as a general sequence with the machine's approved maintenance procedure. Stop the machine and follow its isolation requirements before accessing the tank, pumps or chip-handling equipment. Only run pumps for a cleaning or circulation step when that procedure calls for it and the system is safely reassembled.
Removing old fluid without removing deposits leaves contamination ready to enter the fresh charge.
Stop and isolate the equipment as required by its maintenance procedure. Prepare suitable labeled receiving containers before opening or draining the system.
Skim accessible floating tramp oil. Drain or transfer coolant through a suitable strainer to catch larger chips, keeping the destination consistent with the reuse or waste decision.
Remove accumulated sludge and chips with the approved tools. Clean accessible screens, filters and return passages; inspect for blocked flow and leaks.
Clean dried coolant residue with a compatible cleaner diluted to its labeled instructions. Use the specified contact time and cleaning method; do not invent a stronger mixture.
Remove the spent cleaning solution. Rinse and drain as the machine, cleaner and fluid suppliers specify; capture those liquids for the approved waste route. Account for retained liquid before refilling.
Reinstall components and guards. Prepare fresh coolant by adding concentrate to water at the product's specified concentration, then fill to the machine's operating level.
Restore and circulate the system according to its procedure. Check flow and leaks, measure concentration after mixing, and record the fluid condition, result and service performed.
Use the safety pages for contact, PPE and waste handling
Use the safety pages for contact, PPE and waste handling
Minimize skin contact with coolant and cleaning liquid. Use the SDS for the actual products and the PPE guidance for exposure control. Use Metal Chips and Swarf for removing and handling solids; this maintenance page does not replace those rules.
Manage spent coolant, removed oil, sludge and cleaning liquid through the approved regulated-waste process. Do not pour them down a drain or onto the ground. The responsible waste handler must determine the applicable classification and disposal route from the fluid, contaminants and local requirements. “Water-based” or “biodegradable” is not disposal permission.
Supporting detail: Addendum 192 — Why the waste route depends on what is in the tank.
Machining/Sawing and Grinding
Cutoff Sawing
Choose a saw for the blank, hold the material securely, and leave enough material for the next operation.
Saw a blank with room for finishing
Saw a blank with room for finishing
Sawing often turns a long bar or a large plate into a manageable blank: the starting piece for machining. Plan both the material left for finishing and the kerf, the slot removed by the saw. Kerf is material lost between pieces; it is not finishing allowance.
Choose allowance from the required finished dimensions, cut quality, and later operations. A saw cut is not automatically a finished datum surface. Check dimensions and squareness before using it to locate the next cut. See Choosing Shop Measuring Tools and Shop Layout and Angle Measurement.
Match the saw's motion to the cut
Match the saw's motion to the cut
Saw
How it removes material
Typical use
Power hacksaw
A straight blade moves back and forth, cutting on one stroke and relieving on the other. Cutting-stroke direction depends on the machine.
Occasional straight cutoff work; the return stroke does no cutting.
Horizontal bandsaw
A continuous toothed loop advances through material clamped in a vise.
Bar, tube, and structural sections cut to length. Miter capability depends on the head or vise design.
Vertical bandsaw
The band passes through a table while the work is fed along a path.
Repeatable cutoffs where squareness and surface finish matter. Inspect for burrs even when the cut looks clean.
Abrasive cutoff saw
A thin abrasive wheel grinds through the section.
Cutoff work suited to the wheel's material rating, including some hardened materials. Heat and cut quality can require further finishing.
“Cold” distinguishes chip cutting from abrasive or friction cutting; it does not mean zero heat. Use Saw Blade Selection for toothed blades. An abrasive wheel has its own selection rules.
Hold every piece, including pieces in a bundle; Checklist
Hold every piece, including pieces in a bundle
NEVER hand-hold material for a horizontal saw cut. Use the machine's vise or a suitable fixture. Support long material at the saw's working height so it does not tilt the clamped piece. Arrange support for the cutoff without trapping the blade as the cut closes.
Nesting means arranging several pieces for one cut. Clamping the outside of a bundle does not prove that its inner pieces are held. Use a nesting arrangement and clamping system approved for the machine, and select the blade for the resulting section.
Identify the material, section shape, finished size, and finishing allowance.
Confirm that the vise or fixture grips each piece and that long stock is supported.
Account for the kerf when locating the cut or setting a length stop.
Plan how the cutoff will be supported as the blade breaks through.
After cutting, inspect the blank and remove the burr before the next setup.
Band speed is the distance the blade travels per minute, usually stated in feet/min or m/min. Feed is the rate or force that advances the blade into the work. They are different adjustments. Material grade and hardness, blade material, tooth geometry, and section shape all affect the starting settings.
Use the blade maker's cutting chart for the actual material, then follow the machine manual for setting it. Follow the blade maker's break-in procedure for a new blade. There is no single speed table or fixed percentage adjustment that fits every saw. Connect these terms to Feeds and Speeds.
On a saw designed to use cutting fluid, the fluid helps lubricate the cut, carry away heat, and clear chips. Use the approved fluid, concentration, and delivery method. Some abrasive cutoff systems are dry and others are wet; do not add coolant to a dry-only setup.
Supporting detail: Addendum 193 — Why finer teeth do not fix every bad cut.
Machining/Sawing and Grinding
Saw Blade Selection
Use section shape, teeth in the cut, tooth form, set, and blade material to narrow the choice before consulting the maker's chart.
Pitch spaces the teeth; gullets carry the chips
Pitch spaces the teeth; gullets carry the chips
TPI means teeth per inch along the blade. A higher TPI is a finer pitch. For evenly spaced teeth, pitch in inches is 1 ÷ TPI. The gullet is the hollow between teeth that provides chip space. Set is the sideways displacement of teeth, making clearance for the blade body in the kerf.
Pitch is measured along the blade. Set is seen from a different direction. Shapes are schematic.
Estimate teeth in the cut before choosing TPI; Interactive; Practice
Estimate teeth in the cut before choosing TPI
As a rule of thumb, aim to keep at least about three teeth engaged. For a uniform pitch crossing one continuous thickness of material:
Estimated teeth engaged = contact length in inches × TPI Minimum TPI for three teeth = 3 ÷ contact length in inches
Use thickness measured along the tooth line through solid material, not automatically the height of the part. For 0.25 in of continuous contact at 12 TPI, the estimate is 0.25 × 12 = 3 teeth. At the same thickness, the three-tooth calculation gives 3 ÷ 0.25 = 12 TPI.
Same tooth spacing, different contact length. The thinner section needs a finer pitch to meet the three-tooth estimate.
A calculated minimum is a screening value, not a blade specification. If it falls between available pitches, select a suitable finer option from the maker's chart rather than rounding down. Excessively fine teeth can run out of chip space in thick stock.
Supporting detail: Addendum 194 — Why the answer can be a fraction of a tooth.
Predict first: at mid-depth in the thin-wall tube below, would doubling TPI halve, double, or leave the estimated engagement unchanged? It doubles: the same contact length contains twice as many tooth spacings.
Dashed line = about three teeth; shading = below three. Each plot uses its own vertical scale.
Thin-wall tube, coarse blade
50.80 mm outside diameter; 1.00 mm wall; 6 TPI.
At depth 25.40 mm: 0.47 teeth across 2.00 mm of material. Across the cut: minimum 0.00; maximum 3.33 teeth.
Below the common rule of thumb of about three teeth.
Contact tends to zero at entry and exit. At mid-depth only the two walls count. The peaks occur where the blade touches the inside circle.
Thick solid bar, fine blade
50.80 mm contact thickness; 25.40 mm feed height; 24 TPI.
At depth 12.70 mm: 48.00 teeth across 50.80 mm of material. Across the cut: minimum 48.00; maximum 48.00 teeth.
At or above about three teeth here; this is not a blade approval.
Gullets may fill with chips; check the blade maker's guidance.
Estimated teeth = solid contact length ÷ tooth spacing; mm per tooth = 25.4 ÷ TPI. Readouts round to two decimal places; calculations keep the unrounded, real-valued estimate. Highlighted tooth tips illustrate one blade position, not a guaranteed integer count.
Round-section minima include the exact entry and exit tangencies, where contact is zero. A flat bar has constant contact through its feed height, including the limiting faces. Rotate the flat bar 90° to swap contact thickness and feed height; rotating a round bar or round tube about its axis changes neither. This model is a straight tooth line crossing an ideal section, with uniform pitch and no blade tilt.
The thick-bar, fine-blade preset highlights the full contact region as a reminder: gullets may fill with chips; check the blade maker's guidance. It sets no numeric upper limit. Tooth count alone cannot predict chip filling. For shop practice and hazards, see Cutoff Sawing and Safety collection.
A tube's outside diameter is not its solid thickness; Practice
A tube's outside diameter is not its solid thickness
A solid bar offers continuous material across the blade's path. A tube, angle, or channel presents walls and gaps, and the contact changes as the cut progresses. Select from a chart for tubes or structural sections, using wall thickness, overall dimensions, and orientation as that chart requires.
Thin walls generally need finer teeth than a solid bar of the same outside size. Do not multiply tube outside diameter by TPI and count the empty center as cutting engagement. Nor does simply adding two wall thicknesses describe every stage of a round tube cut.
Variable pitch alternates tooth spacing within a repeating group. It can reduce repeated tooth-impact vibration and suit changing engagement, but it still needs to match the material and section.
Common general-purpose form, typically with a zero rake face. Fine versions suit thinner sections.
Skip
Widely spaced teeth with generous gullets, typically zero rake; useful when softer materials and larger chips need clearance.
Hook
A positive rake face takes a more aggressive bite. Use where the maker recommends it for the material and the machine can support the cut.
Rake describes the angle of the tooth face that meets the material. Exact angles vary by blade; “hook” does not specify one universal angle.
Set pattern
Arrangement and use
Raker
A common sequence is left, right, straight. A general-purpose arrangement; the straight tooth is unset.
Alternate
Successive teeth are set left and right.
Wavy
Groups of teeth vary their sideways set in a wave. Common on fine-pitch blades for thin sections.
Set pattern does not replace pitch selection. Choose the complete blade specification, not a tooth-form name alone.
Choose blade material and dimensions for the machine
Choose blade material and dimensions for the machine
Carbon steel: an economical choice for suitable easy-to-machine materials and lighter service.
Bimetal: high-speed-steel cutting teeth joined to a flexible alloy-steel back; widely used for metal cutoff work.
Carbide-tipped: carbide cutting tips for applications needing greater wear resistance, with a compatible machine and cutting conditions.
Match blade length and thickness to the machine. Blade width, measured from tooth tip to back, also affects contouring; see Vertical Band Machining. Material name alone does not establish a blade's hardness limit or speed. Use the maker's product chart for the actual alloy and condition.
Supporting detail: Addendum 195 — Manufacturer resources for the next selection step.
Machining/Sawing and Grinding
Vertical Band Machining
Plan contour cuts around blade width and turning radius, and recognize the purpose of blade welding, band filing, and polishing attachments.
A vertical band follows a contour through the work
A vertical band follows a contour through the work
A vertical bandsaw supports the work on a table while a continuous band cuts through it. Moving the work along a marked path allows curved outlines as well as straight cuts. This can remove excess material before milling a profile.
A narrow blade can turn a tighter curve; a wide blade better resists wandering in a straight cut. Find the smallest radius on the intended saw path, then use the blade maker's width-versus-minimum-radius chart. Choose a width that fits both that path and the machine.
Radius is measured from the center of a curve to its edge; diameter is twice the radius. A chart's minimum radius is not a guarantee for every blade with that width: blade thickness and kerf clearance matter too. Do not force a wide blade around a tighter corner than its chart permits.
Supporting detail: Addendum 196 — Why relief cuts help with some outlines.
Blade welding closes the loop for some internal cuts
Blade welding closes the loop for some internal cuts
Blades may arrive as ready-welded loops. On equipment designed for it, a suitable open band can pass through a starting hole in the work and then be joined, making an internal contour accessible without a slot from the outside edge.
In general, blade joining involves preparing and aligning the ends, making a butt weld, heat-treating the joint as specified, finishing the weld flush, and inspecting it. The joint must flex around the wheels and pass through the guides. Follow the welder and blade maker's instructions for the exact sequence and settings; not every blade construction is suitable for a shop blade welder.
Supporting detail: Addendum 197 — Why joining includes more than making a weld.
Filing and polishing require their own bands and guides
Filing and polishing require their own bands and guides
Some band machines accept a file band to remove small amounts of material and refine a contour, or an abrasive band to smooth a surface. These are dedicated attachments with matching guides and operating instructions, not ordinary saw blades used differently.
Hold a part in a bench vise, saw by hand, choose and clean files, and remove burrs without losing the intended shape.
Use the vise to make the part steady
Use the vise to make the part steady
A bench vise holds the part while both hands control the tool. Clamp near the working area with enough material between the jaws to resist movement. Excessive projection makes the part flex and chatter. Use suitable soft jaw covers when the ordinary jaws would mark a finished surface, and support long pieces.
A conventional hand hacksaw cuts on the push stroke; Practice
A conventional hand hacksaw cuts on the push stroke
Install the blade with its teeth pointing away from the handle for the conventional push-cut setup, and tension it according to the frame's instructions. Choose pitch for the material actually crossed by the teeth: thin sections need finer teeth. Apply the three-teeth rule of thumb from Saw Blade Selection.
Start a shallow groove with controlled strokes. Once established, use long, even strokes that spread the work over the blade. Apply cutting pressure on the forward stroke and ease it on the return. Keep the blade aligned with the cut instead of twisting it to steer back to the line. Ease pressure as the cut nears completion and plan support for the separated piece.
File cut and coarseness are separate choices; Practice
File cut and coarseness are separate choices
A file removes small chips with many teeth. Choose its shape to reach the surface: flat for a flat face, round for a round opening, or half-round for both flat and curved areas. A safe edge has no cutting teeth, allowing work close to an adjoining surface that should remain uncut.
Cut pattern is not a coarseness grade. The drawing enlarges the tooth spacing for comparison.
Single-cut files have one family of parallel tooth cuts; they are useful for controlled finishing and draw filing. Double-cut files have crossing cuts that divide the teeth into smaller cutting points; they commonly suit faster stock removal.
Coarseness describes tooth spacing. Common grades run from rough, coarse, bastard, second-cut, smooth, to dead smooth, from coarser to finer. Availability varies. Compare grades within the same file family and length; the name alone is not a universal tooth-spacing measurement. “Second-cut” is a coarseness grade, not another name for double-cut.
Fit a suitable handle to a tanged file. For ordinary forward filing, guide the file with both hands, keep it level, apply pressure on the cutting stroke, and ease pressure on the return. Rocking rounds the edges of a surface intended to stay flat. Check progress frequently rather than filing past size.
For draw filing, hold a suitable single-cut file crosswise to the work and move it along the surface, with its length across the direction of travel. Use light, controlled pressure and orient it so the teeth cut on the working stroke. This helps blend marks and refine a flat surface.
Chips lodged in the teeth are called pinning; they can scratch the work. Clean with a file card, brushing with the tooth grooves to clear trapped chips. Store files so their teeth do not rub against other tools.
Supporting detail: Addendum 198 — File selection and care resources.
Remove the burr without changing the required edge
Remove the burr without changing the required edge
Deburring removes the thin unwanted lip left by cutting. Use a file for accessible straight edges, a suitable swivel-blade deburring tool for edges it can follow, or a suitable countersinking tool for a hole entrance. Match the cutter to the material and edge shape.
Take light passes and inspect the result. Removing a burr does not authorize a large chamfer or a rounded edge. Preserve the drawing's dimensions and edge requirements; if an edge break is specified, make that feature deliberately.
Scribers mark; hammers and punches move or indent material
Scribers mark; hammers and punches move or indent material
A scriber makes a fine line with a hard point. Use it for the marking method described in Shop Layout and Angle Measurement, rather than as a substitute for a punch.
A ball-peen hammer supplies controlled blows for appropriate metalworking tasks. A soft-face hammer can reduce surface marking when positioning a part; it does not guarantee that a delicate surface will be unmarked.
A center punch makes an indentation for locating a drill start. A pin punch drives a pin with a flat-ended tip sized for that pin. Choose the tool for the task: the pointed center punch is not a pin driver. Detailed measuring and layout procedures belong in Shop Layout and Angle Measurement.
Machining/Milling
Vertical Mill Anatomy and Motion
Identify what moves on a knee mill or bed mill, and distinguish spindle rotation, quill travel, head tram and part coordinates.
The cutter rotates; feed changes its position relative to the work
The cutter rotates; feed changes its position relative to the work
A vertical mill has a spindle whose axis is vertical in its normal setup. The spindle rotates the tool. The head carries the spindle and its drive; the column supports and guides the machine assemblies. The table carries the workholding.
Do not picture the workpiece as fixed in space. Depending on the machine, the table, head, or both move to feed the rotating cutter through the work. On a typical three-axis vertical mill, X is left–right, Y is front–back, and Z is along the vertical spindle axis.
A CNC position describes the tool relative to the work. A table moving left can therefore produce tool motion to the right relative to the part. Confirm the machine's jog directions and readout before locating a feature. Continue with Milling Operations for what those movements cut.
A knee raises the table; a bed mill supports it without a rising knee
A knee raises the table; a bed mill supports it without a rising knee
Assembly
Typical knee mill
Typical bed mill
Table
Travels along X on the saddle.
Supported by the bed and slides; often travels along X.
Saddle
Travels along Y on the knee.
May provide Y travel beneath the table; layouts vary.
Vertical positioning
The knee raises or lowers the saddle and table.
The head commonly travels vertically on the column.
Quill
A sliding sleeve gives the spindle a shorter axial feed, useful for drilling and fine depth adjustment.
May be absent; the head's Z motion provides the feed.
Identify the actual moving assemblies. “Bed mill” does not mean that every machine assigns Y travel to the head. CNC describes how motion is controlled, not whether the machine has a knee.
The setup checklist follows a Tormach workflow. Use the manual for the installed machine to identify controls and travel; a familiar brand name does not establish its spindle interface, options or limits.
Head tram and vise squareness check two different alignments
Head tram and vise squareness check two different alignments
Tram is the spindle axis's perpendicular alignment to the table in both left–right and front–back directions. An indicator carried around the spindle axis compares points on the table at the same sweep radius. This is an alignment check with spindle power off; head adjustment belongs to the machine-specific procedure.
Squaring the vise makes its fixed jaw parallel to an axis of table travel. It uses a straight sweep along the jaw, not a circular sweep over the table. A square vise does not prove the head is in tram, and a trammed head does not prove the vise is square. See Milling Vises and Strap Clamps.
Supporting detail: Addendum 199 — Why facing can reveal a tram problem.
Machining/Milling
Milling Vises and Strap Clamps
Seat and align a milling vise, support work on parallels or soft jaws, and understand how strap-clamp position divides the clamping force.
Clean contact surfaces before tightening anything
Clean contact surfaces before tightening anything
A vise locates the part against its fixed jaw; the moving jaw supplies the grip. Clean the table and underside of the vise before mounting it. Clean the jaw faces, vise bed, supports and part before loading. A chip trapped underneath changes the position you are trying to establish. Remove raised burrs without rounding away a locating surface.
Choose a grip that leaves access for the cutter while supporting the cut. A part perched high above shallow jaw contact is a different setup from a part seated low in the vise. For the operating rules that govern this work, use Equipment Operating Procedure and Machine Hazards and Housekeeping.
Sweep the fixed jaw, adjust, tighten, then sweep again; Interactive; Practice
Sweep the fixed jaw, adjust, tighten, then sweep again
Mount the vise with its fasteners engaged. Snug one mounting point enough to act as a pivot and leave the other adjustable.
Mount an indicator rigidly with the spindle stopped. Contact a clean, undamaged part of the fixed jaw's locating face with some preload. See indicator setup.
Choose a convenient reference near one end; zero there if it makes comparison easier. Traverse so the contact point follows the jaw toward the other end, keeping contact height and indicator orientation unchanged. Alignment comes from the differences across the sweep, whether or not you re-zero.
Read the difference, then tap the adjustable end of the vise body lightly with a suitable soft mallet. Sweep again. Use the demonstrated indicator response to choose the direction.
Tighten the mounting fasteners to the vise/mounting instructions and repeat the full sweep. Accept the setup against the job's alignment requirement, not an invented universal tolerance.
First use: apply the same small corrective rotation about different illustrative pivots. The tilt can disappear while both ends settle at different common offsets; re-zeroing afterward is optional convenience.
Rotate about a chosen illustrative pivot
Before: +0.060 mm tilt, old zero at the left
Measuring span 0–100 mm; 1 mm face marginsStored zero at 0.000 mmNext pivot P=(25.000, 0) mmAccumulated |d| 0.0000 / 0.0040 mm/mmLeft reference 0.000 mmCenter reference +0.030 mmRight reference +0.060 mmRight − left +0.060 mmModel summary — full sweep range 0.060 mm
After −0.0006 about 25 mm: both ends +0.015 mm
Measuring span 0–100 mm; 1 mm face marginsStored zero at 0.000 mmNext pivot P=(25.000, 0) mmAccumulated |d| 0.0006 / 0.0040 mm/mmLeft reference +0.015 mmCenter reference +0.015 mmRight reference +0.015 mmRight − left 0.000 mmModel summary — full sweep range 0.000 mm
Optional convenience: re-zero at 50 mm
Measuring span 0–100 mm; 1 mm face marginsStored zero at 50.000 mmNext pivot P=(25.000, 0) mmAccumulated |d| 0.0006 / 0.0040 mm/mmLeft reference 0.000 mmCenter reference 0.000 mmRight reference 0.000 mmRight − left 0.000 mmModel summary — full sweep range 0.000 mm
The rotation removes the linear tilt while the chosen pivot determines the common offset. Re-zeroing changes the displayed references, not the alignment.
Equal endpoints can hide a local high spot
Measuring span 0–100 mm; 1 mm face marginsStored zero at 0.000 mmNext pivot P=(25.000, 0) mmAccumulated |d| 0.0000 / 0.0040 mm/mmLeft reference 0.000 mmCenter reference +0.080 mmRight reference 0.000 mmRight − left 0.000 mmModel summary — full sweep range 0.080 mm
The endpoints both read 0.000 mm, while the center reads +0.080 mm. Traverse the whole jaw instead of checking only its ends.
Model: physical jaw position is a + m·x + b·4(x/L)(1 − x/L). Displayed reading = response × physical position − the raw reading stored as zero. A small illustrative rotation d about world pivot P=(p, 0) updates m to m + d and a to a − p·d; the stored zero is unchanged. The fixed 100 mm measuring span is inset 1 mm from each end of the finite modeled face. This is a first-order small-angle model with |d| ≤ 0.001 mm/mm, 0.0001 mm/mm control steps, and total rotation travel ≤ 0.004. The step is model resolution, not real-vise quantization. It does not model adjustment force. The drawing exaggerates deviation and is not a literal scale.
Worked example: over 100 mm, start with left 0.000 and right +0.060 mm. Apply d = −0.0006 about 25 mm: both ends become +0.015 mm, so the tilt is gone but the old zero reveals a common offset. About 50 mm both become +0.030 mm; about 0 mm both become 0.000 mm. Re-zeroing is optional convenience, not an alignment requirement. A real setup is accepted against the job requirement, not a universal tolerance from this model.
Alignment procedure: MIT, Introduction to the Mill, pp. 2–3. The comparison geometry and examples here are original.
Prove the sign first. Check which way the reading changes when the contact is displaced a known small amount toward the indicator body. With the response shown above, a higher right-end reading means that end is nearer the indicator: move it away. A lower right-end reading needs the opposite correction. Reverse the contact arrangement and the tap direction can reverse.
Supporting detail: Addendum 200 — Read the whole sweep, not just two endpoints.
Parallels establish height; soft jaws establish a shaped seat
Parallels establish height; soft jaws establish a shaped seat
Parallels are matched support bars placed beneath the part. Choose a height that gives cutter clearance and enough jaw engagement. Keep the planned drilling and milling paths clear of them.
Snug the part, seat it with light downward taps from a dead-blow mallet, then tighten and check the seating again. Check that both supports are contacting; a loose parallel or visible gap means the part may have lifted. A mallet cannot make a chip underneath disappear.
Soft jaws are machinable replacement jaws. A step or pocket cut into them can support a thin part or fit a contour. Machine the pocket with the jaws preloaded in the intended clamping direction, following the vise maker's method. Clean the pocket and check full seating when loading each part; the jaw shape does not excuse insufficient grip.
Put the clamp stud nearer the part than the heel support; Practice
Put the clamp stud nearer the part than the heel support
A strap clamp bridges the part and a heel support. A step clamp has a toothed heel that mates with a step block. Set the heel to the clamp maker's specified height, normally level with or slightly above the part contact. Locate the part against suitable stops and support it beneath the clamping points; a strap pressing on an unsupported span can bend the work.
Place the stud toward the part end of the strap. Keep adequate contact on the part and full seating at the heel. The stud must lie between these contacts. Plan the straps, studs and supports so the tool and holder can pass them.
A short distance from the part to the stud gives the part a larger share of the same stud load.
In the ideal two-contact model, part force = P × b / (a + b). Here P is the downward force from the nut, a is part-contact-to-stud distance, and b is stud-to-heel-contact distance. With P = 6,000 N, a = 20 mm and b = 60 mm, the part receives 4,500 N and the heel receives 1,500 N.
Supporting detail: Addendum 201 — Why the force divides this way—and what the model cannot tell you.
Choose an indicator for alignment, account for edge-finder radius, and keep machine home, work zero and tool length separate.
A test indicator sweeps with a lever; a dial indicator measures plunger travel
A test indicator sweeps with a lever; a dial indicator measures plunger travel
Instrument
Contact motion
Setup use
Test indicator
A short stylus pivots through a small angle.
Convenient for sweeping a vise jaw or a bore where access is tight.
Plunger dial indicator
The spindle, or plunger, moves straight through a fixed mounting stem into the body.
Useful for displacement checks and alignment when the plunger can face the measured motion.
Digital plunger indicator (shown below)
A spindle/plunger still moves linearly; an LCD replaces the pointer and dial.
Useful for the same kinds of displacement checks when its range, contact geometry and specifications fit the task.
Lever test indicator. The short stylus and contact point pivot at the instrument body. The post, arm and clamps are parts of a separate stand; its magnetic base is only partly visible at the frame edge. Photo: David English (Fixerdave), Wikimedia Commons, CC BY-SA 4.0. Downscaled and converted to WebP; the adapted image remains CC BY-SA 4.0. No endorsement implied.Analog plunger indicator. The body carries the dial, bezel and pointer; the straight spindle/plunger reaches the contact point. The stand is separate from the instrument, and its base is not fully shown. Photo: David English (Fixerdave), Wikimedia Commons, CC BY-SA 4.0. Downscaled and converted to WebP; the adapted image remains CC BY-SA 4.0. No endorsement implied.Digital plunger indicator. The LCD and buttons change the readout, not the contact mechanism. Below the body, the fixed mounting stem surrounds the moving spindle/plunger, which ends at the rounded contact point. No stand is shown. Photo: Huugo, Wikimedia Commons, CC0 1.0. Downscaled and converted to WebP. The manufacturer mark identifies the photographed instrument; no endorsement implied.
These displays do not define the contact mechanism: the digital instrument shown here is still a plunger indicator. Test and plunger indicators can both compare alignment. Use the maker's stylus angle for a test indicator; on a common lever design the stylus lies nearly parallel to the measured surface. Align a plunger with the displacement being measured. Incorrect contact angles change the scale factor.
Keep the mounting rigid, preload within the instrument's range and confirm repeatability. During a fixed-jaw sweep, keep the spindle stopped and the contact geometry unchanged. For a bore-centering sweep, turn the spindle by hand using the approved setup method. Follow Equipment Operating Procedure for the machine state during setup.
Supporting detail: Addendum 202 — Contact angle affects the reading.
An edge finder locates the spindle center one tip radius from the edge
An edge finder locates the spindle center one tip radius from the edge
A mechanical edge finder has a spring-loaded contact tip that becomes concentric and then kicks sideways at contact. Use its specified spindle speed and approach method. Electronic edge finders and probes use different signals and procedures; do not assume they rotate like a mechanical edge finder.
Use a clean, defined edge, repeat the approach and account for the contact-tip radius. If the tip is 10 mm in diameter, the spindle center is 5 mm outside the edge at the trigger point. Setting that center position to zero without the radius correction moves every feature by 5 mm.
Example: the left face is X = 0 and positive X goes into the part to the right. At contact from the left with a 10 mm tip, the spindle center is X = −5 mm. Enter that position in the work-coordinate setting method for the control. On approach from a right-hand face, the sign changes. Sketch the spindle center and edge before choosing a sign.
Supporting detail: Addendum 203 — Check both repeatability and the offset sign.
Find an edge, choose the sign, and check where the hole lands; Interactive
Find an edge, choose the sign, and check where the hole lands
Jog a mechanical edge finder toward any of the four edges, watch the tip wobble, centre and kick, then decide what the readout should read at that position. A check hole shows where your zero really is. The radius used is half the contact diameter, which can differ from the body diameter. Re-approach from the same direction each time; reversing a feed screw adds backlash, which this model does not include.
Wobble, centre, kick
Free: off-centre wobble
0.200 mm before the trigger: nearly concentric
At the trigger: the tip kicks sideways
The offset tip orbits while free, is pushed concentric by the edge, then kicks when the spindle centre is one contact radius from the edge. The wobble and kick are drawn for illustration, not as contact mechanics.
Where the check hole lands
Distance from the datum edge, magnified (mm); the dashed line is the drawing’s 20.000
Check holes: drawing says 20.000 mm from the left edge
Hole
Readout set at kick (mm)
Lands from edge (mm)
Off by (mm)
Your hole
−5.000
20.000
0.000
Radius forgotten
0.000
15.000
5.000 toward edge (1 r)
Wrong sign
+5.000
10.000
10.000 toward edge (2 r)
The sign depends on the side approached (+X right, +Y toward the back)
Edge
Spindle approaches moving
Edge position
Set readout at the kick (10 mm contact)
Left edge
+X
X = reading + r
−5.000 mm
Right edge
−X
X = reading − r
+5.000 mm
Front edge
+Y
Y = reading + r
−5.000 mm
Back edge
−Y
Y = reading − r
+5.000 mm
Worked example (left edge, 10 mm contact, r = 5 mm): at the kick the X readout shows +32.460 mm in its old, arbitrary frame. The edge is at reading + r = +32.460 + 5.000 = +37.460 mm. Setting the readout to −5.000 mm at that position makes the edge read 0, and a hole programmed at X 20.000 lands 20.000 mm from the edge. Setting 0 instead (radius forgotten) puts the hole at 15.000 mm: off by r. Setting +5.000 (wrong sign) puts it at 10.000 mm: off by 2r.
Model: top view; positions are the spindle centre relative to the part, whichever of them actually moves. The trigger occurs when the spindle centre is exactly one contact radius (half the contact diameter, not the body diameter) from the edge, on the approach side. Lengths are exact to 0.001 mm; jog steps are 1, 0.1 and 0.01 mm. A step that crosses the trigger leaves the readout past it by up to one step. The other axis is assumed already located. Backlash, tip wear, edge condition and speed are not modelled; use the edge finder’s specified speed.
Sources: MIT 2.670, Milling Machine, “Using an Edge Finder”, p. 6; Starrett 827MB and 827A product pages (how to use; 6 mm and 0.200 in contact diameters). The part, readings and drawings are original illustrations.
Home the machine, locate the part, then account for each tool's length
Home the machine, locate the part, then account for each tool's length
Machine home establishes the machine's reference positions. It does not locate the part.
Work zero is the origin chosen on the part or fixture. Its work offset relates that origin to the machine coordinates.
Tool length offset accounts for where a particular tool tip lies relative to the control's tool reference.
Choose the origin used by the drawing and program, locate X and Y, and establish Z using the approved touch-off or probing method. Account for any gauge or touch plate thickness. Confirm the active work offset, tool number and tool length before a trial path. Recheck after moving the part or changing how a tool is seated.
Two tools touch the same surface at different readings; Interactive
Two tools touch the same surface at different readings
Once X and Y are located, Z still depends on which tool is in the spindle. Predict the readout for two tools of different lengths touching the same part top, with ideal contact or through a block of stated thickness. CNC Axes and Offsets shows how a control applies a stored length value.
Two tools touched off on the same surface
Touch-off through a 10.000 mm block
Tool
Length, gauge line to tip (mm)
Z reading at touch-off (mm)
Length value vs T1 (mm)
T1 · 10 mm end mill (reference)
82.000
+10.000
0.000
T2 · 6 mm drill
109.500
+37.500
+27.500
Touch-off with ideal zero-thickness contact
Tool
Length, gauge line to tip (mm)
Z reading at touch-off (mm)
Length value vs T1 (mm)
T1 · 10 mm end mill (reference)
82.000
0.000
0.000
T2 · 6 mm drill
109.500
+27.500
+27.500
Worked example: the readout follows the spindle and reads T1’s tip height, with the part top at Z 0. T2 is 27.500 mm longer than T1. Touching T2 onto a 10.000 mm block, the readout shows Z = 0 + 10.000 + (109.500 − 82.000) = +37.500 mm. T2’s length value is that reading minus the block: +27.500 mm. With that value applied, the tip Z is the reading minus 27.500. Without it, a move to Z +2.000 with T2 would put its tip at 2.000 − 27.500 = −25.500 mm: 25.500 mm below the part top.
Model: Z reading at touch-off = surface Z + gauge thickness + (Ltool − LT1). Lengths run from the spindle gauge line to the tip and are illustrative. The gauge is either an ideal zero-thickness contact or a stated 10.000 mm block. Controls store and apply tool length in different ways; follow the control’s documentation for the actual offset entry.
Machining/Milling
Mill Toolholders and Collets
Match the spindle interface, compare tool-gripping mechanisms by five job criteria, and assemble ER collets with the required grip and reach.
The spindle connection and the tool grip are separate choices
The spindle connection and the tool grip are separate choices
A holder has a machine end and a cutting-tool end. “ER” describes a collet system at the tool end; it does not tell you which spindle the holder fits.
Interface
How to recognize the idea
R8
A taper seats in the spindle and a drawbar threads into the collet or holder to pull it in. A direct R8 collet grips a matching tool shank.
CAT / BT
Steep-taper holder families with flanges and retention knobs, also called pull studs, for compatible spindle retention and tool changing. Similar-looking tapers do not establish interchangeability: family, size, flange and retention knob must match the machine.
TTS
The Tormach Tooling System uses a straight holder shank gripped in a compatible collet and a shoulder that seats against the spindle face. TTS is a toolholding system, not a CAT/BT-style taper. Its seated shoulder provides a repeatable axial reference.
Identify the installed interface before selecting a holder. A Tormach name alone does not identify the spindle system or drawbar arrangement.
Supporting detail: Addendum 204 — Public toolholder references.
Compare what actually closes around the tool shank
Compare what actually closes around the tool shank
Ordinary keyed or keyless drill chuck: adjustable jaws grip drilling-tool shanks. A key or a hand-operated sleeve closes the jaws. Jacobs and Albrecht are brands, not gripping-mechanism categories. Do not assume an ordinary drill chuck or its mounting is suitable for milling side loads.
Weldon / side-lock / set-screw end mill holder: a fitted bore locates the shank and a screw bears on its designated flat. Match the bore, shank and flat. This retention feature does not guarantee that a tool cannot move under every load.
ER collet: the nut draws a split collet into a taper, closing it around the shank. Match the series and stated gripping range. A direct R8 collet is a different system.
Shrink fit: controlled heating expands the holder bore; cooling around the matching shank produces an interference grip. Tool changes need the compatible heating/cooling equipment and the maker's process.
Hydraulic expansion chuck: an actuator pressurizes fluid inside the holder; a sleeve deforms against the shank. The actuating screw pressurizes the system rather than bearing directly on a Weldon flat.
Mechanical milling chuck: a mechanical drive compresses the gripping bore or a special collet. Designs differ: some use a nut and needle bearings; Albrecht APC uses gearing and a tapered collet. APC is a milling-chuck product, distinct from Albrecht's jaw drill chucks.
REGO-FIX powRgrip: a dedicated unit presses a matching tapered collet into the holder. The retained grip is a mechanical press fit, not an ER nut, thermal shrink fit or hydraulic-expansion sleeve.
Grip the intended shank surface, not the cutting flutes. Keep the tool's specified engagement in the holder while leaving only the reach needed to cut and clear the part.
Different force paths can produce similar-looking holders. Schematics identify mechanisms, not assembly instructions, dimensions or performance rankings.
Supporting detail: Addendum 205 — Manufacturer examples and the drill-chuck exception.
Choose against runout, balance, grip, clearance and total system cost
Choose against runout, balance, grip, clearance and total system cost
Runout concerns the tool's rotating geometry; balance concerns the distribution of rotating mass. Grip must resist the required turning and axial loads. Clearance and reach must work throughout the path. Cost includes the holder, collets or sleeves, setup equipment, inspection, maintenance and change time.
Use this matrix to shortlist actual products. Each cell names a useful check, not a universal quality grade or approval to run at a particular speed. On a narrow screen, scroll the table sideways; keyboard users can focus it and use the arrow keys.
Compare the assembled setup, not just the holder family
Mechanism
Runout / high-RPM balance
Grip / clearance and reach
System cost and upkeep
Ordinary drill chuck
Check jaws, mounting and the exact speed rating.
Drilling use; body and jaws need clearance.
Adjustable diameter coverage; inspect jaws and mounting.
Side-lock
Verify the screw/flat assembly's runout and balance.
Collets cover sizes; correct nut, wrench and torque equipment.
Shrink fit
Check the assembled tool, not concentric appearance.
Slim-nose options; verify shank match and engagement.
Heating/cooling equipment, compatible tooling and change cycle.
Hydraulic
Check the sleeve's condition and product specifications.
Check the exact milling application and engagement limits.
Approved actuation and sleeves; inspection/service requirements.
Mechanical milling chuck
Clamping configuration can change grip and runout.
Roughing candidates; compare the actual body/nut envelope.
Maker's wrench and approved parts; mechanism-specific care.
Pressed collet / powRgrip
Check the matched collet, holder and complete assembly.
Correct collet diameter; compare actual nose profiles.
Matching collets and a dedicated press-in/out unit.
Supporting detail: Addendum 206 — A real trade-off within one product family.
Snap the ER collet into its nut before threading the nut onto the holder
Snap the ER collet into its nut before threading the nut onto the holder
Match the ER series, nut, collet and tool shank. Read the collet's actual range; the ER series number is not the tool diameter. Do not force an oversized shank into it or collapse it below its rated range.
Clean and inspect the holder socket, collet, nut and tool shank. Follow the manufacturer's lubrication instructions for the named surfaces; do not treat every taper and gripping surface alike.
Engage the collet's extraction groove with the nut's eccentric retaining ring. Tilt and snap it into place as instructed by the maker.
Thread the nut-and-collet assembly loosely onto the holder.
Insert the tool with the required shank engagement and planned stickout. Tighten to the specified torque using the proper wrench and holding fixture.
The nut captures the collet before either goes on the holder. Do not place the collet in the holder first and try to force the nut over it.
Range example: a collet explicitly rated 9–10 mm can grip a 9.5 mm shank; it cannot grip a 10.2 mm shank. This is a reading exercise, not a universal collapse range for every ER collet.
Supporting detail: Addendum 207 — Why the snap matters.
A low runout reading does not establish high-speed balance
A low runout reading does not establish high-speed balance
Runout is the variation seen as a tool or reference shank rotates about the spindle axis. If one cutting edge projects farther than the others, it can carry more of the load. Dirt, damaged seating surfaces, a poor collet fit, the tool, holder or spindle can contribute. Clean and reseat before blaming cutting data; measure against the job and tool requirements.
A geometrically straight assembly can still have uneven mass around its axis. A holder's balance marking may apply without the tool, collet or other fitted parts. Check the complete rotating assembly, the stated measurement conditions and every applicable operating-speed limit. Balancing does not raise a component's permitted speed.
Supporting detail: Addendum 208 — Why adding the tool can change the answer.
Measure the reach you need without losing the required grip
Measure the reach you need without losing the required grip
Physical tool stickout is the unsupported tool length beyond the effective grip. For the bending model, identify the clamp-to-load distance. Holder projection or gauge length refers to dimensions on the holder drawing, often measured from the spindle's gauge reference to a specified holder feature. Flute length is the length of the tool's cutting portion. These are different measurements; read the endpoints on the actual drawing.
A longer holder can move the grip closer to a deep feature while the cutter keeps adequate engagement. It also adds holder projection to the system, so check stiffness and the complete collision envelope. Do not gain reach by pulling a tool out below its required clamping length. Explore Tool Stickout and Deflection for unsupported length and Milling Chatter for the wider cutting system.
Practice choosing the governing constraint before naming a holder
Practice choosing the governing constraint before naming a holder
Shallow roughing: start with a milling-rated assembly's torque transfer and axial retention. A matching side-lock holder is one candidate when the tool has the designated flat; compare other approved systems against the job rather than declaring one family the strongest.
Deep, narrow feature: compare nose/body clearance and required tool reach. A slim holder may avoid a collision that a large collet nut would create. Verify engagement and the holder's projection as well as the exposed cutter.
High-speed finishing with a small cutter: prioritize measured runout, assembly balance and the actual speed limits. A holder family name, shiny finish or high gripping-force claim settles none of those checks.
Supporting detail: Addendum 209 — Check your selection reasoning without a video.
Use short Haas video stops to test the mechanism comparisons
Use short Haas video stops to test the mechanism comparisons
The native explanations and prompts below work without video or network access. The links open selected moments in two Haas videos; they are study references, not this shop's operating procedures or equipment inventory.
Tool Holder Essentials — compare the choices
1:21 — the five criteria. Before watching, choose which criterion governs each of the three situations above. Check: the job determines the priority; one overall winner is not established.
15:50 — torque guidance. Identify where the correct value comes from. Check: the manufacturer of the actual nut, collet and holder combination, not a number generalized from a demonstration.
Machining/Milling
End Mill Anatomy and Cutter Selection
Read end mill geometry, compare flute counts and tool materials, and choose a cutter for the material and operation.
End Mill Anatomy
End Mill Anatomy
An end mill has cutting teeth separated by recessed flutes. Read the side and the cutting end together: the flute hollow, the cutting edge and the relieved face behind it are different features.
Oblique view: the flutes blend out into a plain shank. This representative tool has no reduced neck.
Side view: OAL 76 mm, functional LOC 26 mm; the runout finishes at 33 mm. Runout is not extra functional cutting length.
End detail: two long lips and two short lips meet real recessed gash pockets. This is the cutting end, not a section through the fluted body.
Original Blender-authored representative geometry. Use the lab below to orbit the same model, locate the named features and inspect the end. These are teaching dimensions, not a manufacturer part specification or setup recommendation.
Flutes are grooves beside the teeth that provide room for chips. The sharp edges bordering them do the cutting.
Helix angle describes the spiral relative to the tool axis. It affects how the edge enters the cut and the direction of cutting forces; it is not the spindle's rotation direction.
Cutting diameter is the diameter swept by the cutting edges. Shank diameter fits the holder and may differ from cutting diameter.
Overall length (OAL) runs from tool tip to shank end. Length of cut (LOC) is the axial cutting-edge length, not permission to cut that entire depth in one pass.
Length below shank (LBS) runs from the start of a reduced neck to the tip, so it includes both relieved neck and LOC. It is not the neck-only length.
Square end makes a flat-bottom form with a sharp nominal corner. A corner-radius or bull-nose end rounds that corner. A ball end has a rounded tip for curved surfaces.
Center-cutting geometry can cut at the tool center, allowing axial entry when the manufacturer permits it. Flute count alone does not prove a tool can plunge; check its entry method and limits.
Peripheral and end cutting edges
The sharp intersections of the rake and relieved faces cut on the side and the end respectively. An edge is not the same thing as the whole flute groove.
Rake face
The face ahead of the cutting edge, along which the newly formed chip flows.
Primary relief and land
The narrow ground surface just behind an edge clears the newly cut surface. Further relief behind it provides additional clearance; the exact grind varies with the tool.
Flute or gullet
The hollow beside a tooth provides chip space. The material between the flutes forms the teeth and the central core.
End gash and end relief
A gash is a recessed pocket at the end near the lips; the relieved face behind an end edge provides clearance. Neither is a decorative line drawn on a flat cap.
Core, runout and reduced neck
The core is the central material remaining between the flutes. Runout is where a groove blends into the shank. A reduced neck is a separate relieved reach region; the displayed four-flute model does not have one.
Helix and radial pitch
The helix angle is measured relative to the tool axis on its cylindrical surface. Radial pitch is angular spacing between teeth: four equally spaced flutes give 90°. These describe different directions.
Holder-face projection is the mounted distance from holder face to tip. Pulling the same tool farther out changes projection and insertion, not OAL, LOC or LBS. Follow the tool and holder makers' gripping requirements. Use Mill Toolholders and Collets for the holder system, Tool Stickout and Deflection for the cost of extra reach and Milling Operations for the shapes these cutters produce.
Supporting detail: Addendum 210 — Public anatomy reference.
End Mill Anatomy Lab; Interactive
End Mill Anatomy Lab
Approved fixed model: 12 mm diameter, four flutes, 30° helix, LOC 26 mm and OAL 76 mm; no reduced neck. The same geometry is shown in the live viewer.
Side and oblique surfaces show the flute hollows and cutting teeth.
End gashes and relieved faces are real geometry, not markings on a flat cap.
Separate catalog comparison: reach and mounting
The following two schematic catalog examples differ from the fixed 3D model. Their 100 mm OAL, LOC and LBS stay fixed when the holder moves.
First use: compare one reduced-neck tool mounted at 75 and 85 mm projection. Its OAL, LOC and LBS do not stretch when the mounting changes.
LBS includes LOC plus any relieved neck. It is neither neck-only length nor holder projection.
Model boundary: the approved fixed mesh represents a square-end cutter with end gashes and relief. The separate catalog sketches are dimension illustrations, not manufacturing CAD or proof of a permitted plunge, cutting depth or grip.
The 3D lab uses the approved fixed four-flute model. The separate static catalog comparisons explain reduced-neck and long-flute examples; they are not selectable shapes of this GLB. A reduced neck provides clearance, not proof of strength or permission to use a particular depth or holder projection.
Choose flute count for chip space and engagement, not material alone
Choose flute count for chip space and engagement, not material alone
Flutes
Useful starting point
Check before choosing
2
Generous chip space, often useful for aluminum slots.
Geometry, edge strength and the maker's slotting recommendation.
3
Common aluminum-specific choice balancing chip space with another cutting edge.
That the tool is designed for the material and engagement; three flutes alone are not a material specification.
4
Common for steel and for cuts where chip space is less restrictive.
A full-width slot can pack the smaller flute spaces. Do not assume more teeth always improve removal rate.
A side cut and a full-width slot load the same cutter differently. Select the actual tool's data for the operation, then use Feeds and Speeds for the calculations and Climb and Conventional Milling for feed direction.
Supporting detail: Addendum 211 — Why the two-for-aluminum, four-for-steel rule is only a starting point.
Match HSS, carbide and coating to the job and machine; Practice
Match HSS, carbide and coating to the job and machine
High-speed steel (HSS) is relatively tough and often economical. It can be a useful choice at lower cutting speeds, especially where the setup cannot take full advantage of carbide. Cobalt HSS is an HSS family with improved hot hardness.
Cemented carbide retains hardness at higher cutting temperatures and is stiffer than HSS, but is less tolerant of impact and poor support. A carbide tool does not make a loose setup rigid. Select its grade and geometry as well as its material.
Coatings change wear, friction and heat behavior. TiN and TiCN are familiar options; AlTiN/TiAlN are common on tools for hot-running ferrous applications. For aluminum, choose an uncoated polished tool or a coating explicitly recommended for that alloy, such as TiB2 where specified. Color is not a reliable selection method, and no coating guarantees a fixed multiple of tool life.
Job examples: for an aluminum slot, start by comparing aluminum-specific two- and three-flute tools with enough chip space. For steel side milling on a rigid setup, a steel-rated four-flute carbide tool may be a good starting point. For a modest-speed, interrupted job, a suitable HSS tool may be more forgiving. Check the manufacturer's recommendations before selecting the cutting data.
Supporting detail: Addendum 212 — Check the coating's material recommendation.
Face mills and fly cutters cover broad flat surfaces
Face mills and fly cutters cover broad flat surfaces
A face mill uses several cutting edges, often replaceable inserts, to machine a broad face. Match its diameter, insert geometry, holder and power demand to the machine and part.
A fly cutter carries a single cutting point that sweeps a circle. It can make a broad finishing pass, but its single edge and interrupted loading need suitable rigidity, balance and cutting data. It is not simply a face mill that can use the same feed setting.
What milling chatter is, why it damages finish, accuracy and tools, and how to diagnose the force path before changing one permitted variable at a time.
Chatter is a self-reinforcing vibration during cutting
Chatter is a self-reinforcing vibration during cutting
Milling chatter is vibration that grows through the cutting
process instead of simply following a steady outside disturbance. The changing motion changes
chip thickness and cutting force, which can feed more energy into the motion. Left uncontrolled,
it can spoil surface finish and dimensional accuracy, increase tool deflection and accelerate
cutting-edge wear or failure.
A common mechanism, regenerative chatter, is self-excited: one cutting edge leaves a waviness that changes the chip thickness seen by the next edge, and the changing force can reinforce the motion. That mechanism does not describe every vibration or finish defect. A repeating surface pattern, a loud cut or another forced vibration can be clues; they do not prove regenerative chatter by themselves.
Supporting detail: Addendum 213 — Several faults can look or sound like chatter.
Stop the cut before inspecting or changing the setup; Watch out
Stop the cut before inspecting or changing the setup
Do not tune around a part, tool or holder that moved. A shifted workpiece, incomplete seating, damaged edge or visibly slipping tool is a mechanical problem to correct or report before another cutting trial.
Record the evidence before trying another cut
Record the evidence before trying another cut
Record where the symptom began, where it appears on the part, which operation and tool were active, and the actual speed, feed, engagement and holder projection. This creates a comparison for the next check instead of relying on sound or memory.
Trace force through the complete cutting system
Trace force through the complete cutting system
The cut closes the loop. A stiff cutter cannot compensate for a moving part, and rigid workholding cannot correct a damaged holder interface.
Route suspected machine or spindle faults to authorized staff
Route suspected machine or spindle faults to authorized staff
After the cutter, holder, workholding, path and chips have been checked, a persistent symptom is evidence worth giving to authorized staff. Abnormal motion or a visibly damaged or contaminated interface also calls for that route. It does not prove one component failed. Do not remove covers, adjust bearings or gibs, or service a drawbar; manufacturer guidance treats those as separate checks for trained personnel.
Check the holder, collet and cutter as one assembly
Check the holder, collet and cutter as one assembly
Confirm the correct holder and collet, complete seating, clean contact surfaces under the approved procedure, adequate shank engagement, and no visible damage. Compare tool and holder projection with the last stable setup. Inspect for wear, chipping, built-up material and chip damage. Check runout only with the approved instrument and method; compare it with the tool, holder and job requirements. See Mill Toolholders and Collets, End Mill Anatomy and Cutter Selection and Tool Stickout and Deflection.
Check the fixture, workpiece and support
Check the fixture, workpiece and support
Check that the fixture is seated and secured, the work is against its locators, clamps direct force into supports, and the part is not perched or springing. A symptom confined to an unsupported end, thin wall or one clamping orientation points first toward support and force direction. Do not keep tightening until the part distorts. See Milling Vises and Strap Clamps.
Check engagement, path and chip evacuation
Check engagement, path and chip evacuation
Compare where the pattern begins with changes in radial or axial engagement, entry and exit, cornering, cutter engagement, and chip evacuation. A clean straight wall followed by chatter in an inside corner is evidence to inspect the corner path and the sudden engagement change. Packed or re-cut chips call for the approved chip-control method and a review of the operation, not an automatic speed change. See Milling Operations and Cutting Fluids and Application Methods.
It changed with a longer tool or holder
It changed with a longer tool or holder
Check: tool projection, holder projection, shank engagement and both interfaces. Next: restore the shortest permitted assembly that reaches the feature, then repeat the same cut conditions.
Straight walls are clean; an inside corner chatters
Straight walls are clean; an inside corner chatters
Check: the engaged arc, chip load through the corner and programmed path. Next: use an approved path or engagement change, then compare the same corner again.
Only an unsupported or thin area vibrates
Only an unsupported or thin area vibrates
Check: workpiece support, clamp-force path and local flexibility. Next: improve support or revise force direction without distorting the work; verify the setup before cutting.
One edge is chipped or marks repeat once per revolution
One edge is chipped or marks repeat once per revolution
Check: edge condition, chip re-cutting, holder seating and runout. Next: correct the physical cause or replace the damaged tool before tuning speed.
It persists after the student-controlled setup checks; Practice
It persists after the student-controlled setup checks
Check: after the cutter, holder and workholding are verified, ask whether the symptom still follows the same path, engagement or chip condition. Next: if it persists across different permitted cutting conditions, stop and give the complete evidence to authorized staff. It is evidence for inspection, not proof of a spindle fault.
Clear mechanical causes and unnecessary leverage first
Clear mechanical causes and unnecessary leverage first
Clear mechanical causes first. Verify seating, condition, projection, support and chip clearance. Do not use a parameter change to hide motion or damage.
Reduce unnecessary leverage. Shorten the permitted tool and holder projection, improve support, or choose a more suitable assembly. Keep the required shank engagement and feature clearance.
Review engagement and cutter geometry after the setup is sound
Review engagement and cutter geometry after the setup is sound
Review engagement and force direction. A smaller radial or axial engagement, different entry, or revised corner path may reduce the force variation. Stay inside the approved process and tool limits.
Reconsider cutter geometry. Diameter, flute count and pitch, helix, edge geometry and material suitability can change force and excitation. Record the selected tool and why it was changed.
Run one permitted speed trial
Run one permitted speed trial
A stable speed can be higher or lower. Change to one permitted speed, then compare the same feature. Do not assume that slowing down is always the answer.
Review feed when speed changes
Review feed when speed changes
If the trial is intended to preserve feed per tooth, calculate the matching table feed rather than changing chip load accidentally. Too little feed can rub; excessive feed can overload the edge. Use Feeds and Speeds and the tool maker's data.
Record the controlled result
Record the controlled result
Record the observation, the one intentional change and the result. If two settings move together to preserve a stated quantity such as feed per tooth, record both and the quantity held constant. That is one controlled trial, not two unexplained changes.
Manufacturer references behind this diagnostic order
Manufacturer references behind this diagnostic order
A Tormach-based sequence for preparing the machine, locating the part and tools, checking a path, and closing down.
Use the checklist with the installed machine's procedure
Use the checklist with the installed machine's procedure
This checklist follows a Tormach vertical-mill workflow. Match each control, inspection method and tool-change step to the installed machine and controller. It is a setup reminder for trained users, not a substitute for instruction or the machine manual.
Confirm the machine and controller have power available. Turn on the controller computer, then the mill as directed by the installed-machine procedure.
Reset depressed emergency-stop controls after completing the prescribed checks, then use the machine's Start/enable control to activate its motor controllers.
When the controller is ready, reference (home) all installed axes by the machine's procedure. Confirm that referencing completed; homing has not set the part zero.
Part and tool setup: seat, grip, locate and record; Checklist
Part and tool setup: seat, grip, locate and record
Plan the datum faces, work zero, tool access and fixture clearance for the intended operations.
For a vise setup, clean and inspect the vise and part, remove raised burrs, and check the fixed-jaw alignment. See Milling Vises and Strap Clamps.
Fit parallels if needed. Snug the part, seat it with light dead-blow taps, tighten the vise and recheck seating.
For table clamping, have the support, locating and clamp arrangement checked against the job and installed procedure; confirm every intended contact is seated and every clamp is firm. Use strap-clamp geometry to review placement.
Choose the cutter and matching holder. For ER tooling, capture the collet in its nut, thread the assembly loosely, insert the shank with the planned reach, and tighten as specified. For a set-screw holder, align the designated shank flat and follow its seating method. See Mill Toolholders and Collets.
Install the holder using the procedure for the actual spindle and drawbar. For a manual drawbar arrangement, verify completion of its spindle-lock release and spindle-cover closure steps before operation; do not apply that sequence to a different retention system.
Set and verify tool lengths and the work offset using Mill Indicators and Part Zero. Confirm the active tool number, units and work coordinate system.
Before cutting: verify the program or manual movement plan; Checklist
Before cutting: verify the program or manual movement plan
Confirm cutter, spindle direction, speed, feed, width and depth of cut against the tool data and Feeds and Speeds.
For programmed work, load the intended program and check the displayed path, tools, offsets and limits. See G-code and Toolpaths.
Perform the approved air-cut or dry-run procedure with verified clearance. If that method changes offsets or modes, restore and verify them before cutting the part.
For manual movement, confirm the selected axis, direction, jog rate and increment. Use a low approach rate near a surface and incremental motion for fine positioning, as directed in the machine procedure. Select cutting feed from the tool data rather than treating a low approach rate as a cutting-feed prescription.
Complete the cutting-readiness checks in Equipment Operating Procedure, then perform the operation and its planned measurements.
Shutdown: end operation, shut down the controller and restore the work area; Checklist
Shutdown: end operation, shut down the controller and restore the work area
Follow the installed Tormach shutdown sequence. In this workflow: depress emergency stop, shut down the controller computer normally, then remove its power and turn off the mill.
Use the machine-specific instructions for any required parking position, tool removal, lubrication or power sequence. These details vary with the machine and its options.
Machining/Milling
Milling Operations
Make a part on a simulated vertical mill: choose each tool, move it through the metal, and check what is left against the drawing. Facing, shoulders, pockets, slots, drilled, tapped and bored holes, countersinks and chamfers.
A vertical mill shapes a block with a turning tool moved in X, Y and Z
A vertical mill shapes a block with a turning tool moved in X, Y and Z
On a vertical mill the cutting tool turns in a spindle above the work. The work is
clamped on the table, the table moves it front to back and side to side, and the tool comes down
into it. Every shape the mill makes is the space the turning tool swept through.
X and Y
The two directions across the table. In this lesson X
runs left to right as you face the machine and Y runs away from you, toward the
back.
Z
Up and down, along the tool. Z+ is up, away from the work, so
negative Z is below the finished top face. The raw top is at Z +1, so facing can remove
metal at zero or positive Z while taking off that allowance.
Readout
The display that shows where the tool is, in X, Y and Z. A readout on a
manual mill is often called a DRO, for digital readout. Here it shows the position of
the tool’s tip.
Work zero
The point the readout counts from. In this lesson X 0, Y 0 is
the front left corner of the block and Z 0 is the finished top face. Every dimension on the
drawings is measured from those same edges and that same face.
The setup used in every job: a block 100 × 60, finished 20 thick, held by its
front and back faces in a vise and resting on two parallels, bars of equal height
that lift it off the floor of the vise. The raw block stands 1 mm proud of the finished top. Below
Z −8 the vise jaws are in the way at the front and back, and a hole drilled through
along those edges would run into a parallel.
On a real knee mill the table carries the work under a spindle that stays put in X and Y. In
the simulator you move the tool instead. The readout tells the same story either way: where the
tool’s tip is, measured from work zero.
Each kind of tool cuts a shape of its own, and some cannot cut sideways
Each kind of tool cuts a shape of its own, and some cannot cut sideways
The tools in the simulator, side on and at one scale, each with its tip on the same
line. The darker part of each is the part that cuts.
Face mill
A wide body with cutting inserts round its rim. It is fed
across the work to leave a broad flat face. The one in the simulator takes at most
4 mm in one pass. The inserts sit at the rim, not across the middle, so it is brought down beside the work
and then fed in, never pushed straight down into the metal.
End mill
Cuts on its sides and its end. The end mills here are
centre-cutting: their end teeth reach the middle, so they can be fed straight
down into the metal and then moved across to cut pockets, slots, steps and walls. An inside
corner they leave is rounded to the cutter’s own radius.
Spot and chamfer tool
A pointed tool with a 90° point. Fed down, it cuts a
cone: the start of a hole, or a countersink round the mouth of one. Run along an
edge, it bevels the edge, which is a chamfer.
Drill
Cuts only at its point, as it feeds down along its own axis. It leaves a
round hole its own size, with a cone at the bottom from its point. It must never be pushed
sideways in the metal.
Tap
Cuts a screw thread into the wall of a hole that is already there. It only
goes straight in and straight back out.
Boring head
An adjustable single cutting point on an offset bar. Set to a
diameter and fed down a hole, it opens the hole to that size. Its bar has no cutting edge at the
centre, so it needs a hole to start in.
This is a teaching rack, not a list of what to buy or use. The sizes are
illustrative. A real cutter’s length, number of teeth and depth of cut come from its own
data and from the person responsible for the machine.
The tool’s centre runs one radius away from the wall it cuts
The tool’s centre runs one radius away from the wall it cuts
The readout shows where the centre of the tool is. The metal is cut by its
edge. To leave a wall at a given place, put the centre one radius away from it, on
the side being cut away.
Worked example. A shoulder’s wall belongs at X 75, with the metal to
the right of it cut away. A Ø12 end mill has a 6 mm radius, so its centre runs along
X 75 + 6 = X 81. Run it along X 75 instead and the
wall ends up at X 69, 6 mm too far into the part. That metal cannot be put back.
Inside corners take the cutter’s radius. A round tool cannot reach into a
sharp inside corner, so a pocket’s corners come out rounded to the radius of the cutter that
made them. A drawing that allows R4 at most calls for a cutter no bigger than Ø8.
Outside corners stay sharp. Going round the outside of a corner, the tool
swings about it and never cuts into it.
A slot is the width of the cutter that made it in one pass. A cutter moved in a
straight line leaves a groove exactly its own width, with round ends of its own radius.
When a cutter cuts with its side, the metal is on one side of it or the other. With the
cutter turning clockwise seen from above, metal on the cutter’s right as it moves is
climb milling, and metal on its left is conventional milling. The
simulator says which each side cut was. Climb and Conventional Milling explains the difference.
Holes: drilled to size, threaded by a tap, opened up by a boring head
Holes: drilled to size, threaded by a tap, opened up by a boring head
A drill leaves a hole of its own diameter. A hole’s depth on a drawing is measured to where
the hole stops being full size, not to the tip of the cone the drill point leaves below that.
A tapped hole starts as a smaller drilled hole
A tap cuts its thread into the wall of a hole, so the hole has to be drilled smaller than the
thread first, to the tap drill size. For the common metric coarse threads that
size is close to the thread’s outside diameter minus its pitch, the distance from one thread
to the next:
Drilled too small, the tap has to cut too much metal and can break. Drilled too big, the thread is
shallow. The simulator checks the hole against a simplified minor-diameter band and refuses
a severely undersize pilot. This does not establish functional thread fit: pitch diameter,
thread form and a real thread gauge are separate checks.
Drill deeper than the thread you need
The first few threads of a tap are ground away to a taper so that it can start in the hole. Those
threads cut only part of a thread, so full thread stops short of the tap’s tip. In a hole
with a bottom, the tap has to go deeper than the full thread you need, and the drilled hole deeper
again, past the drill’s point. This simulated tap has a 4-pitch cutting chamfer; real taps
vary. The job calls for full thread reaching Z −10 from the finished face. Its
countersink removes the first part of the thread, so that is not 10 mm of surviving full-thread length.
Sizes no drill gives
Drills come in fixed sizes. A boring head is set to the size you need and fed down a hole already
big enough for its bar, which makes it the tool for a hole of an exact, larger size.
Simulator: make the part on the drawing, then inspect it; Interactive
Simulator: make the part on the drawing, then inspect it
Job 1: Face the top, then cut a shoulder. Face the top flat at Z 0.00, then mill a shoulder 25 mm wide and 6 mm deep across the right-hand end.Job 2: A pocket with tight corners, and two clearance holes. Face the top, mill a 40 × 24 pocket 6 deep whose inside corners are no rounder than R4, and drill two Ø6.6 holes right through.Job 3: A slot and two tapped holes. Face the top, mill a slot 10 wide with full-round ends, and make two countersunk M6×1 holes whose full thread reaches Z −10 or deeper, measured from the finished face.Job 4: A boss with a bored hole and chamfered edges. Face the top, mill away everything round a 50 × 30 boss so it stands 5 high, bore a Ø20.00 hole through it, and chamfer its top edges 1 × 45°.
Start by examining the finished Target, then choose a tool and cut Your work.
In Compare, gold is metal still to remove and striped red-orange is metal cut past the
drawing. The inspection measures the part that is left
after every move. Nothing checks which tools you used or in what order: any way of making the right
part passes.
How to drive it.Target shows the finished nominal part;
Your work shows the block you are making. Compare marks what still needs work,
using the drawing’s allowed limits. In Inspect / orbit, dragging and the arrow keys
move only the camera. Home restores the view; the View list also offers top, front,
below and 2D sections.
Choose a tool and its size, then choose Feed X, Feed Y or Feed Z
to drag its tip along that machine axis. The path previews while you drag; releasing starts the
feed. Place XY places the centre at the current Z. In these feed modes the arrow keys
move the selected machine axis. To go to an exact place, type X, Y and Z under Move to and press Move; the
tool goes up before it goes across, and across before it goes down. The handwheel buttons and the
selected-axis keys move one step at a time. A move that would break a tool or hit the vise stops where it
would happen, and says why. Undo takes back the last move: the one thing a real mill
cannot do.
Things to try in the simulator; Checklist
Things to try in the simulator
In job 1, load the face mill, move it over the block and try to lower it straight onto the
metal. Read why it stops.
Lower the face mill to Z 0.00 beside the block and drag it across. Watch the top view and
the sections: the raw top is 1 mm above Z 0. Overlap a second pass until the top face
check matches.
Cut the shoulder with the Ø12 end mill with its centre on X 75 instead of X 81.
Read the inspection, then use Undo and cut it again in the right place.
In job 2, clear the pocket with the Ø12 end mill and read what the inspection says about
its corners. Undo, and clear it with a smaller cutter.
Watch the gold as you cut: it is metal the drawing does not keep. Cut one pass a little too
deep and see where the striped red-orange appears in the top view and the section.
In job 3, try to tap a hole you drilled with the Ø6.0 drill, then one you drilled with the
Ø4.2. Then drill Ø5.0 only 10 mm deep and tap it as deep as it will go. How much
full thread do you get?
In job 4, try the boring head before there is any hole. Then drill one first.
Make one part two different ways, for example job 4 with the face mill doing the area round the
boss, and again with an end mill. Both pass.
What the simulator leaves out
What the simulator leaves out
The 3D target is a nominal guide sampled at 0.25 mm in X and Y. Its flat floors have the
drawing’s depth; its small curved outlines are approximations. The cut surface is derived
separately from the analytic tool paths. Neither picture is a dimensional gauge: inspection uses
the drawing’s allowed limits, including smaller corners where the drawing says R4 max.
Complex conical histories or very long cut histories switch to 2D sections to keep the controls
responsive. The work is kept, and Undo or a fresh block can restore the 3D view.
The simulator is a model of where metal is and where tools can reach. It does not check speeds,
feeds, forces or finish, and passing a job here says nothing about whether a real setup could take
the same cuts. Feeds and Speeds is about those numbers.
Only straight down and straight across. The tool axis is always vertical and
nothing is undercut, so every shape is a height above each point of the table.
Tools are exact and rigid. A hole is exactly the drill’s size, a cutter
never bends or wears, and edges come out without burrs.
Threads are recorded, not drawn. The simulator keeps the size of the hole a
thread was cut in and how deep its full thread runs, and checks that later cuts have not taken the
metal it is in. It does not model the thread’s form or fit.
No chips, coolant or heat, and no limit on depth of cut except where a
tool’s cutting edges run out.
Supporting detail: Addendum 214 — How the inspection decides, and what its numbers are.
Machining/Milling
G-code and Toolpaths
How a CNC mill reads a program line by line: rapid and feed moves, absolute and incremental coordinates, units, arcs and a drilling cycle. Build a program from blocks and watch it cut a simulated block.
What is G-code?
What is G-code?
A CNC mill moves its tool by reading a program from the top down, one line at a
time. The language most mills read is called G-code. Each line holds a few
words, and together they say where the tool goes next, how fast, and what the spindle and
tool are doing.
Start with CNC Control Fundamentals for the control and machine types,
CNC Axes and Offsets for coordinate references, and CNC Program Structure for common
Fanuc-style milling codes. G- and M-code meanings vary by control. The simulator below uses
its own documented subset; check the machine's manual for real programs.
Word
A letter and a number, such as X20, G1 or
F300. The letter says what the number means: X, Y and
Z are positions, F is the feed rate, S the spindle speed,
T a tool number. G and M words are codes that choose what
kind of move or machine action the line is.
Block
One line of the program. Machinists often call a line a block; in
the simulator below, each block you snap into place is one line of G-code, with the same
number.
Work zero
The point the program’s numbers count from. Here, as in
Milling Operations, X 0, Y 0 is the front left corner of the block and Z 0 is its
finished top face. The uncut stock starts at Z +1. Positions refer to the tip of the tool,
on its centre line: Z −3 is 3 mm below work zero and 4 mm below that raw top.
A pointed drill reaches its programmed Z at its tip; the full-diameter hole is shallower.
Modal
Most codes stay in force until another code from their group replaces
them. After a G1, a line with only X80 is still a G1 move; a
feed rate set with F remains available until changed. Not every word is modal.
For ordinary G0/G1 moves, an omitted axis stays in place; it does not repeat the preceding
incremental displacement.
A first cut: one slot
(A first cut: a closed-ended slot)
G21 G90 G17
T1 M6
S2500 M3
G0 X10 Y30
G0 Z2
G1 Z-3 F100
G1 X90 F300
G0 Z20
M5
M30
A first cut: one slot. Mill a closed-ended slot 10 mm wide to Z−3 with a Ø10 end mill. The raw top is Z+1, so the cut is 4 mm deep. Lift clear and stop. The program on the left, numbered line by line, and the block after it has run. Solid lines are feed moves, dashed lines are rapids; the darker the cut, the deeper it goes.
Read the program above from the top. Line 2 sets millimetres, absolute positions and the XY
plane. Line 3 puts tool 1, a Ø10 end mill, in the spindle, and line 4 starts the
spindle at 2500 rpm. Lines 5 and 6 move the tool through the air to just above the start of
the slot. Line 7 feeds it to Z −3, cutting 4 mm below the raw top at
Z +1. Line 8 feeds it along the closed-ended slot, and
line 9 lifts it clear. Line 10 stops the spindle and line 11 ends the program.
Rapid moves put the tool in place through the air; feed moves cut
Rapid moves put the tool in place through the air; feed moves cut
G0 is a rapid move. The control uses its rapid positioning rate, subject to machine limits and applicable overrides. It is
for getting the tool to where a cut starts, through the air, never for cutting.
G1 is a feed move. The tool moves in a straight line at the feed
rate set by F, here in millimetres per minute. It can cut or feed through air.
The spindle has to be turning first.S sets its speed in
revolutions per minute, M3 starts it turning clockwise seen from above, and
M5 stops it. T1 M6 changes to tool 1.
A move goes in one straight line.G1 X80 Y40 Z-2 moves all three
axes together and they all arrive at once. An axis left out of the line stays where it is:
G1 X80 moves along X only.
A rapid into metal is a crash: the tool arrives at full traverse speed with nothing to say it
should be cutting. The simulator stops a rapid at the point where it would touch the block and
says so. It does the same if a feed move reaches the metal with the spindle stopped.
This simulator moves a rapid in one straight line, the way the
LinuxCNC G-code reference
describes G0. Controls differ in how they move during a rapid, so check how the one you
use moves before you count on the path a rapid takes.
G90 and G91, G20 and G21: two modes that change what every number means
G90 and G91, G20 and G21: two modes that change what every number means
G90, absolute
A number is a position, measured from work zero.
With the tool at X 10, G1 X30 moves it to X 30.
G91, incremental
A number is a distance from where the tool is
now. With the tool at X 10, the same G1 X30 moves it 30 mm, to X 40.
G21, millimetres
X30 means 30 mm and F300 means
300 mm per minute with the simulator's G94 feed mode.
G20, inches
The same X30 means 30 inches, which is 762 mm,
and, with G94, the feed rate is in inches per minute. A millimetre program read in inches asks for moves 25.4
times as long.
Because these modes change the meaning of every line after them, a program sets both near its
start, before the first move. The simulator insists on it: a move before G20 or
G21 and G90 or G91 have been set stops the program, and so
does a change of units after the machine has started moving.
Work through a point list in Absolute and Incremental Positioning. Units and feed mode
are separate settings; G95, where supported, uses feed per spindle revolution.
G2 turns clockwise and G3 counterclockwise, seen from above; Practice
G2 turns clockwise and G3 counterclockwise, seen from above
An arc move cuts along part of a circle in the XY plane (G17) at the feed rate. Its
direction is the way it turns as seen looking down on the work from above: G2
clockwise, G3 counterclockwise. The line gives the arc’s end
point with X and Y, and its centre in one of two ways.
I and J say where the centre is, measured in X and Y from the point where the
arc starts. That is the usual mode, G91.1, and it holds even while
G90 makes every X and Y a position. G90.1 makes I and J a position
too in this simulator. Those decimal codes are not universal; check the control's centre-mode rules.
R gives the radius instead, and the control works out the centre. A positive
R selects an arc of up to half a turn, a negative R the longer way round in the convention used here. An R arc cannot be a
full circle, because a circle through one point has no single centre; a full circle uses I and J
with its end point the same as its start.
Worked example. The tool is at X 72, Y 15, moving right along the
bottom of an outline. G3 X80 Y23 I0 J8 puts the centre 0 in X and 8 in Y from the start,
at X 72, Y 23. Turning counterclockwise about it, the tool rounds a corner of radius 8 and
ends heading up the right-hand side at X 80, Y 23. The end point has to lie on the circle:
change J8 to J6 and the start radius is 6 mm while the end radius is
√(8² + 2²) = √68, about 8.246 mm, so
the simulator stops at that line instead of guessing.
In the diagram, absolute endpoints and start-relative centres give
G03 X22 Y18 I0 J10 from A to B, then G02 X12 Y8 I-10 J0 back to A.
Each start point needs its own centre offsets. Radius format can instead use
G03 X22 Y18 R10 for the first arc under the stated convention.
G17 uses X/Y and I/J; G18 uses X/Z and I/K;
G19 uses Y/Z and J/K. I, J and K correspond to centre components along X, Y and Z.
Judge arc direction looking from the positive normal axis toward the plane: +Z for XY,
+Y for XZ, +X for YZ. The simulator supports XY arcs only.
Arcs: a rounded outline. With a Ø6 end mill, follow a 60 × 30 rounded rectangle with R8 corners at Z−1.5. The groove is 2.5 mm below the raw top, Z+1. Four G3 arcs turn the corners. The program on the left, numbered line by line, and the block after it has run. Solid lines are feed moves, dashed lines are rapids; the darker the cut, the deeper it goes.
A drilling cycle packs a whole hole into one line
A drilling cycle packs a whole hole into one line
G81 X15 Y15 Z-8 R2 F120 drills a hole at X 15, Y 15. The tool moves there at
rapid, comes down at rapid to R, the height just above the work where feeding begins,
feeds down to Z, the drill-tip depth, and rises back up at rapid.
How high it rises. In this simulator G99 rises to R between
holes, and G98 rises to the height the tool was at when the cycles began, or to R if
that is higher. The simulator needs one of the two before the first G81.
The cycle is modal. After a G81, a line with only X or Y drills
another hole with the same depth, R and feed. G80 ends the cycle; after it, a line
with only X or Y is an error until a G0 or G1 says how to move.
Without cutter compensation, program the tool centre path
Without cutter compensation, program the tool centre path
With cutter compensation off, as in this simulator, X and Y describe where the centre of the tool goes. The metal is
cut by its edge, one radius further out. A Ø10 end mill fed along Y 30 cuts a slot from
Y 25 to Y 35. To leave a wall at X 80 with the metal beyond it cut away, the centre runs
along X 85. Milling Operations works through the same rule for a shoulder and a pocket.
Controls can do that offset for you with cutter radius compensation, G41 and
G42. The simulator does not model it, so every program here is written as the path of
the centre, and a line with G41 or G42 stops with a message.
CNC Axes and Offsets explains left/right compensation and tool-length offsets.
Simulator: build a program from blocks and watch it run; Interactive
Simulator: build a program from blocks and watch it run
Pick a program, change it, and run it on a simulated block of metal in a vise. Every
block is one line of G-code; the same interpreter reads it whether you build it from blocks or type
it, and the machine runs exactly what it reads.
How to drive it. Press a block in the program to open it and change its
numbers; leave a number empty to leave that word out of the line. Add a block from the row above
the program, either by pressing it, which puts it after the open block, or by dragging it into
place. Drag a block by its handle to move it; with the keyboard, focus the handle and press Alt with
↑ or ↓. Play runs the program, Step runs one block and stops,
Back goes back one block and Restart starts again with fresh stock. The block
that is running is outlined in gold, and its move is drawn in gold on the views; press a move in
the top view to open the block that makes it. Any change to the program puts the simulation back to its
start, so it always shows the program as it now is.
Holes: a drilling cycle
(Four holes with a drilling cycle)
G21 G90 G17
T3 M6
S1500 M3
G0 X15 Y15
G0 Z10
G98 G81 X15 Y15 Z-8 R2 F120
X85
Y45
X15
G80
G0 Z20
M5
M30
Holes: a drilling cycle. Drill four Ø6 holes with the tip reaching Z−8: 9 mm below the raw top, Z+1. Full-diameter depth is shorter because of the drill point. G81 drills the first hole; X or Y lines repeat it until G80. The program on the left, numbered line by line, and the block after it has run. Solid lines are feed moves, dashed lines are rapids; the darker the cut, the deeper it goes.
Things to try in the G-code simulator; Checklist
Things to try in the G-code simulator
Step through the slot program one block at a time. Watch the machine state change at blocks 2,
3 and 4 before anything moves.
Make the slot deeper and shorter, then run it again. Which numbers did you change?
Drag the Spindle on block below the first feed move, and read why the machine
stops.
Open block 7 of the slot program and switch it from G1 to G0. What
does a rapid do when it meets the metal?
Change the slot program to G91. Before you press Play, work out where its first
move will go.
In the arcs program, swap one G3 for a G2, and see which way that
corner turns now.
In the holes program, try G99 instead of G98, then add a fifth
hole.
In the G-code text, type a line the simulator does not read, such as G41 or
M7, and read what it says.
What the simulator reads, and what it leaves out
What the simulator reads, and what it leaves out
The simulator reads a small part of G-code, modelled on the way the LinuxCNC control reads it.
Any other code, or a line that is not G-code at all, stops the program at that line with a message
saying what is wrong. Nothing is skipped.
Motion
G0 rapid, G1 feed, G2 and
G3 arcs in the XY plane, G81 drilling cycle and G80 to end
it.
Modes
G17 XY plane, G20 inches, G21
millimetres, G90 absolute, G91 incremental, G90.1 and
G91.1 for I and J, G94 feed per minute, G98 and
G99 for the drilling cycle. G40, G49 and G54 are
read as the settings the simulator always has: no cutter compensation, no tool length offset, and
its one work offset.
Machine
M3 spindle on, M5 off, M6 tool
change, M8 and M9 coolant on and off (shown, with no effect on the cut),
M2 or M30 program end: stops spindle and coolant, restores G90 and
G1, and leaves the tool at its last position.
Words
X Y Z positions, I J arc centre, R
arc radius or drilling R plane, F feed rate, S spindle speed,
T tool, N line number, and comments in brackets or after a
semicolon.
Tools
T1 Ø10 end mill, T2 Ø6 end mill,
T3 Ø6 drill, T4 Ø12 spot and chamfer tool, T5
Ø50 face mill: the tools of Milling Operations, with the same rules about what each can
cut.
Some rules are the simulator’s own. It needs units and distance mode
set before the first move, a speed before M3, G98 or G99
before a drilling cycle, and, for a tool change, the spindle stopped and the tool at Z +20 or
higher. A real control may be less strict, or strict about different things.
Only straight down and straight across, through metal. The block is modelled
as a height above each point, so the tool can cut moving along Z alone, or in X and Y at one
height. A move in X or Y and Z at once is followed exactly through the air, but stops if it would
reach the metal: ramping and helical moves are not modelled.
Arcs are cut as short straight chords, each within 0.01 mm of the true
arc. They are drawn as true arcs.
Simple timing. Feed moves run at their F and rapids at 5000 mm per minute,
with no acceleration, no blending of one move into the next, and no time for tool changes.
Not a check of a real program. The speeds and feeds in the examples are round
teaching numbers, not cutting recommendations; Feeds and Speeds is about choosing them. A
program that runs here has met only this simulator’s rules. Controls differ in the codes they
accept, in their starting modes and in how they change tools, so a program for a real machine is
checked against the manual for its control. See CNC Programming and Prove-Out for graphics,
dry run, single block and overrides; follow Equipment Operating Procedure for machine use.
Supporting detail: Addendum 215 — How the simulator reads and runs a program.
Machining/Milling
Climb and Conventional Milling
Climb and conventional milling name the cutter's rotation relative to the feed; that relationship changes chip formation, force direction, chip evacuation and the importance of backlash.
Climb versus Conventional Milling
Climb versus Conventional Milling
A milling cutter turns while the work and cutter move past each other. At the
part of the cutter that is making the cut, climb milling means the cutting edge
moves in the same direction as that relative feed; conventional milling means it
moves against the feed. Those two relationships are the whole distinction—not a universal
left or right direction on the machine.
Climb milling
Also called down milling. Where a tooth is
cutting, it moves the same way the work is fed. Each chip starts
thick and ends thin.
Conventional milling
Also called up milling. Where a tooth is
cutting, it moves against the feed. Each chip starts thin and
ends thick.
Feed per tooth, width of cut (radial engagement) and axial depth of cut are defined together
on Feeds and Speeds. This page uses them only to show what changes when the direction changes.
How to read the drawings on this page. Each drawing is a slice straight
across the fluted part of an end mill, seen looking down its axis from the spindle; the small
side view in the corner marks where the slice is taken, the way a section view does on a
drawing. This sketch places the cutter’s axis horizontally, with the
table below it; screen-down is toward that table. It is not a top view of a vertical spindle.
From the spindle end a standard right-hand cutter turns clockwise. The cutter
stays where it is and the work is fed past it, the way a mill table carries the work. Every
Work feed arrow is the work’s motion. On a machine that moves the
cutter instead, nothing changes: the cutter simply travels the opposite way to that arrow.
The cutter is the same in both modes and spins the same way. What switches climb to
conventional is the direction of feed relative to the side of the cutter that is doing the
cutting. The down/up force arrows belong to this horizontal arrangement. A top view of a
vertical end mill would show forces across the table, not axial force into or away from it.
Climb and Conventional Milling Lab; Interactive
Climb and Conventional Milling Lab
The dashed gold outline is the slice of metal the cutting tooth has taken so far,
drawn where it was. The solid gold shape is that metal as a chip, curling off the cutting edge
into the flute. The curled chip is scaled to fit the flute at this exaggerated feed; its drawn
size is not a thickness measurement. Play it, or drag the tooth through the cut, and use the
dashed slice to compare thickness.
Both cutters turn clockwise, and each cutting tooth is about a third of the way
through its cut. In climb milling the work feeds left and the tooth has
already taken the thick end of its chip. In conventional milling the work
feeds right and the tooth is still in the thin end. The graph says the same thing as a line:
climb runs down from its peak, conventional rises to it. The feed per tooth is drawn many
times larger than it would be on a machine so the chip can be seen at all. The dashed outline
is the slice as the tooth cut it; the solid chip is the same metal curled into the
flute.
Six things to try in the demo; Checklist
Six things to try in the demo
Choose Compare both and step until each tooth has only just entered the
work. Which chip is already thick, and which is barely there?
Drag Tooth position in the cut from 0% to 100%, once in each mode. Watch
the uncut-thickness readout: in climb it runs down from the peak, in conventional it runs
up to it.
Set the width of cut to 50%. The tooth now cuts through a quarter of a
turn and the chip reaches the full feed per tooth. Drop it to 10%: the peak falls to
60% of the feed. At the same feed, a narrower cut makes a thinner chip.
Raise the feed per tooth and watch the dashed uncut slice
grow thicker. Its thick-to-thin trend stays the same. The curled chip is scaled to fit the
flute and may stop growing on screen; compare thickness using the dashed slice.
Follow one chip from start to finish. Pause just before a tooth leaves the work, then
step forward. In which mode is the thick end of the chip at the curled tip, and in which is it
still on the edge? Where does each chip go once it is free?
Watch the red-orange arrow, the pull of the cut on the work. In climb it pulls the work the
way it is already going and presses it down. In conventional it pushes back against the feed
and lifts. Keep that in mind for the card on backlash.
Chip Forming Characteristics
Chip Forming Characteristics
A chip does not stay where the slice was. The cutting edge shears it off the work,
it slides along the face in front of the edge and curls into the flute, and the flute carries it
round until it is thrown clear. The drawings compare chip paths in the cross-section of this
horizontal-cutter setup; they do not predict a universal chip-flight direction.
Swipe the four moments sideways on a narrow screen, or focus the
drawing and use the arrow keys to scroll.
One chip from each direction, at four moments. In climb milling
the chip is finished at the finished surface, where the tooth leaves the work, and the end that
curled furthest is its thick end. It is thrown out behind the cutter, over the surface that has
already been cut. In conventional milling the chip is finished at the top of
the cut with its thick end still on the edge, and this cross-section carries it toward the
uncut side.
Reading the cutter
Cutting edge: the tip of each tooth, the only part that touches the
finished surface. The tooth that is cutting is outlined in blue.
Rake face: the face just in front of the edge. The chip slides along it as
it forms.
Flute: the curved valley in front of each tooth. The chip curls in it and is
carried out of the cut in it, so a flute packed with chips cannot take the next one.
Core: the solid centre, hatched because the drawing cuts through it. In
this illustrated family, more flutes leave a thicker core and less room for chips. Actual
proportions depend on the tool design.
The chip is drawn shorter and thinner than the slice so it fits the flute at a feed drawn many
times too large. A continuous metal chip usually becomes shorter and thicker through
deformation; IIT Kharagpur’s chip-formation lesson
explains the change. The path it takes is illustrative. Actual chip motion depends on the
rotation/feed relationship, engagement, flute helix and chip space, material and chip-breaking
geometry, and coolant or air delivery. Helical flutes can also move chips along the cutter axis;
this in-plane drawing does not show that axial evacuation. The cutter’s flutes and chip space follow
Harvey Performance’s end mill anatomy.
Starting thin means rubbing; starting thick means a bite
Starting thin means rubbing; starting thick means a bite
A real cutting edge has a rounded tip. When the uncut layer is extremely thin, the edge can
push and rub the metal before a chip forms. The peripheral cuts shown here make that difference
visible.
Conventional milling starts every chip at zero, so every tooth rubs before
it bites. Rubbing makes heat and wears the edge. Look at where the tooth enters, too:
on the finished surface, the one you are keeping.
Climb milling starts the chips shown here at their thickest, so the tooth bites at
once, with a knock each time a tooth enters.
That is the main reason climb milling is often the preferred direction when the machine can
hold the work steady against it. Whether it can is the next card.
Supporting detail: Addendum 216 — When a rough or hard exterior can change the choice.
Which way the cut pulls on the work
Climb: the teeth drag the work along the way it is already being fed, and
tend to push it down onto the table in the peripheral arrangement shown.
Conventional: the teeth push back against the feed and tend to lift the
work in this arrangement, so whatever holds the work has to resist that lift.
Backlash: why climb milling depends on the machine; Watch out
Backlash: why climb milling depends on the machine
A feed screw moves the table by turning inside a nut. Unless the drive is built to
take it out, there is some clearance between the screw’s thread and the nut. That clearance
is called backlash, and it lets the table shift a little while the screw stands
still.
The clearance is drawn far larger than it is, and a real drive engages many turns of
thread, not one. What matters is which side of the gap the nut ends up on.
Conventional: the cut pushes the table back, against the feed. That holds
the nut against the flank of the thread the screw is driving with, so the gap stays on the far
side and the table moves only as fast as the screw turns.
Climb: the cut pulls the table forward, the way it is already moving. If
there is clearance, the table can slide across it ahead of the screw, and the cutter takes a
bigger bite than the feed was set for, all at once. That sudden, oversized bite is hard on the
cutter and on whatever is holding the work.
This is a question to ask about a machine, not a rule. How much clearance a
feed drive has, and whether it is built to take it out, differs from machine to machine. This
page does not tell you which direction to use on any machine you will meet. Ask the person
responsible for that machine.
Supporting detail: Addendum 217 — Why some machines climb mill without trouble.
A slot is both at once
A slot is both at once
When the cutter is buried across its whole width, cutting a slot, each tooth enters at one
wall and leaves at the other. Its chip starts thin, is thickest halfway across, and ends thin. The
first half of the sweep moves against the feed, like conventional milling, and the second half
moves with it, like climb milling, whichever way the work is fed. That is why the demo stops at
half the cutter’s diameter: past that point the two can no longer be pulled apart.
Engineering Fundamentals/Power Transmission
Backlash and Lost Motion
After a feed screw reverses, the handwheel turns through the thread clearance before the carriage moves. Predict that dead band from clearance and lead, and finish every approach in one direction.
The dial counts screw rotation; the indicator finds the carriage
The dial counts screw rotation; the indicator finds the carriage
A handwheel dial does not measure the carriage. It counts how far the screw has turned and multiplies by the lead. That is the carriage's travel only while the screw keeps pushing the nut in one direction.
A screw and its nut need some clearance between their thread flanks (a flank is the sloping side of a thread). After the screw changes direction, it must turn through that clearance before its other flank meets the nut and the carriage moves again. That clearance is backlash, the same idea defined for threads in Screw Threads and for gear teeth in Gear Drives and Tooth Geometry. The turn spent crossing it is lost motion: input that produces no output.
Dial reading: travel predicted from screw rotation, turns × lead. See Lead Screws.
Carriage position: where the carriage really is, as an indicator touching it would show.
The difference is zero after a forward approach (the direction the dial was zeroed in) and one full clearance after a reverse approach.
Supporting detail: Addendum 218 — Where the definition comes from.
Experiment: reverse the handwheel and watch the carriage wait; Interactive
Experiment: reverse the handwheel and watch the carriage wait
What the lab does: a handwheel turns an axially fixed lead screw. The dial reports travel calculated from screw rotation; an indicator on the carriage reports where the carriage really is. With a total axial clearance B between screw and nut flanks, the two agree only while the screw keeps pushing in the direction the dial was set in.
Dead band after a reversal = clearance ÷ lead, as a fraction of a turn:
angle = 360° × B ÷ Ldial divisions = B ÷ (L ÷ 100) on a dial with 100 divisions per turn.
Worked example: lead L = 5 mm/rev, so one division is 0.05 mm. Clearance B = 0.20 mm. Angle = 360° × 0.20 ÷ 5 = 14.4°; divisions = 0.20 ÷ 0.05 = 4. For four divisions after the reversal the dial changes and the carriage does not.
Driven forward to 1.00 mm, then reversed four divisions: the dial reads 0.80 mm (the shaded graduations passed under the index) while the indicator still reads 1.00 mm. Illustrative dial, lead 5 mm, clearance 0.20 mm.Forward 0 → 1.00 mm, back to 0, forward to 1.00 mm again. Each reversal runs along a flat step 0.20 mm long, so the path is a loop B wide measured along the dial axis.The same three moments in the thread, drawn to scale for lead 5 mm and clearance 1.0 mm (the exaggerated clearance of the 3D model). The heavy blue line marks the flank in contact. Reversing moves the contact from one flank to the other; between the two, nothing pushes the carriage.
Landing on 25.00 mm after overshooting to 25.60 mm (lead 5 mm, clearance 0.20 mm). The dial was zeroed after a forward approach, so it equals the carriage position only for forward approaches:
Same dial number, two approaches.
Method
Dial moves
Dial
Carriage
Error
Reverse straight to the number
25.60 → 25.00 mm
25.00 mm
25.20 mm
+0.20 mm
Back past it, approach forward again
25.60 → 24.50 → 25.00 mm
25.00 mm
25.00 mm
0.00 mm
Reversing straight to the number stops the carriage one full clearance away from the dial reading, still on the overshoot side: the dial shows 25.00 mm while the carriage is at 25.20 mm. Backing past the target by more than the clearance and finishing in the original direction puts the screw back on the flank the dial was set against.
Model limits: rigid parts and a kinematic dead band only. Friction is assumed to hold the carriage still inside the clearance, and nothing else pushes it along the axis; there is no force, stiffness, preload or stick-slip model. Lead, clearance and the 3D dimensions are illustrative and exaggerated, not a standard thread or a measured machine.
Predict the dead band: clearance divided by lead, as a fraction of a turn
Predict the dead band: clearance divided by lead, as a fraction of a turn
Once the screw reverses, the carriage stays still until the screw's helix has moved one full clearance B. One turn moves the helix one lead L, so the dead band is B ÷ L of a turn.
dead-band angle = 360° × B ÷ L
dead-band divisions = B ÷ (value of one division); with 100 divisions per turn, one division is L ÷ 100.
Same clearance, two leads (illustrative values, 100-division dial).
Lead L
One division
Clearance B
Dead band
5 mm/rev
0.05 mm
0.20 mm
4 divisions = 14.4°
2 mm/rev
0.02 mm
0.20 mm
10 divisions = 36°
The carriage error after a reverse approach is the same 0.20 mm in both rows. A finer lead only spreads that same clearance over more of the handwheel turn.
Land on a dimension: finish every approach in the direction the dial was set
Land on a dimension: finish every approach in the direction the dial was set
If you overshoot a target, turning straight back to the number leaves the carriage one clearance away from it, because the screw is now pushing on the other flank. Instead:
Back the handwheel past the target by more than the backlash.
Turn in the original direction again and stop on the number.
The same reasoning applies when setting a dial. MIT's 2.670 milling notes say to “be certain that the backlash in the mechanism driving the table is taken up prior to setting the dial indicator”. A dial set with the clearance taken up in one direction reads true for approaches in that direction. For edge finding, Mill Indicators and Part Zero repeats the touch from the same direction for the same reason.
Supporting detail: Addendum 219 — A readout that measures the slide, and when the clearance still matters.
What the lab model includes and leaves out
What the lab model includes and leaves out
Included: a rigid screw that turns but never slides along its axis, a nut fixed to the carriage, and a total axial clearance B. The carriage position c stays within B/2 of the screw's helical phase s = −Lφ/360° (right-hand thread, φ the screw rotation); inside that band it does not move.
Assumed: friction holds the carriage still inside the clearance, and no outside force pushes it along the axis.
Left out: forces, friction values, stiffness and elastic wind-up, preload, stick-slip and wear. Drives designed to remove the clearance, such as preloaded ball nuts or adjustable split nuts, are beyond this model.
Illustrative: the leads, clearances and the 3D screw (5 mm lead, 1.0 mm clearance, 30° flanks) are chosen to be seen, not taken from a standard thread or a measured machine.
For drive design in depth, Alexander Slocum's Precision Machine Design (1992) covers actuators and transmissions in Chapter 10, including section 10.8, Linear Power Transmission Elements.
Mill around an island: X and Y backlash change the material left behind; Interactive
Mill around an island: X and Y backlash change the material left behind
A perfect 4 mm diameter cutter makes one contour groove around a 24 mm circular island. The dashed outline is the intended island; span errors compare with zero backlash. Material in the middle and outside the groove remains: this is not a pocket-clearing path. Only X/Y drive clearance changes.
Cut as intendedExtra cutMissed cut
Zero backlash · X 0.00 / Y 0.00 mm
X span at Y = 024.000 mm0.000 mm error
Y span at X = 024.000 mm0.000 mm error
X only · X 0.50 / Y 0.00 mm
X span at Y = 023.500 mm−0.500 mm error
Y span at X = 023.989 mm−0.011 mm error
Y only · X 0.00 / Y 0.50 mm
X span at Y = 023.989 mm−0.011 mm error
Y span at X = 023.500 mm−0.500 mm error
Both axes · X 0.50 / Y 0.50 mm
X span at Y = 023.500 mm−0.500 mm error
Y span at X = 023.500 mm−0.500 mm error
All four start at the right side and run counterclockwise. Before the plunge, both axes approach the start in their positive directions and the coordinates are calibrated there. On reversal, the actual cutter can stay still along one axis while moving along the other. Its full circular footprint removes material along that path.
The spans above are sections through X = 0 or Y = 0, not a best-fit circle or the greatest overall width. They come from intersections with the swept cutter, not pixel counting. Changing the start, winding or initial seating can change the local shape; do not infer that every circle becomes the same oval.
Approximation: circular paths use 1° chords (under 0.001 mm sag here). These printed diagrams use 0.20 mm cells; the live area shading uses 0.10 mm cells. The millimetre span readings use the underlying swept chords.
The cutter removes the upper layer at one fixed depth. Grey is material still at its original height; the groove floor is not drawn. A boundary pass leaves both an island and the surrounding stock, so it is not a cleared pocket. The dashed line is the intended island boundary, not the cutter-centre path: that path is one cutter radius outside it.
Supporting detail: Addendum 220 — What the model means, and why it is not a prediction for every CNC.
Machining/Milling
Feeds and Speeds
Six key quantities connect cutting data to the machine and the cut: cutting speed, feed per tooth, spindle speed, table feed, radial engagement and axial depth.
Six quantities connect the cutting data, machine and cut
Six quantities connect the cutting data, machine and cut
Start by separating six quantities. Cutting speed and feed per tooth describe
what the cutting edges should experience. Spindle speed and table feed are the corresponding
machine settings. Width of cut and axial depth describe how much of the cutter is engaged. The
exact starting values come from cutting data for the tool, material and operation.
Cutting speed
How fast the cutting edge moves through the material: the speed
at the outside of the cutter. Written in surface feet per minute (SFM) or
metres per minute (m/min). Also called surface speed. Comes from cutting
data.
Feed per tooth
How far the work moves while the cutter turns from one tooth to
the next, in inches or millimetres per tooth. Also called chip load, because it sets the
size of the bite each tooth takes. Comes from cutting data.
Spindle speed
How many turns the cutter makes each minute, in revolutions per
minute (rev/min, usually said RPM). Set on the machine.
Table feed
How fast the work moves past the cutter, in inches or millimetres per
minute. Also called the feed rate. On a machine that moves the cutter instead, it is how
fast the cutter travels. Set on the machine.
Width of cut, ae
The cutter’s radial engagement in
the work, measured across the cutter in inches or millimetres. It is also called radial
depth of cut; those names describe the same quantity, not two separate settings.
Axial depth of cut, ap
The distance engaged along the
cutter’s axis, in inches or millimetres: the difference between the uncut and cut surfaces in
that axial direction.
"Speeds" are the cutter turning; "feeds" are the work moving. That is all
the phrase feeds and speeds means. The two are set separately on the machine, and the
rest of this page is about how they depend on each other, how width and axial depth set the
engaged cut, how much metal that cut removes, and the power it takes. Climb and Conventional Milling
explains how feed direction relative to rotation changes the chip from thin-to-thick or
thick-to-thin.
Spindle speed: the turns it takes to reach the cutting speed
Spindle speed: the turns it takes to reach the cutting speed
Cutting speed is a distance per minute, measured at the edge of the cutter. In one turn, a point
on that edge travels once around the cutter: its circumference, π × D.
So the spindle speed is the cutting speed divided by the distance one turn covers, once the two
are in the same units.
One turn of a 0.5 in cutter carries its edge 1.571 in. A cutting speed of 300 SFM
asks the edge to cover 300 ft, which is 3,600 in, every minute.
The 12 is there because cutting speed is in feet and the diameter is in inches:
12 inches to the foot. In metric units the same idea needs a 1000, millimetres to
the metre:
Worked example, with illustrative numbers. A 0.5 in cutter, with cutting data
that calls for 300 SFM: 12 × 300 ÷ (π × 0.5) = 2,292 rev/min.
The 300 SFM is there to make the arithmetic concrete. It is not a recommendation for any tool or
any material. The feed value below is illustrative too; use the later material guide for the
carbide starting bands.
Look at where the diameter sits: underneath. Halve the diameter and the spindle speed
doubles. A small cutter has to turn faster to give its edge the same cutting speed, which
is why small cutters so often ask for more speed than a machine has. That case has its own card
below.
Table feed: each tooth takes one chip load as it passes
Table feed: each tooth takes one chip load as it passes
Each time a tooth passes, the work should have moved one feed per tooth. The number of teeth
passing each minute is the spindle speed times the number of flutes, so:
Worked example, continued. A 4-flute cutter at 2,292 rev/min, with a feed per
tooth of 0.002 in: 2,292 × 4 × 0.002 = 18.3 in/min. The units work out
on their own: turns per minute, times teeth per turn, times inches per tooth, leaves inches per
minute.
Turned around, the same relation tells you what chip load a feed gives. That is the way to check
a feed someone else has set:
Flutes here means the teeth that actually take a chip in each turn. For an
ordinary end mill that is simply the number of flutes.
Removal rate: width × depth × table feed
Removal rate: width × depth × table feed
Two more numbers describe the cut itself. The width of cut is how far the
cutter reaches sideways into the work, across the direction of feed. The depth of
cut is how far down its side the cutter is buried, along its axis. A side cut can be no
wider than the cutter; a wider path takes more than one pass.
While the table feeds, the cutter sweeps through the work and leaves a channel behind it. In a
stretch of time the cutter travels table feed × time, and the solid metal it
takes out in that stretch is a slab as wide as the cut, as deep as the cut, and as long as that
travel. Per minute, that is the material removal rate:
Removal rate (in³/min) = width of cut (in) × depth of cut
(in) × table feed (in/min)
The front of the cut is curved, because it is the cutter’s own shape. The slab’s
two ends are the same curve, one travel apart, so whatever the curve, the slab holds exactly
width × depth × travel.
Worked example, continued. The same cutter, 0.1 in wide (20% of its diameter)
and 0.5 in deep, at 18.3 in/min: 0.1 × 0.5 × 18.3 ≈ 0.917
in³/min, or 15.0 cm³/min. In 5 seconds the cutter travels 1.53 in and removes
0.0764 in³.
That is the volume of solid metal. Once it is chips, the same metal lies loose
and takes up far more space, so the removal rate is not the size of the chip pile.
Cutting power: removal rate times the energy each cubic inch takes
Cutting power: removal rate times the energy each cubic inch takes
Cutting a cubic inch of a given material takes roughly a given amount of energy. That is its
specific cutting energy, and it is why the same cut needs more power in steel than
in aluminum. Written as power per unit of removal rate, it turns a removal rate straight into
power:
Cutting power (hp) = removal rate (in³/min) × unit power
(hp per in³/min)
Cutting power (W) = removal rate (mm³/min) × specific
energy (J/mm³) ÷ 60
The 60 turns minutes into seconds, because a watt is a joule per second. One
mechanical horsepower is 745.7 W.
Worked example, continued. For 6061-T6 aluminum the guide in the calculator
gives a band of 0.16 to 0.30 hp per in³/min. At 0.917 in³/min that is about
0.15 to 0.28 hp, or 110 to 210 W. The same cut in 304 stainless steel, whose band
is 0.65 to 1.3 hp per in³/min, needs about 0.60 to 1.2 hp.
The answer is usually a band. Some table rows give one factor; that still
produces an estimate, not a measured certainty. Published bands cover a family of materials over
a range of hardness, and the energy a real cut takes also depends on chip thickness and
cutting-edge geometry. Treat the band as the size of the job, not a
prediction to the watt.
Three different powers get called “the power”, and they are not the same:
Cutting power is what the cutting edge spends. That is the estimate
above.
Motor shaft power is more, because the belts, gears and bearings between the
motor and the cutter lose some on the way. If the drivetrain passes on 80% of what the motor
delivers, the motor must deliver the cutting power ÷ 0.8.
Electrical power drawn from the supply is more again, because the motor and
its drive lose some too.
None of these tells you whether a machine can take the cut. A spindle motor’s rating is
not necessarily available at every speed, and power is only one limit: the tool, the holding and
the machine’s stiffness are others. Use the estimate to compare cuts and to see why a cut
is heavy, not to approve one.
Calculator: from material guidance to removal and power; Interactive
Calculator: from material guidance to removal and power
Choose a material to see generic carbide starting ranges for it, then enter the
cutter, the cutting data and the cut. Nothing is filled in for you. Each result appears as soon as
the fields it needs are filled, and says what it is still waiting for until then. Use the middle
of these ranges fills in only the cutting speed and feed per tooth.
How to read the drawings. You are looking at a block of work from the front,
a little above and to the right. The cutter feeds to the right along the front top edge.
Gold is the solid metal removed in the time shown, drawn where it was before the
cutter took it. The dashed blue curve is where the front of the cut stood when that time began;
the outlined cylinder is the cutter now. The three labeled axes use the same length scale, and the
drawings in one comparison share that scale, so a slab twice as long is twice the volume. The
block around the cut is there only to hold it; its size means nothing. The cut is already
underway when the interval starts; only the gold volume counts toward that interval.
The comparison below the drawings prices the setup’s removal rate in every material.
The cut is the same in every row; only the energy per cubic inch changes.
Setup2,292 rev/min · 18.3 in/min
In 5.00 s: travel 1.53 in, removed 0.0764 in³Removal rate 0.917 in³/min · power ≈ 0.15–0.28 hp
In 5.00 s: travel 3.06 in, removed 0.153 in³Removal rate 1.83 in³/min · power ≈ 0.29–0.55 hp
MaterialEstimated cutting power at 0.917 in³/min
6061-T6 aluminum0.15–0.28 hp
7075-T6 aluminum0.15–0.28 hp
1018 mild steel0.56 hp one factor
1045 steel0.56–0.59 hp
4140 prehard steel0.72–0.83 hp
304 stainless steel0.60–1.2 hp
316 stainless steel0.60–1.2 hp
Class 30 gray cast iron0.40–0.60 hp
C360 brass0.28 hp one factor
Ti-6Al-4V titanium0.69–1.1 hp
01.02.0 hp
The worked example, 0.5 in cutter, 0.1 in wide and 0.5 in deep, three ways over
the same 5 seconds and at one scale. Doubling the spindle speed with the table feed held leaves
the slab unchanged: the same metal is removed, in chips half as thick. Doubling it with the chip
load held doubles the table feed, so the slab is twice as long and the removal
rate and power estimate double. Below, the setup’s 0.917 in³/min priced in each
material, from the guide’s cutting-energy bands.
Things to try in the calculator; Checklist
Things to try in the calculator
Before typing anything, read the results. Each one names the fields it is waiting for.
With 6061-T6 aluminum chosen, enter a 0.5 in diameter and
4 flutes, then press Use the middle of these ranges. Cutting speed and
feed per tooth fill in at 400 SFM and 0.00415 in/tooth. Nothing else changes.
Enter a width of 0.1 in and a depth of 0.5 in. Check the
removal rate against width × depth × table feed in the arithmetic.
Change the material to 304 stainless steel. The drawings, the table feed and
the removal rate stay exactly as they were; only the power estimate moves. The guide now marks
your cutting speed as above its range for stainless, but the calculator leaves your entries
alone.
Hold the table feed and drag the spindle speed to 200%. The slab does not
change and nor does the removal rate: the same metal comes off, in chips half as thick.
Now hold the chip load and do the same. The table feed doubles, the slab
grows twice as long in the same time, and the removal rate and power estimate double.
Switch to metric and back. The cut and every result stay the same, written
in other units, and any field you left empty stays empty.
Try a width larger than the diameter. The calculator refuses it: that is more than one
pass.
Enter a 0.125 in cutter with a 4,000 rev/min machine top
speed. Compare the speed the cutting speed asks for with the speed the machine can reach, and
where the cutting speed actually reached sits against the guide.
When the machine cannot turn as fast as the formula asks
When the machine cannot turn as fast as the formula asks
Because small cutters ask for high spindle speeds, the formula can easily give more than a
machine’s top speed. A 0.125 in cutter at 300 SFM asks for 9,167 rev/min. On a machine that
stops at 4,000, it runs at 4,000.
Work the feed from the speed the spindle really turns. At 4,000 rev/min, with
2 flutes and 0.0008 in per tooth, that is 4,000 × 2 × 0.0008 = 6.4 in/min. Each tooth
then takes the chip load you meant it to.
The cutting speed is what you give up. At 4,000 rev/min the edge of a 0.125 in
cutter moves at π × 0.125 × 4,000 ÷ 12 = 131 SFM, not the 300 the data
asked for.
Working the feed from the speed that was asked for, rather than the one the spindle is turning,
gets the chip load wrong by the same ratio. A feed worked from 9,167 rev/min would give each tooth
9,167 ÷ 4,000 = 2.3 times the chip load intended.
The same applies to a machine that offers only certain speeds, through belts or gears: set the
nearest speed it has, and work the feed from that one. The calculator’s machine top
speed box does this for a top speed.
Generic ranges are a starting point, not your tool’s data; Watch out
Generic ranges are a starting point, not your tool’s data
What determines the surface speed?
Start with the material and its hardness, then the cutting tool. Carbide is
a tool material, not one universal cutting edge: its grade, coating and geometry matter, as do
coolant and how steadily the setup can cut. A harder material generally calls for a lower
starting speed. Once that surface speed is chosen, the diameter determines the RPM;
a smaller cutter must turn faster to reach the same surface speed.
What determines the feed per tooth?
Choose a bite the cutting edge can carry and the flute can clear. That is why
the guide changes with cutter diameter: small cutters generally take smaller bites. Width and
depth of cut, a full-width slot, a long tool and a flexible setup change the loading and chip
clearance. The number of flutes then tells you how many of those bites happen per turn; it does
not by itself choose the size of each bite. Use the diameter-based range as a starting point,
with its stated engagement, and refine it from the actual tool’s cutting data.
The arithmetic on this page is exact. Its inputs are the part that takes
judgement. The ranges in the calculator are generic starting bands for solid-carbide end
mills, by material family, from published toolmaker tables. The cutting data for your
tool comes first: normally the toolmaker’s for that tool, that material and that kind of
cut, or the person responsible for the machine.
Cutting data accounts for things these formulas cannot see: the exact grade and hardness of the
material, the tool’s coating and geometry, how far it reaches out of the holder, coolant, and
how the setup is held. The guide’s feed-per-tooth ranges assume a side cut about 20% of the
cutter’s diameter wide; a full-width slot or a long reach needs the tool’s own data. A
calculator turns data into machine settings. It cannot tell you whether the data suit your cut.
Supporting detail: Addendum 221 — Feed per tooth is not always the thickness of the chip.
Machining/Milling
Tool Stickout and Deflection
A longer tool reaches farther, but bends much more under the same sideways load. Predict a change, test it, and compare the tool with a fixed baseline.
Experiment: how much does a shorter tool help?; Interactive
Experiment: how much does a shorter tool help?
Predict first: keep the same solid tool, force and material. If its unsupported length drops from 80 to 40 mm, will it bend half as much, one eighth as much, or the same amount?
Halving the clamp-to-load length, from 80 to 40 mm, cuts ideal tip bending from 57.947 to 7.243 µm: one eighth as much. Both drawings use the same geometry scale and ×100 bend magnification. Dashed outlines are the unloaded tools.In this ideal one-sided wall pass, the cutting edge bends away from the work. The short setup leaves 7.243 µm of extra material at the tip. This is a geometric consequence of the assumed load, not a prediction of a real finished part.
The length that matters starts at the clamp
The length that matters starts at the clamp
Stickout is unsupported length. Here it is the distance from the rigid clamp face to the point where the sideways force acts. It is not the total tool length, and it is not automatically the flute length.
A force bends the tool and moves its cutting edge away from its unloaded position. The clamp end stays in place and keeps its direction; the bend grows along the unsupported length. In a real cut, force acts over the engaged cutting edges rather than at one perfect point.
Reach is a tradeoff. The tool must reach the feature and clear the work and holder. Within those constraints, reducing unnecessary stickout improves bending stiffness. A larger diameter can also help if the feature has room for it.
Length is cubed; diameter is raised to the fourth power
Length is cubed; diameter is raised to the fourth power
For the ideal solid round tool in this lab, tip bending is proportional to F × L³ ÷ (E × d⁴). Change one input at a time to see which factor is responsible.
½ length → ⅛ bendHalf × half × half. Shortening the unsupported reach is a powerful change.
2× diameter → ¹⁄₁₆ bend2 × 2 × 2 × 2 goes into the denominator. This comparison is for solid round sections.
2× force → 2× bendForce acts linearly. Double E instead, with the other inputs fixed, and bending halves.
Try a combined change: start at L = 40 mm and d = 10 mm, save that baseline, then set L = 80 mm and d = 20 mm. The length contributes 8× and the diameter contributes 1/16×, leaving half the bending at the same load and modulus. The two changes compete.
Supporting detail: Addendum 222 — The calculation and its units.
Use the trend; know what this model leaves out
Use the trend; know what this model leaves out
This is a static, linear-elastic, slender-beam model: a uniform solid round tool, a perfectly rigid clamp, a steady sideways point load at the free end and deflections small compared with the length. Elastic modulus E measures stiffness, not hardness or breaking strength.
The lab starts at E = 600 GPa, a chosen teaching value within Hyperion's published 430–690 GPa range for cemented-carbide wear grades. It is not a universal value for carbide cutters. The force is an assumed input, not calculated from a milling operation.
Flutes and necks change stiffness. The holder, spindle and workpiece can move too, and a milling force changes as teeth engage. Static bending alone does not predict chatter thresholds, surface roughness, fracture, safe loads or guaranteed finished-part error.
The lab flags L/d below 4 and bending above 1% of L as prompts to question this simplification. Those are teaching checks, not certification or safety limits.
Identify lathe parts, choose workholding and tools, and explore turning operations in a simulator before studying tapers and threads.
Identify the parts that rotate, guide and feed
Identify the parts that rotate, guide and feed
Typical engine-lathe arrangement. Controls and drive arrangements vary by machine.
Headstock and spindle
The headstock supports the rotating spindle and its drive. The spindle carries the chuck, faceplate or other workholding. Its axis is the reference for turning.
Bed and ways
The bed supports the assemblies. Its guide surfaces, called ways, guide carriage travel and locate the tailstock.
Tailstock
Supports the far end of work with a center, or holds axial tools such as drills and machine reamers. Its quill extends along the spindle axis when aligned.
Carriage, cross slide and compound rest
The carriage moves along the bed. The cross slide moves across the axis. The compound sits above it and swivels to guide short angled movements. The tool post holds the cutting tool on the compound.
Apron
The assembly on the front of the carriage contains feed mechanisms and controls.
Feed rod and leadscrew
On machines with separate drives, the feed rod powers ordinary turning or facing feeds; the leadscrew synchronizes threading. Some lathes combine functions, so identify the actual drive arrangement before selecting a feed.
Half-nuts and quick-change gearbox
The half-nuts close around the leadscrew to drive the carriage during threading. The gearbox selects ratios for feeds or thread pitches; its chart tells you which control combinations produce each ratio.
Choose workholding for the shape and the surface that must run true
Choose workholding for the shape and the surface that must run true
Running true means the reference surface is centered on the spindle axis, with little measured runout. Gripping a part does not automatically establish that alignment.
One device can perform several roles, but the roles are not interchangeable. The drive path shown for work between ordinary centers runs from the drive plate through the dog; the centers support and locate the axis.
Read the role before choosing the device. A setup can combine location, grip, drive and support. Support is not the same as drive, and gripping a surface does not by itself establish that it runs true.
Three-jaw scroll chuck
Moves its jaws together for quick gripping of round or suitable hexagonal stock. Self-centering is convenient, but does not promise zero runout, especially after removing and replacing a part.
Four-jaw independent chuck
Moves each jaw separately. Useful for square or irregular work, intentional offsets, or indicating an existing surface true. Adjustment takes more time.
Collet
Grips around a matching stock shape over a limited size range. Useful for repeated work and small diameters; choose the correct collet and its permitted clamping range.
Centers and drive dog
Centers locate work through prepared center holes. A dog clamped to the work transmits torque from a drive plate; the centers provide support. Useful when several surfaces must share the center-hole axis or the work must be removed and returned.
Faceplate
Provides slots or mounting features for clamping work that does not suit chuck jaws. The fixture must locate the intended axis and account for the off-center mass.
The steady rest stays at one bed position. The follow rest moves with the carriage near the cutter. In both examples the chuck remains the primary drive; the rest contacts support the rotating work.
Steady rest
Mounts on the bed and supports a long workpiece at a fixed position. It can support work when the end must remain accessible for drilling or boring.
Follow rest
Mounts to the carriage and travels with the tool. It supports slender work near the cut to reduce bending under cutting force. Its support contacts must suit the diameter being supported.
Supporting detail: Addendum 224 — Reference examples for these mechanisms.
Match tool travel to the feature, and set the edge on center
Match tool travel to the feature, and set the edge on center
Facing feeds across an end to establish a plane perpendicular to the axis. Straight turning feeds parallel to the axis to make a cylinder. Shoulder turning joins a cylindrical diameter to a step face; the tool needs clearance to reach both surfaces without its holder or unused edge contacting the work.
Center drilling prepares the seat for a supporting center. It is not automatically the best starting method for every drill. Tailstock drilling makes an axial hole; reaming removes a controlled small allowance to improve hole size and finish. Select that allowance from the reamer maker. A reamer generally follows the existing hole, so it is not a reliable way to correct a misplaced hole. Boring uses a single-point tool to enlarge an existing hole and establish its surface relative to the spindle axis.
Grooving makes a recess; parting continues a similar radial cut until the part separates. Chamfering makes a bevel at an edge. Form knurling presses a pattern into the surface and increases the diameter over the raised points; cut knurling is a different process.
Use spindle center height as the starting reference for ordinary turning and threading tools, then follow any tool-specific instruction. An off-center edge changes the effective rake and clearance. In facing, a tool that cannot reach the axis leaves a small central nub. Boring also needs clearance between the tool and the curved hole wall.
Supporting detail: Addendum 225 — Rake and chipbreakers depend on the whole cutting setup.
A lathe spins the work and moves the tool on two slides
A lathe spins the work and moves the tool on two slides
In ordinary turning the work rotates while the tool feeds along it or toward its
center. This simulator models parts that are round about the spindle’s axis.
The shape comes from where the tool is put against the turning work, and in what
order.
Chuck
Grips the bar and turns with the spindle. The jaws hold one end; the tool
works on the part of the bar that sticks out.
Carriage (Z)
Carries the tool along the bed, parallel to the axis. On this page
Z minus is toward the chuck and Z plus toward the
tailstock.
Cross slide (X)
Moves the tool straight toward or away from the axis. The
simulator’s X readout is the diameter the tool would cut. On a real lathe,
find out whether a dial or readout shows diameter or radius before you trust it.
Tailstock
At the far end of the bed, on the centerline. It holds the center drill,
the drills and the countersink, which feed straight along the axis.
Z0
Where the drawing’s finished front face belongs. Every length on the
drawings is measured from the front face.
How to read the simulator’s picture. It is the lathe seen from the front,
with the whole work in one of two views; the switch under the picture changes view at any time
without changing the work. Section cuts the work in half along its centerline, the
way a section drawing shows a part: metal is hatched, a hole shows open, and a thread or knurl shows
as its profile. Normal shows the outside, as you would see the part on the machine,
with its thread and knurl; a hole is drawn as a dashed hidden line, and a tool working inside the
part is hidden by it. Tools on the cross slide come in from above, in the plane the section is cut
on, so a tool and the metal it cuts are in the same plane.
The dashed blue outline is the drawing, placed at Z0. Tinted metal is still to come off. A heavy
red-orange dashed line marks work that is already smaller than the drawing allows. On each tool, the
gold edge is the part that cuts and the small ring is the point the readout follows.
Before using a real lathe, read Machine Hazards and Housekeeping. The chuck key stays in your
hand until it is out of the chuck.
Lathe simulator: make the part on the drawing; Interactive
Lathe simulator: make the part on the drawing
The stepped pin part-way through. The facing blade made the end flat; the body
was rough-turned short of its shoulder. Its angled allowance still needs radial facing.
The rougher is halfway along the first pin pass. The tinted metal is still to come off.
Each target is shown in a complete Normal outside view and a
complete Section through its centerline. Dashed lines in Normal identify hidden
internal features. Section thread bands are schematic crest/root envelopes; the knurl remains a
surface callout. Dimensions are nominal inches; the simulator’s feature table gives the limits.
Stepped pin. Two turned diameters, a chamfer on the end and a head left at bar size. From 1.000 in bar. Facing, turning in passes, square shoulders, chamfering and parting off.
Bushing. A turned sleeve with a through bore, two outside chamfers and a chamfer at the bore mouth. From 1.250 in bar. Center drilling, drilling, boring, countersinking and chamfering a back edge before parting.
Thumb screw. A knurled head, a thread relief groove and a 16-per-inch thread. From 1.000 in bar. Knurling, grooving, external threading in passes, and why a thread needs somewhere to stop.
Knurled nut. A knurled ring with a 13-per-inch thread inside it. From 1.000 in bar. Drilling to the thread's inside size, internal threading and parting off a ring.
Pick a part and read its drawing (Drawing opens it). Then make it from bar: choose a
tool, start the spindle, and move the tool against the work. Measure the part against the drawing
whenever you stop.
Move the tool by dragging it in the picture, one slide at a time as if you were
turning one handwheel; with the handwheel buttons, which repeat while held; with the arrow keys once
the picture is selected; or by typing a position and pressing Feed to Z or Feed to
X. Stop feed, or Escape, stops a feed part-way.
The spindle has to be running for anything to cut, and stopped before you change
a tool, change the drill size or thread pitch, or measure the part. A caliper or micrometer never
goes on turning work.
Each tool does only its own kind of work. When a move would ask a tool for
something it cannot do, the simulator stops the tool there and says why. What the tool in use can
and cannot do is listed under the tool rack. Turn / face offers two actual tools in its
Cutting tool selector; stop the spindle before changing between them.
Undo takes back one cut at a time. New bar starts the part again,
and undo brings the old bar back.
Measure compares every feature with the drawing. The list under the simulator
says what each feature still needs, or whether it has already gone too far to save.
Each simulator tool has a defined job; its form knurl displaces metal
Each simulator tool has a defined job; its form knurl displaces metal
Facing, turning, drilling, threading and knurling are not the same action with a
different shape of tool. Each tool reaches different places and moves in different ways.
Turning tool
The roughing tool supplied here has a 10° lead and a
0.008 in nose radius. Its angled edge reaches ahead of its readout point. Stopping an axial
pass leaves an angled shoulder; leave allowance instead of running the nose to the finished
shoulder plane.
Facing tool
A square, 1/16 in wide finishing blade set for radial feed.
Put its left corner at the finished Z and feed X across the end or shoulder. Its actual sweep
removes the allowance and leaves the face flat. Retract clear before moving Z. These are the
simulator’s selected tools; other turning tools and settings can both turn and face.
Chamfer tool
A 90° point. Plunged at an edge, each side cuts a 45°
chamfer.
Grooving and parting blade
Cuts only on its front edge. Plunged part of the way it
makes a groove; plunged to the center, or into the hole, it parts the work off.
Center drill, drill, countersink
Fed from the tailstock along the axis. A center
drill makes a small pilot and a 60° seat for a lathe center; a spotting drill has different
starting geometry. The twist drill makes the hole and the countersink chamfers its mouth. Choose
a real drill’s starting method and spot angle from its maker’s guidance.
Boring bar
Turns the inside of a hole that is already there, the way the turning tool
works on the outside. Its bar has to fit in the hole.
Threading tools
Form tools with a 60° point, one for outside threads and one on a
bar for inside threads. For a threading pass the carriage is driven by the leadscrew, so the tool
moves one thread lead for every turn of the work; for the single-start threads here, lead equals pitch.
Knurling tool
A straddle head with two opposed forming wheels, with left-hand and
right-hand diagonal teeth. Their axles lie parallel to Z; together they roll a diamond pattern.
Gap Ø is a simulated gap/contact-diameter control. A real tool’s arm adjustment and
locking are separate from cross-slide infeed. The picture shows the barrels and axles in side
projection; the highlighted rims are the forming contact.
What makes the simulator stop a move. Each of these is something the real tool
cannot do, or should not be asked to:
The spindle is stopped, so the tool would only rub.
More of the cutting edge would be in the work than the tool takes in one pass. Take it in more
passes.
A part of the tool that does not cut would touch the work: the holder, the top of an insert, the
bar of a boring tool, the side of a blade.
The tool would hit the chuck jaws.
A threading tool is still in the thread when the carriage moves. Back it out first.
A knurl is pressed past full depth, or into a shoulder.
A drill is three of its own diameters into a cut without being backed out to clear its
chips.
The simulator’s limits are teaching values chosen for these four parts. A real
tool’s limits come from its maker and depend on the machine, the material and the setup.
Tool shape and setting matter:
Sherline’s tool-grinding guide
describes cutting edges, clearance and form tools. The particular blade widths, nose radius and
operating limits used here are declared teaching choices, not specifications for every lathe tool.
Most parts start with a facing cut and end with parting
Most parts start with a facing cut and end with parting
More than one order can make the same part, and the simulator accepts any order that
gets there. Some orders are still better than others, for reasons you can see in the work.
Face first. The faced end is the datum: every length on the drawing is measured
from it. A sawn end is neither flat nor square to the axis.
Rough, then finish. A large step comes off in several passes, and only the last
one goes to the size on the drawing. On the stepped pin, stop the roughing passes 0.040 in
short of each shoulder, retract clear and change to the facing tool. With its left corner at the
final shoulder Z, feed X to the smaller diameter. A deeper shoulder needs more clearance for the
angled edge; the facing blade can remove its allowance in slices up to 0.0625 in wide.
Drill, then bore to size. The boring bar needs a hole its bar fits in. A center
drill is available here to explore its pilot and center-seat shape, but it is not a universal
prerequisite for drilling. On a real machine, use the starting method recommended for the
following drill.
Heavy work before thin sections. Knurling pushes hard on the work. Knurling
before the thin sections next to it are turned keeps the work stiff while it happens.
Make room for the threading tool. A thread needs somewhere for the tool to stop:
a relief groove, or a stop short of the shoulder. Chamfer the end first so the thread starts on a
clean edge.
Chamfer the back edge before parting. Once the part is cut off, its back edge is
out of reach without a second setup.
Part off last. The part falls free, and anything not done to it by then needs
another setup.
The small Chuck end circle is a separate axial view, looking from the tailstock
toward the chuck. Its forward-rotation arrow and animation run counterclockwise in that view.
The main picture is longitudinal, not a view along the spindle. See the viewpoint diagram in
Haas’s
spindle-direction training, page 16.
A thread is cut in several passes along one helix
A thread is cut in several passes along one helix
For a threading pass the carriage is coupled to the leadscrew, so the tool advances
exactly one lead for every turn of the work. For the single-start threads here, that is one pitch: 1/16 in for 16 threads per inch. Every pass follows
the same helix, so every pass deepens the same groove.
The section uses a schematic thread envelope. Its unhatched bands lie between
the surviving crests and dashed roots; they are not solid annular thread teeth. A real single-start
helix intersects opposite sides half a pitch apart. The model samples a thread profile for depth
checks and preserves its material envelope for later cuts and parting. The carriage still stops at
the requested Z, even between full turns. Sandvik
explains the lead/pitch relation for single- and multi-start threads.
A little deeper each pass. The simulator allows 0.015 in of infeed per pass
outside and 0.012 in inside. The thread is done when its roots reach the root diameter on the
drawing.
Back out before you come back. At the end of a pass the tool is still in the
groove. Bringing the carriage back without backing the tool out would cut the crests off.
Keep the pitch. A pass at another pitch cuts a second helix across the first: a
crossed thread.
Leave somewhere to stop. The tool runs into a shoulder unless a relief groove
gives it room, which is why the thumb screw has one.
Supporting detail: Addendum 226 — How a manual lathe keeps every pass on one helix.
A form knurl moves metal instead of cutting it
A form knurl moves metal instead of cutting it
The knurling tool makes no chips. Its wheels press a pattern into the turning work,
and the metal they push aside has to go somewhere: it rises between their teeth. The diameter over
the points ends up larger than the blank was.
Blank
The diameter turned before knurling. On these drawings it is not given: the
knurled size is, and you work back to the blank.
Full points
The wheels pressed deep enough that the diamond points are fully
formed. Too shallow leaves flat tops; pressing past full depth crushes and flakes the
points.
Over the points
The knurled diameter, measured across the crests.
In the simulator the roots sink exactly as far as the crests rise, 0.010 in each
at full depth, so a full knurl adds 0.020 in to the diameter. A real knurl’s growth depends
on its pitch, the material and how hard it is pressed.
On the stepped pin, try to turn the body from 1.000 to 0.750 in in one pass.
Read why the tool stops, then do it in two.
Stop a roughing pass short of a shoulder and Measure. Choose Face without
cutting and measure again. Then make the radial facing cut: which geometry actually changed?
Face the end but stop the cut at X 0.200. Measure: what is left at the
center?
Face 0.010 in past Z0 and make the rest of the pin to the readout. Measure
the lengths. Which ones moved, and why?
On the bushing, bring the boring bar to the end before there is a hole. Then
drill a 1/4 in hole and try again. Which drill gives the bar room?
Drill the bushing without the center drill and read the note under the inspection.
On the thumb screw, try a threading pass up to the head before cutting the
relief groove.
Take one threading pass at 16 per inch, change to 13 and take another. Measure the
thread.
Knurl the head straight on the 1.000 in bar, without turning a blank first. Measure it
against the drawing.
On the knurled nut, part the ring off and watch where the blade breaks
through.
What this simulator leaves out
What this simulator leaves out
The simulator is about which tool does what, in what order, to what size. It leaves out:
Speed and feed. The spindle is on or off. Spindle speed, feed rate and what they
do to the cut are on Feeds and Speeds.
The cut itself. No tool wear, heat, chatter, deflection or surface finish. A
drill cannot wander, so a hole started without a center drill is only noted, not drawn off
center.
Setups. One setup only: no turning the part around, no second operation, no
tailstock center supporting long work.
Threads and knurls, simplified. Thread pitch, crests and roots are checked along
the required length; pitch diameter and functional thread fit are not verified. The form knurl
illustrates displaced material and diameter growth. Its patterned section is schematic, not an
exact volume-conservation calculation. Form
and cut knurling use different mechanisms.
Its numbers. Inch only. The tolerances, the tool limits and the parts are teaching
values, not tool-maker data and not a standard.
Tolerances on the drawings mean the same as on Tolerances and Fits: a size on a
limit passes.
Follow tooth counts through pairs, idlers and compound trains; multiply stage efficiencies and choose gears to meet speed and torque limits.
Experiment: trade speed for turning effort; Interactive
Experiment: trade speed for turning effort
Predict first: a 20-tooth gear turns at 120 rpm clockwise and drives a 40-tooth gear. Will the larger gear turn faster or slower? What changes if you add an idler between them?
One mesh: 2:1 reduction
B has 2× as many teeth as A. Each passing tooth advances B by one tooth space; B turns 0.5× as fast, in the opposite direction. At 120 rpm clockwise and 2 N·m input, output B is 60 rpm CCW and 4 N·m ideally. The dashed circles are pitch circles, where the speeds match.
Add an idler: still 2:1
The idler changes direction twice: A → I → B. Its 30 teeth cancel from (30 ÷ 20) × (40 ÷ 30). At 120 rpm clockwise and 2 N·m input, output B is 60 rpm CW and 4 N·m ideally. The dashed circles are pitch circles, where the speeds match.
Two stages: 2 × 2 = 4:1
B and C turn together. Multiply the two reductions: (40 ÷ 20) × (40 ÷ 20) = 4. At 120 rpm clockwise and 2 N·m input, output D is 30 rpm CW and 8 N·m ideally. The two front-view meshes are separated on the page; the dashed connector represents their common shaft.
All three examples use the same ideal input: 120 rpm and 2 N·m. Input power is 25.13 W, and ideal output power is also 25.13 W. More output torque comes with less speed.
With each actual mesh at 96% efficiency, the pair delivers 3.84 N·m and 24.13 W; the idler train delivers 3.6864 N·m and 23.16 W; the compound train delivers 7.3728 N·m and 23.16 W. Their output speeds remain 60, 60 and 30 rpm. This comparison charges a loss at both idler meshes.
Count the teeth to find the speed
Count the teeth to find the speed
The driver supplies motion; the driven gear receives it. For one external gear mesh, each tooth passing on the driver advances the driven gear by one tooth space. A gear with twice as many teeth needs twice as many passing teeth to complete a turn.
This lesson uses reduction ratio i = input speed ÷ output speed, with speed magnitudes. A 2:1 reduction means two input turns for one output turn. Ratios above 1 reduce speed; ratios below 1 increase it. At zero speed, use tooth counts to find the ratio; do not divide 0 by 0.
Notation map: this page's original equations use N for teeth and n for speed. The course uses n for teeth, ω for angular velocity and τ for torque. Thus page N = course n; page speed n is written ω in the additions below. GR and i name the same reduction ratio.
In course notation, using magnitudes: GR = nout/nin = dout/din = ωin/ωout = τout/τin for an ideal single pair. Here d is pitch diameter; the torque equality assumes no losses. For a compound train, multiply the stage ratios; the first and last tooth counts alone do not give the overall ratio.
Supporting detail: Addendum 227 — Why tooth counts work, and what the dashed circles mean.
An idler and a compound shaft do different jobs
An idler and a compound shaft do different jobs
One mesh reverses
A → B turns the output opposite to the input, viewed from the same end of each shaft.
An idler cancels
A → I → B reverses twice. I affects its own speed and the spacing, but its tooth count cancels from the end-to-end ratio.
Compound stages multiply
A → B, then C → D, with B and C fixed together: i = (NB/NA) × (ND/NC).
Same shaft means the same angular speed. A large B and a small C fixed to one shaft make the same number of turns in the same direction. Their rim speeds differ because their radii differ. They do not mesh with each other.
In the compound example, 20 → 40 teeth halves the speed. A second 20 → 40 stage halves it again: 120 → 60 → 30 rpm. The two external meshes make the final output turn in the same direction as the input.
An idler is not another reduction stage. Drop its tooth count when finding the end-to-end ratio, but count every external mesh for direction: odd means opposite; even means the same, viewed from the same end of the parallel shafts. Do not drop a gear that shares a shaft with a different gear in a compound train.
More torque costs speed; it does not create power
More torque costs speed; it does not create power
Torque is turning effort. In this ideal, lossless train at steady load, output torque magnitude = input torque magnitude × reduction ratio. A 2:1 reduction changes 120 rpm and 2 N·m into 60 rpm and 4 N·m. The 4:1 compound example gives 30 rpm and 8 N·m.
Rotational power is torque × angular speed: P = T × 2πn/60 when T is in N·m and n is in rpm. Both sides of either example carry 25.13 W ideally. Real friction and other losses leave less output power. Tooth strength, bearings, shafts, lubrication and the motor all limit usable torque.
At zero speed, mechanical power is zero. A loaded, stationary gear train can still carry torque. The lab shows ideal static torque balance in that case; it does not model motor stall behavior or promise a safe load.
Supporting detail: Addendum 228 — Primary references and model boundaries.
Each stage receives only the power that survived the stage before it. Use decimal efficiencies and multiply: ηtotal = η1 × η2 × η3. Never add or average them. See Power and Efficiency for the general meaning of efficiency.
Power-flow schematic, with gear pairs shown by pitch circles. The stages are separated for clarity; each connecting shaft turns its attached gears together.
At 98% per stage, three stages give 0.98³ = 0.941192: about 5.88% total loss, not 6%. Fewer, higher-quality stages often beat many cheap stages for efficiency, provided they can meet the ratio and load requirements.
Supporting detail: Addendum 229 — Why adding losses is only an approximation.
Positive drives keep the speed ratio; losses reduce torque
Positive drives keep the speed ratio; losses reduce torque
A positive drive keeps input and output linked in a fixed ratio without slipping. Gears, chains and timing belts are positive drives. A slipping flat belt or V-belt is not. Follow Rotation and Linear Speed for the connection from rotation to belt travel.
At a stated steady input speed and load, use magnitudes:
ωout = ωin/i τout = τin × i × ηtotal Pout = ηtotal × Pin
The teeth still set the speed exactly in this model. Efficiency reduces output torque from its ideal value. It does not reduce output rpm as well. Use matching torque units on both sides: lbf·ft or N·m. The course conversion is 1 rpm ≈ 0.1047 rad/s when angular speed in rad/s is needed.
Supporting detail: Addendum 230 — Follow both stages of one loaded train.
Count stages for ratio, meshes for direction and stated losses
Count stages for ratio, meshes for direction and stated losses
For a simple train A → I → B, the idler cancels from (NI/NA) × (NB/NI) = NB/NA. The two external meshes still reverse direction twice.
Follow the loss assumption in the problem. Real meshes lose some power, but a problem may explicitly ignore it. If every actual mesh is 96% efficient, A → I → B has ηtotal = 0.96². If a whole stage including its idler is assigned 96%, use that stage value once. If η = 1.00 is stated, ignore losses. Do not infer the loss count from the reduction-stage count when an idler is present.
Choose teeth, then check both output limits; Checklist; Practice
Choose teeth, then check both output limits
Record input speed and torque, the output speed ceiling and torque floor, available integer tooth counts, maximum ratio per stage, and the loss assumption.
Use the speed ceiling to find i ≥ ωin/ωceiling. With at most R:1 per stage, k reduction stages can provide at most Rk:1.
For each candidate stage count k, calculate ηtotal and check the torque bound i ≥ τfloor/(τin × ηtotal). Use the larger of the speed and torque bounds.
Choose whole-tooth pairs within the range and per-stage limit. Connect successive pairs by shared shafts. Multiply their actual ratios; do not assume a rounded target is achievable.
Calculate output speed and torque, keeping full precision for both limit checks. Check direction by counting external meshes. An added idler may require recalculating losses.
To choose the faster of feasible designs at the same input speed, compare their actual overall ratios: the smaller one is faster. A feasible design is not automatically the fastest possible design.
Supporting detail: Addendum 231 — Worked design: a winch with a speed ceiling and torque floor.
The permitted size ranges on a hole and a shaft decide whether the two have clearance, interference, or could have either.
A size tolerance gives two limits
A size tolerance gives two limits
Manufacturing produces variation. For each diameter in this lab, the drawing gives
a size between two limits. A measured diameter inside that interval passes this
size check.
Nominal size
The size a feature is named by, such as Ø0.7500 in.
Ø means diameter. Every limit is measured from this number.
Deviation
How far a limit sits above (+) or below
(−) nominal. +0.0010 puts a limit 0.0010 in above it.
Limits
Nominal plus each deviation: the largest and smallest sizes that pass
inspection. Ø0.7500 +0.0010 / 0.0000 means anything from 0.7500 in to
0.7510 in.
Tolerance
The width of that range: largest limit minus smallest limit. Here,
0.0010 in.
A size exactly on a limit passes. On this page the limits are part of the
allowed range: a 0.7500 in hole and a 0.7510 in hole are both good. A 0.7511 in hole
is not.
Clearance is the hole size minus the shaft size
Clearance is the hole size minus the shaft size
Put a shaft in a hole and the number that decides the fit is the
difference between their two diameters.
clearance = hole size − shaft size
Positive: the hole is bigger. There is a gap, and the shaft slides in.
Negative: the shaft is bigger. That is interference: on paper
the parts overlap, so the shaft has to be pressed in, or it does not go at all.
Zero: exactly the same size, called line-to-line. No gap and no
overlap.
Clearance is measured across the whole diameter. With the shaft centred in the hole, the gap you
would see on each side is half of it:
gap on each side = clearance ÷ 2
The gap is drawn hugely enlarged. At the size of this drawing, a
0.00025 in gap would be far too thin to see. Hatching marks the cut face of the
block.
Three kinds of fit, decided by the two worst cases
Three kinds of fit, decided by the two worst cases
You do not have to check every pair of parts a drawing allows. Two pairs settle it:
the tightest and the loosest.
Tightest legal pair
The smallest hole with the largest shaft. Its clearance is
the least any good pair can have: hole minimum − shaft maximum
Loosest legal pair
The largest hole with the smallest shaft. Its clearance is the
most any good pair can have: hole maximum − shaft minimum
The fit is named by where those two numbers land.
Fit
Tightest pair
Loosest pair
What it means
Clearance
gap, or exactly zero
gap
No permitted pair has dimensional overlap. Equality has no gap.
Transition
overlap
gap
Some good pairs slide together; some have to be pressed.
Interference
overlap
overlap, or exactly zero
No permitted pair has a positive gap. Equality has no overlap.
The zero cases are deliberate. When the tightest pair comes out at
exactly zero, every good pair either has a gap or just meets, so this page counts it as a clearance
fit and the lab marks it zero at the limit. The same goes the other way for interference.
Higher means bigger. Each box is the range of sizes one part may
have; the dashed line is the nominal size. The hatched band in the middle panel is the range of
sizes both parts are allowed to have, which is what makes an overlap possible.
Fit lab: make two parts, then try them together; Interactive
Fit lab: make two parts, then try them together
Pick a drawing, then set the size each part actually came out at. Watch whether
each part passes inspection, and whether the two go together.
The section view is the pair you made, cut in half. The gold and blue bands
are where each wall is allowed to be.
The pair map is every pair the drawing allows. Anything above the diagonal
has a shaft bigger than its hole.
The lab’s example drawings. All are made-up teaching limits on a
Ø0.7500 in nominal, not values from any standard.
Drawing
Hole limits
Shaft limits
Tightest pair
Loosest pair
Fit
Slides freely
0.7500 to 0.7510
0.7480 to 0.7490
+0.0010
+0.0030
Clearance
Could go either way
0.7500 to 0.7510
0.7498 to 0.7506
−0.0006
+0.0012
Transition
Pressed together
0.7500 to 0.7510
0.7515 to 0.7525
−0.0025
−0.0005
Interference
Two good parts can still make a bad pair; Watch out
Two good parts can still make a bad pair
Checking each diameter against its own limits does not by itself check the
clearance of the selected pair.
Take the transition drawing from the lab: holes from 0.7500 to 0.7510 in, shafts from 0.7498
to 0.7506 in.
Hole made at 0.7502
Inside 0.7500 to 0.7510. Passes.
Shaft made at 0.7505
Inside 0.7498 to 0.7506. Passes.
Together
0.7502 − 0.7505 = −0.0003 in. The shaft is
bigger than the hole. They overlap.
Neither part is wrong. The drawing allows that pair, and that is what
transition fit allows. To exclude dimensional overlap for every permitted pair, the
tightest pair must have zero clearance or more. To guarantee a positive dimensional gap, it
must be greater than zero. Neither check by itself guarantees assembly: shape, surface finish,
temperature and the assembly method also matter.
Call the fit from the drawing alone; Interactive
Call the fit from the drawing alone
Read the two callouts, work out the tightest and loosest pairs, and call it before
you look.
Five drawings, each on a Ø0.7500 in nominal. Work out the limits, then the tightest and
loosest pairs. The answer follows each one.
The lab compares two diameters and nothing else. A real assembly also depends on:
Shape. No hole is perfectly round or straight, and no shaft is either. A shaft
can measure in tolerance everywhere a micrometer touches it and still be bent too far to go
in.
Temperature. Parts grow when they warm up, so the same part can measure
differently straight off the machine and an hour later.
Surface finish and measurement. A rough surface and an imperfect measurement
both blur the last decimal place the drawing asks for.
Force. Whether an interference pair can be pressed together, how hard, and what
that does to the parts are questions about the material, not about the two sizes.
The limits in the lab are made-up teaching values. Real drawings often take limits
from published tables of standard fits; those tables are not reproduced here.
A machined surface has a lay, a waviness and a roughness; a stylus trace and a filter turn them into Ra, Rz and Rt, and a drawing symbol says what is required and how the surface may be made.
A surface has lay, waviness and roughness
A surface has lay, waviness and roughness
Every manufactured surface carries marks from the process that made it. Surface
texture describes those marks: which way they run, how far apart they are, and how tall they
stand.
Roughness
The finest, closely spaced marks, such as the feed marks a cutting tool
leaves at each pass or the scratches of abrasive grit.
Waviness
A longer, gentler undulation that the roughness sits on, for example from
vibration or deflection while the part was made.
Lay
The direction of the main surface pattern, set by how the tool or the part
moved.
Form
The overall shape, such as a face that is slightly curved. Size and geometric
tolerances control form; surface texture is what is left on top of it.
Heights drawn 50 times larger than widths. A made-up
5.6 mm patch of surface with parallel marks 0.2 mm apart running front to back,
on a gentle waviness. At true scale the marks would be far too small to see. The lines are the
crests of the marks; the blue line is a stylus trace across them.
A stylus traces one line, and a filter splits it; Watch out
A stylus traces one line, and a filter splits it
A contact instrument drags a fine stylus along a straight line and records its height.
That record is the measured profile. Everything else is worked out from it.
Trace direction
Usually across the lay, so the stylus crosses the marks. If the
drawing specifies a measuring direction, that direction governs.
Mean line
A smooth line the filter draws through the measured profile, a weighted
average of the heights around each point. This mean line is the waviness.
Cutoff λc
The wavelength where the filter splits the profile. Undulations
much longer than λc stay in the mean line; marks much shorter than λc are left over
for the roughness. A wave exactly λc long is shared half and half.
Roughness profile
The measured profile minus the mean line.
Evaluation length
The part of the trace the numbers come from. In this lab it is five
sections, each λc long. The trace runs one more λc at each end so the filter has heights
on both sides of every evaluated point.
The same trace, before and after the filter, with λc 0.8 mm.
Top: the measured profile and its gold mean line; the shaded ends are the extra trace. Bottom: the
roughness profile over the five sections, with each section’s peak (▼) and valley
(△), its height as a red bar, and ±Ra dashed. Heights are drawn far larger than lengths;
each plot gives its factor at the right.
The filter decides what counts as roughness, not the size of the undulation.
Change λc and the same undulation can move from the waviness into the roughness. That is why
a measurement result needs its cutoff, and why a drawing or its standard says which one applies.
Ra, Rz and Rt read the roughness differently
Ra, Rz and Rt read the roughness differently
All three come from the same roughness profile. They answer different questions about
it. This lab uses the older ISO 4287 convention with five sections for Rz; the drawing-symbol
comparison separately shows older and current graphics.
Ra
The average distance of the roughness profile from its mean line over the
evaluation length. Peaks and valleys count alike.
Rz
The average of the sections’ peak-to-valley heights. Each section counts once, whatever is in it.
Rt
The largest peak-to-valley height over the whole evaluation length: the single
highest peak to the single deepest valley.
Ra = average of |roughness| over the evaluation length
Rz = (Z1 + Z2 + Z3 + Z4 + Z5) ÷ 5
For the trace above: Ra 1.55 µm; Rz = (6.55 + 6.56 + 6.70 + 6.57 + 6.87) ÷ 5 = 6.65 µm;
Rt 7.10 µm.
The values are in micrometres (µm). They can also be given in microinches (µin): one inch is
exactly 25.4 mm, so 1 µin is exactly 0.0254 µm, and Ra 1.6 µm is
63.0 µin.
Name the standard. Current documents use the ISO 21920 series. Many existing
drawings and instruments use the older ISO 4287 parameters and ISO 1302 symbols. The names
Ra, Rz and Rt carried over, but the standards are not identical, so this page says which one each
symbol comes from and does not mix them. For a real part, check which standard the drawing
invokes.
Surface texture lab: trace a surface and hold it to a drawing; Interactive
Surface texture lab: trace a surface and hold it to a drawing
Change the surface, the trace and the drawing, and watch the numbers. Start with
experiment 1.
The block is a few millimetres of surface. Lines are the crests of the marks;
the blue line is the stylus trace, solid over the evaluation length.
The plots are that trace: the measured profile with its mean line, then the
roughness profile with its five sections.
The drawing holds one requirement against this one trace and writes it as a
callout in the view you choose.
Parallel marks 0.2 mm apart, mark height 6 µm, λc 0.8 mm unless
stated. Teaching surfaces, not predictions for any process.
Experiment
Setting
Ra, µm
Rz, µm
Rt, µm
Across or along the marks
Trace left to right, across
1.55
6.65
7.10
Trace front to back, along
0.328
1.59
1.70
Where waviness ends
12 µm waviness, λc 0.8 mm
1.57
6.75
7.43
Same surface, λc 2.5 mm
2.11
11.3
11.8
One deep scratch
No scratch
1.55
6.65
7.10
Scratch three times the mark height
1.88
10.5
23.4
The same-Ra experiment is the figure in the next section.
Same Ra, different surfaces
Same Ra, different surfaces
These three roughness profiles all have Ra 1.6 µm. They are not the
same surface. All three plots use the same height scale.
Rounded valleys, sharp crests. Ra 1.6, Rz 6.86,
Rt 7.32 µm.Flat tops, narrow grooves. Ra 1.6, Rz 10.8,
Rt 11.2 µm. Most of the profile sits above the mean line.Narrow peaks, flat valleys. Ra 1.6, Rz 10.8,
Rt 11.2 µm. Most of the profile sits below the mean line.
Ra alone cannot tell these apart.
Rz separates the rounded marks from the other two, but not flat tops from narrow
peaks.
Where the extremes sit, above or below the mean line, separates those two.
One number does not describe a surface. That is why a drawing names the parameter, not just a
value.
Reading a surface texture symbol
Reading a surface texture symbol
The symbol’s point touches the line that represents the surface in a drawing
view. Its shape says how the surface may be made; the text beside it says what texture is
required.
The three process requirements, in the older and the current graphics. Schematic drawings:
the standards dimension the symbols exactly.
Symbol
Older, ISO 1302
Current, ISO 21920-1
Meaning
Basic
Any manufacturing process is permitted. This does not forbid machining; it simply does not require it.
Bar
Material removal is required: the surface must be produced by removing material, for example by machining.
Circle
Material removal is prohibited: the surface must not be machined or otherwise have material removed to meet this requirement.
Current or older
An ISO 21920-1 symbol carries a short separate dash above the
short leg, touching neither leg. The older ISO 1302 graphic has none, so the familiar older marks
are not the current symbols unchanged.
The requirement
The parameter and its limit, such as Ra 3.2, sit below the
long line, to the right of the long leg, in both.
The lay
In an ISO 21920-1 callout the process and the lay sit above the long
line. In the older symbols the lay symbol sits beside the long leg, below the line.
A complete specification can state more than this page draws, such as the measuring
direction. The process mark is a requirement about how the surface is made; a profile measurement
checks the texture, not whether material was removed.
Lay symbols belong to the drawing view
Lay symbols belong to the drawing view
A lay symbol says which way the marks run. = and ⊥
are judged against the plane of projection of the view the symbol is drawn in, not against the page or
the screen.
=Parallel. Parallel to the plane of projection of the view in which the symbol is used.⊥Perpendicular. Perpendicular to the plane of projection of the view in which the symbol is used.XCrossed. Crossed in two oblique directions relative to the plane of projection of the view in which the symbol is used.MMultidirectional. Multidirectional.CCircular. Approximately circular relative to the centre of the surface to which the symbol applies.RRadial. Approximately radial relative to the centre of the surface to which the symbol applies.PParticulate. Particulate, non-directional or protuberant.
The first two figures are the same surface. Its marks run front to back: parallel to the right
side view’s plane of projection, so = there, and perpendicular to the front
view’s, so ⊥ there. The arrow shows which way each view looks.
Lay and trace direction are different things. The lay says how the marks run. The trace direction
says how they were measured; it is usually across the lay unless the drawing specifies one.
The lay symbols and meanings here are those of ISO 1302:2002.
Older notation: N grades and triangle marks; Interactive
Older notation: N grades and triangle marks
Older drawings may give a roughness grade number or a row of triangles instead of a
parameter and value.
Roughness grade numbers
Each grade number stands for one Ra value. A grade is an Ra value: it does not convert to Rz.
Grade numbers and the Ra values they stand for. Microinches are exact conversions, rounded
for display.
Grade
Ra, µm
Ra, µin
N1
0.025
1.0
N2
0.05
2.0
N3
0.1
3.9
N4
0.2
7.9
N5
0.4
15.7
N6
0.8
31.5
N7
1.6
63.0
N8
3.2
126
N9
6.3
248
N10
12.5
492
N11
25
984
N12
50
1969
Triangle marks
One catalog prints a comparison of downward triangle marks with Ra values, under the heading
“Extract from JIS B 0601-2001”. It calls the comparison approximate, not rigorous.
It gives no acceptance limits, no dates for the marks, and no Rz equivalents, so read it as a rough
historical guide.
The catalog’s comparison, as printed.
Marks
Ra values listed, µm
4 triangles
0.012, 0.025, 0.05, 0.1, 0.2
3 triangles
0.4, 0.8, 1.6
2 triangles
3.2, 6.3
1 triangle
12.5, 25
One requirement, four ways
Slide the Ra limit and compare the current symbol, the older symbol, the grade number and the
triangle marks for the same value.
Read the callout; Interactive
Read the callout
Ten short questions on the symbols, the lay, the older notations and what the numbers
respond to.
The older ISO 1302 symbol with a circle in its V, and Ra 3.2. May this surface be machined to reach Ra 3.2 µm? No: material removal is prohibited. The circle in the V prohibits material removal. Material removal is prohibited: the surface must not be machined or otherwise have material removed to meet this requirement.
A current symbol with an open V, no connecting material-removal crossbar or circle, a separate identifying dash above the short leg, and Ra 6.3. Does this callout forbid machining the surface? No, any process is permitted. The V has no connecting material-removal crossbar or circle: it is the basic symbol. The separate floating dash identifies ISO 21920; it does not require machining. Any manufacturing process is permitted. This does not forbid machining; it simply does not require it.
A symbol with a bar closing its V, a short separate dash above the short leg, and Ra 0.8. Which standard's graphic is this? ISO 21920-1 (current). The short separate dash above the short leg, touching neither leg, marks an ISO 21920-1 symbol. The older ISO 1302 graphic has no dash.
A block of surface whose marks run front to back. An arrow shows the right side view looking at its right side. The marks run front to back. Which lay symbol belongs on this surface in the right side view? =. The right side view looks along the arrow. Marks running front to back are parallel to that view's plane of projection, so the symbol is =. The same surface takes ⊥ in the front view: the symbol depends on the view, not on the screen or page.
A block of surface whose marks run front to back. An arrow shows the front view looking at its front. The marks run front to back. Which lay symbol belongs on this surface in the front view? ⊥. The front view looks along the arrow. Marks running front to back are perpendicular to that view's plane of projection, so the symbol is ⊥. The same surface takes = in the right side view: the symbol depends on the view, not on the screen or page.
The grade number N8. An older drawing gives grade N8. What does that stand for? Ra 3.2 µm. N8 stands for Ra 3.2 µm (126 µin). Each step of the grade number doubles or halves the Ra value, near enough.
Three downward triangles. In the catalog comparison, which Ra values sit beside three triangles? 0.4, 0.8, 1.6 µm. Three triangles sit beside Ra 0.4, 0.8, 1.6 µm. The catalog calls this comparison approximate, not rigorous. Read it as a rough historical guide, not as acceptance limits.
A current symbol with Rz 6.3. Which N grade means the same as this Rz 6.3 µm requirement? None: grades are Ra values. Grade numbers each stand for an Ra value; N9 is Ra 6.3 µm, not Rz 6.3 µm. Ra and Rz measure different things, and how they compare depends on the shape of the profile, as the same-Ra experiment in the lab shows.
One deep scratch crosses this otherwise even trace. Which number has the largest proportional change? Rt. In the lab, a scratch three times the mark height takes Rt from 7.10 to 23.4 µm, Rz from 6.65 to 10.5 µm and Ra from 1.55 to 1.88 µm. Rt spans the highest peak to the deepest valley over the whole length. Rz averages five section heights, diluting localized extremes; filtering can spread a scratch across section boundaries. Ra averages every point.
A block of surface with parallel marks running front to back, and a stylus trace running left to right across them. The trace on this surface crosses the marks. Traced along the marks instead, Ra would be: Much smaller. In the lab, Ra is 1.55 µm across the marks and 0.328 µm along them: the stylus misses the marks when it runs beside them. Tracing across the lay is the usual choice, but a direction the drawing specifies governs.
What this lab leaves out
What this lab leaves out
The lab is a teaching model of one straight trace. A real measurement and a real acceptance
decision involve more:
The instrument. A real stylus has a tip radius, and instruments apply a
short-wavelength filter and remove the part’s form before filtering. The lab’s stylus is
sharp and its part is flat.
The filter and parameters. This lab follows the older ISO 4287 teaching
convention of five sections for Rz, with a Gaussian mean line having 50% transmission at
λc. Dense samples resolve the narrow marks; numerical integration on a coarser grid computes
the smooth mean line. This is not a compliant instrument or a complete ISO 21920 inspection
setup, and a drawing or standard can call for other settings.
The decision. The lab compares one trace with one limit. The drawing and its
standard say how many traces are taken, where, and how the results are judged.
The process. No trace shows whether material was removed. The process
requirement is checked against how the part was made.
Scratches and pits. Whether an isolated flaw counts against a texture
requirement is for the drawing and its standard to say.
Symbols. The drawings are schematic. The lay symbols are those of
ISO 1302:2002; the lab writes the same symbols in the ISO 21920-1 lay position. Check the
current standard before relying on one there. Inch-drawing (ASME) practice is not covered here.
Trace torque through a keyed shaft-hub joint, identify common key forms, and distinguish key fit from axial retention.
A key joins the shaft slot to the hub slot to transmit torque
A key joins the shaft slot to the hub slot to transmit torque
A key is a separate piece fitted between a shaft and the bore of a hub, the part of a pulley, sprocket or gear that fits around the shaft. Contact between the key and slot faces transfers turning force. Here, keyseat means the recess in the shaft and keyway means the matching slot in the hub. Other references sometimes use keyway for both; always identify which part is being cut.
Schematic parallel-key joint. Clearances are exaggerated; obtain dimensions and fits from the drawing.
Trace the turning load through the connection: shaft slot face → key → hub slot face, or the reverse when the hub drives the shaft. At the rim, the pulley, sprocket or gear transfers the load through its belt, chain or mating gear teeth. Not every hub is keyed; check how the actual assembly connects the hub to the shaft.
Identify the key by its cross-section and seating shape; Practice
Identify the key by its cross-section and seating shape
Key
Recognizing feature
Square parallel key
Equal width and height in cross-section; uniform section along its working length.
Rectangular parallel key
Unequal width and height; uniform section along its working length.
Woodruff key
A segment of a disk, with a curved bottom seated in a matching circular recess in the shaft.
Gib-head key
A tapered key with a projecting head that provides a place to engage it for removal.
Supporting detail: Addendum 232 — Public reference for key forms.
Check key fit and axial retention as separate requirements
Check key fit and axial retention as separate requirements
For a parallel key, the side fit controls how the turning load is carried. Excessive side clearance permits movement; an overly tight fit can prevent assembly. Verify the specified top clearance too. A tapered key has a different seating action, so do not apply a parallel-key fit rule to it.
Use the drawing's key designation, dimensions and tolerances. Do not choose a key size from shaft diameter alone or assume that half the key height belongs in each part.
The key does not by itself define how the hub is held against movement along the shaft. Check the assembly drawing for axial retention as well as torque transmission. A hub that turns with the shaft is not necessarily secured against sliding along it.
Bearings support the shaft relative to the housing; the keyed hub transfers torque between the shaft and the attached rotating part. For the bearing arrangement and the shaft's axial location, see Shaft Support and Axial Adjustment.
Choose a shaft or hub cutting method, then check keyseat or keyway location, width, depth and fit.
A key joins the shaft slot to the hub slot to transmit torque
A key joins the shaft slot to the hub slot to transmit torque
Before choosing a cutting method, identify which part needs the recess: the keyseat in the shaft or the keyway in the hub. See Keys and Keyways in Shaft-Hub Connections for the joint's terminology, diagram and torque path.
Identify the key by its cross-section and seating shape
Identify the key by its cross-section and seating shape
Use the specified key form and drawing dimensions to choose the feature you need to make. Review key forms, fit and axial retention before planning the cut.
Mill a shaft keyseat with the cutter that matches its end and bottom shape
Mill a shaft keyseat with the cutter that matches its end and bottom shape
An end mill can make a straight, flat-bottom shaft keyseat that ends within the shaft's length. Its diameter leaves rounded ends in plan view; confirm that the key and drawing allow that shape. Use a permitted entry method for the selected cutter.
A Woodruff keyseat cutter is a disk-shaped cutter on a shank. Its diameter forms the curved recess for a Woodruff key and its cutting width establishes the slot width. Match both dimensions to the required recess. Not every tool sold as a keyseat cutter is the correct tool for every key.
Read the keyseat's width, depth, length or cutter diameter, and axial location from the drawing.
Align the shaft axis with the intended machine travel and locate its centerline using Mill Indicators and Part Zero. Set the cutter's cutting plane or path on that centerline, with the specified axial location and depth reference.
Supporting detail: Addendum 233 — Why cutter selection includes more than width.
Broach a through hub keyway; consider slotting when the geometry needs it; Practice
Broach a through hub keyway; consider slotting when the geometry needs it
A conventional keyway broach and guide bushing are useful for a straight keyway through a hub bore. See Broaching for the pass sequence. The same arrangement does not make a closed-end keyseat on the outside of a shaft.
Shaping or slotting uses a reciprocating single-point tool to remove material in successive strokes. A suitable internal slotting setup can make a hub keyway when a through broach is unsuitable. Blind work still needs a planned tool runout and chip space; the method must fit the actual geometry.
Check width, depth and location before using assembly as a fit check; Checklist
Check width, depth and location before using assembly as a fit check
Clean the feature and remove burrs without rounding the functional edges.
Check width at several accessible positions using a suitable slot gauge, gauge blocks or measuring contacts. Select a tool with enough access and resolution for the tolerance; see Choosing Shop Measuring Tools.
Measure depth from the drawing's stated reference. A depth instrument needs a stable reference bridge or fixture on a round shaft; resting it arbitrarily on the curved surface changes the result.
For a hub, establish the specified bore-to-keyway measurement with an appropriate internal/keyway gauge or fixture. A reading across the bore and slot includes the bore dimension; it is not automatically the radial slot depth.
Check length, axial position and centerline location. Compare actual measurements with the drawing limits.
Check the specified key fit and assembly clearance. Investigate interference or unwanted movement instead of forcing the assembly together.
A key that enters the slot is a useful functional check, but it does not prove depth, location or dimensional compliance.
Machining/Production and Nontraditional Processes
Broaching
See how progressive teeth cut a profile, how a guided keyway broach works, and where rotary broaching differs.
A broach divides a shaped cut among a row of teeth
A broach divides a shaped cut among a row of teeth
In conventional broaching, a tool moves in a straight line relative to the work. Successive cutting teeth reach farther into the material. Rise per tooth is that increase in cutting height between successive teeth; it is not the tooth spacing along the tool. The spaces between teeth hold chips.
Roughing teeth remove most of the allowance. Semi-finishing teeth approach the final profile with smaller cuts. Finishing teeth establish size and finish; several may have the same height. The exact arrangement depends on the tool.
Schematic side profile. Tooth heights are exaggerated; the small teeth enter first.
Supporting detail: Addendum 234 — Why the finishing teeth need not keep getting taller.
Push or pull describes the drive; internal or external describes the surface
Push or pull describes the drive; internal or external describes the surface
A push broach is driven from behind; a pull broach is drawn through by its leading end. An internal broach works inside a prepared opening. An external broach works on an outside surface, such as a flat or an external spline. These are separate distinctions: internal does not mean pull-only.
A suitable hole broach can produce a square, hexagon or internal spline; a keyway broach cuts a slot in an existing bore. Conventional through broaching needs an exit path. Choose the tool from the required finished profile and starting-hole specification, not just a nominal shape name.
Supporting detail: Addendum 235 — Production advantages depend on the job.
A bushing guides the keyway broach; shims move its cutting edge outward
A bushing guides the keyway broach; shims move its cutting edge outward
The hub is the part surrounding the shaft. A slotted bushing fits its bore and guides the broach. A shim is a thin spacer behind the broach that increases the depth reached on a later pass. Broach, bushing and shims must be a compatible set.
Conceptual later-pass setup, not a construction drawing or a statement of shop inventory. The shim is behind the broach, opposite its teeth.
Check the drawing, prepared bore and required keyway. Select the matching broach, bushing and specified shim schedule.
Seat the bushing in the hub. Insert the broach in its slot for the first pass, normally without a shim on a multi-pass set.
Support the hub squarely on the press bed with clearance below for the entire broach to pass through. Align the ram, tool and guide.
Apply the specified lubricant and press the broach through according to its instructions.
After the completed pass, remove the broach and clean its teeth. If another pass is specified, insert the prescribed shim behind it, reinsert, lubricate and check alignment again.
Repeat with the specified shim stack for each remaining pass. Stop at the prescribed final setup; deburr and inspect as described in Machining Keyseats and Keyways.
Do not add a shim after the final pass. One-pass tools and some small broaches require none. Adding arbitrary shims is not a way to correct an uncertain dimension.
Supporting detail: Addendum 236 — Manufacturer reference for the pass sequence.
Count the first pass separately from the added shim passes; Practice
Count the first pass separately from the added shim passes
Rise per tooth and depth per pass are different quantities. For a simple planning exercise, let d1 be the depth reached by the unshimmed pass and s the extra depth from each added shim increment. After N passes, depth is d1 + (N − 1)s.
For a target depth D greater than d1, the minimum count to reach at least the target is 1 + ceiling((D − d1)/s). Ceiling means round upward to a whole number. If the first pass already reaches the target, the count is one. All depths here are measured radially from the original bore surface.
Example: an invented first-pass depth of 1.0 mm and two 0.5 mm increments give 1.0, 1.5 and 2.0 mm: three passes. This is counting practice, not a real broach specification. If rounding upward exceeds the allowed finished depth, that shim schedule cannot make the part to size.
Rotary broaching can make polygon forms such as a hex socket using a special holder on a suitable lathe or mill. A small angular offset makes successive portions of the tool's end engage as the tool and work move relative to one another. It does not use the long row of progressively taller teeth shown above.
It needs a prepared opening for internal work. Tool form, available thrust, material, depth and chip clearance limit the application; a blind socket needs a planned place for the chips. This is a process overview, not a setup procedure.
Supporting detail: Addendum 237 — How the rotary holder produces the cutting motion.
Machining/Drilling and Threading
Twist Drills and Drill Sizes
Identify the parts that cut and guide a twist drill, compare point shapes, and read the four common drill size systems.
The lips cut; the flutes give chips a way out
The lips cut; the flutes give chips a way out
A twist drill makes a round hole with cutting edges at its point. The lips run from the center region toward the outside diameter. The helical grooves are flutes: they provide space for chips and a route for cutting fluid. The web is the central core between the flutes.
The chisel edge crosses the center of a conventional point. It pushes material aside with substantial thrust. Narrow strips called margins run along the outside of the drill body and help guide it in the hole. The relieved body behind them reduces rubbing. The shank is the portion held by the machine.
The point does the cutting. The body supports it and provides room for chips. Views are schematic, not sharpening templates.
Point angle and split point describe different features
Point angle and split point describe different features
118° and 135° are included point angles, measured across the point in an axial view. A 135° point is flatter and shorter than a 118° point of the same diameter. A 118° point is common on general-purpose drills; 135° points are common on drills intended for tougher materials. Select the complete tool for the material and setup, not by angle alone.
A split point has extra grinding near the center to reduce the chisel edge and improve starting behavior. “135°” does not automatically mean “split point.” A split point is also not a guarantee that the hole will be located accurately without a suitable setup.
Supporting detail: Addendum 238 — Why a damaged or uneven point makes a poor hole.
Read the diameter system before selecting the drill
Read the diameter system before selecting the drill
System
What the marking means
Fractional inch
A diameter in fractions of an inch, such as 1/4 in. Convert the fraction when a calculation needs a decimal.
Number
A size label, such as No. 7. In the common numbered series, a larger number means a smaller drill. The number itself is not a diameter.
Letter
A size label from A toward Z, increasing in diameter. Look up the actual diameter; letters are not equal increments.
Metric
A diameter in millimeters, such as 5.0 mm. It is not interchangeable with a nearby inch size just because both fit in the chuck.
Read the marking and confirm the cutting diameter when identification is uncertain. A drill index is storage, not proof that someone returned the drill to the correct slot. Use the specified diameter and a checked chart when selecting a tap drill.
Match the shank to the holder and the hole to the job
Match the shank to the holder and the hole to the job
A straight shank fits an appropriate chuck or collet. A reduced shank is smaller than the cutting diameter; it does not increase the machine's drilling capacity. A taper shank fits its matching taper socket or approved adapter, rather than being gripped as though it were a straight shank.
Choose enough flute length and reach for the hole, with as little unnecessary projection as the setup permits. A drill's nominal diameter does not guarantee a finished hole's size, location or surface finish. Plan the drilling sequence, then choose a finishing operation if the drawing calls for it.
Machining/Drilling and Threading
Drilling on a Drill Press or Mill
Plan hole location, workholding, starting, chip evacuation and depth before drilling, then inspect and deburr the result.
Locate and secure the work before starting a hole
Locate and secure the work before starting a hole
A drill press feeds a rotating drill along its spindle axis. A mill adds controlled table positioning, which helps place a pattern of holes from drawing datums. On either machine, the hole follows the relationship between spindle, tool and workholding.
Clamp the work or hold it in a suitable vise or fixture rather than by hand; see Machine Hazards for why. Round stock needs support that prevents rolling, such as a properly clamped V-block arrangement. Provide clearance for a through drill without drilling into the table, vise or supports.
A spot starts the hole; a pilot removes the center material
A spot starts the hole; a pilot removes the center material
Spot drilling makes a short starting feature to help locate the next drill. A center drill is primarily designed to produce a center hole for supporting work between centers; its small pilot and conical portion make it different from a spot drill. Select a starting tool compatible with the following drill, rather than treating the two tools as interchangeable.
A pilot hole is a smaller hole drilled before a larger one. It can reduce the thrust required at a conventional drill's chisel edge. It is not automatically required: some drill geometries are intended to enter solid material. Follow the drill maker's starting-hole and pilot recommendations.
Supporting detail: Addendum 239 — Why “always center drill first” is too broad.
Choose speed and feed for this drill and material; Practice
Choose speed and feed for this drill and material
Use Feeds, Speeds and Removal Rate for the surface-speed-to-RPM calculation. For drilling, its diameter input is the drill's cutting diameter. Surface speed is a cutting condition; RPM is the spindle setting. They are not the same quantity.
Feed per revolution describes how far the drill advances each turn. Select cutting data for the tool material, work material, diameter, depth and coolant arrangement. A generic material table is a starting reference only when its tool assumptions match. Use an available machine setting consistent with the tool and machine instructions.
Peck drilling advances in stages with retractions to break or evacuate chips. The needed stroke and retraction depend on the drill, material, hole depth and fluid delivery; there is no universal peck distance. Do not add a peck cycle to a tool that calls for continuous feed without checking its instructions.
For a blind hole, distinguish the depth reached by the tip from the depth that has the full drill diameter. The conical point extends beyond the full-diameter portion. A tapped blind hole also needs space for the tap's lead-in and chip clearance. For a through hole, account for breakthrough and the drill point below the work.
If chip shape, sound, thrust or finish changes unexpectedly, stop and inspect the setup before resuming; use Metal Chips and Swarf for chip handling.
Supporting detail: Addendum 240 — Why changes in the cut matter.
Compare advance, retracing and withdrawal paths
Compare advance, retracing and withdrawal paths
Open G-code and Toolpaths. In the playground's Program picker, choose these named examples in order: Drilling path: continuous advance, Drilling path: short in-bore retract, and Drilling path: withdrawal above the mouth. Use Step to follow each G0 and G1 move.
Program
Motion to watch
What the model reports
Continuous advance
G1 Z-8
One feed enters new modeled stock to final depth.
Short in-bore retract
G0 Z-1, then G1 Z-4 and G1 Z-8
The first feed back removes no additional modeled stock; the separate deeper feed does.
Withdrawal above the mouth
G0 Z2, then G1 Z-4 and G1 Z-8
The first feed back removes no additional modeled stock; the separate deeper feed does.
Mark where the drill enters material that has not yet been removed. That is new cutting in this geometric model.
Mark where the drill returns through the bore it already made. That travel retraces the prior path and removes no additional modeled stock; the separate deeper feed begins after the point reaches the previous bottom. The model does not show possible wall or chip contact, rubbing, force or heat during the return.
Compare the retraction heights with the raw top at Z+1. The short retraction stays inside the bore. The other withdrawal carries the point above the hole mouth, creating a clearer opportunity for chips to leave the hole.
Compare the finished holes. The three illustrative programs intentionally reach the same final tip depth and geometry even though their travel paths differ.
The playground shows programmed motion and removed geometry. It does not model chip transport or packing, cutting heat or force, coolant delivery, or whether chips actually cleared. A retraction creates an opportunity for chip escape; it is neither proof of chip clearance nor the only way chips can leave. Haas describes its G83 return as a chip-clearing motion and places the R plane above the cut so chips can get out, but these G0/G1 illustrations are not G73, G83 or Q implementations.
The coordinates, spindle speed and feed in these three examples are comparison values for the simulator, not operating recommendations. Select any real drilling cycle, retract amount, speed and feed from the drill maker's guidance, the machine/control manual and the approved shop procedure. Continue to follow the machine instructions and Metal Chips for observation and chip handling.
Read point depth and full-diameter breakthrough separately
Read point depth and full-diameter breakthrough separately
Open Milling Operations and its simulator. Choose Job 2 / Pocket and holes. From View, choose 2D sections. Under Drill: choose a size, choose Load the drill Ø6.6. With the tool clear above the block, use the Move to X and Y inputs to place it at X 15, Y 30, then use the Z input and Move to advance to each row below. Watch the Front section and DRO, then scroll to Inspection of the part as it is now and find Ø6.6 through at X 15, Y 30.
These are illustrative coordinates in this simulator: its raw top is Z +1 and its stock bottom is Z −20. They are not operating depths, safe overtravel or an allowance for a real part.
Drill-tip DRO
What the Front section represents
Read the individual checks
Z −20
The point reaches the stock bottom, but the full drill diameter stops higher.
Diameter can read Ø6.60 while THRU says Not through yet: full size only to Z −18.02.
Z −21
The point extends below the stock and leaves a partial bottom opening; the full diameter still has not reached the bottom.
Diameter can still read Ø6.60 while THRU says Not through yet: full size only to Z −19.02.
Z −22
The modeled opening at the bottom reaches the inspection's minimum allowed diameter.
THRU changes to Through at the minimum allowed diameter.
Why does a drill-tip DRO of Z −20 not mean the full Ø6.6 body has reached Z −20?
Which inspection result changes between Z −21 and Z −22: the measured diameter, the THRU subcheck, or both?
Why can the left hole's diameter subcheck pass before its THRU subcheck?
Why can the feature row or overall job remain incomplete even after this THRU subcheck passes?
For this feature, THRU checks the bottom opening against a minimum allowed diameter of 6.50 mm. Passing it does not guarantee an exact Ø6.6 opening, and the unfinished top face, pocket or right-hand hole can keep other checks incomplete. Read the Diameter and THRU subchecks separately; do not use the overall job result as the answer to this comparison.
Check the hole before calling it finished; Checklist
Check the hole before calling it finished
Confirm the hole location, required diameter and whether it is through or blind.
Check the tool, starting method, workholding, exit clearance and depth plan.
Set suitable speed, feed and chip-evacuation conditions.
After drilling and stopping the machine, inspect the hole and remove burrs without changing the specified feature.
Measure the required dimensions and complete any specified finishing operation.
Deburring removes the raised edge left by cutting. It does not automatically mean making a large countersink. Preserve the drawing's edge requirements and inspect the exit side too.
Machining/Drilling and Threading
Reaming, Boring and Hole Seats
Choose a finishing operation by the feature needed: a sized bore, a cylindrical recess, a conical seat or a flat bearing surface.
Choose the operation from the finished shape
Choose the operation from the finished shape
Section views through the hole axis. Gray is material; white is open space. A spot face provides a bearing surface; a counterbore provides a recess.
Needed feature
Operation
Improve the diameter and finish of a nearly correct hole
Ream
Enlarge an existing hole with control of its axis and diameter
Bore
Cylindrical recess with a flat shoulder for a fastener head
Counterbore
Conical seat for a matching flat-head fastener
Countersink
Local flat bearing surface around a hole
Spot face
Ream for size and finish; bore when the axis needs control
Ream for size and finish; bore when the axis needs control
A reamer removes a small amount of material with multiple cutting edges. Prepare an undersize hole with enough material for the reamer to cut, rather than rub. Too much allowance overloads the tool; too little may leave the previous surface. Use the reamer maker's allowance for that diameter and material, not one stock allowance for every hole.
A reamer tends to follow the existing hole. Do not rely on it to relocate a badly misplaced or crooked hole. Boring enlarges an existing hole with a cutting edge whose path can be set relative to the machine axis. With a suitable setup and enough material left to clean up, it can correct location and straightness as well as diameter.
Use Tolerances and Fits to interpret the size limits and select inspection methods. See Lathe Operations for boring and threading on the lathe.
Supporting detail: Addendum 241 — A nominal tool size is not a finished-hole guarantee.
Compare the old opening with the final bore envelope
Compare the old opening with the final bore envelope
A centered final bore can remove material around a smaller opening when that entire opening lies inside the final bore's removal circle. It cannot add material back where an earlier opening protrudes outside that circle. Setting the boring head to the drawing diameter does not erase the earlier geometry.
Open Milling Operations and choose Job 4 / Boss and bore. From View, choose 2D sections. Before each case, choose Start this job over, then Sure? Start over, so each comparison begins with a fresh block. Use the Move to X, Y and Z inputs and Move. Keep tool and boring-head changes at Z +20 by using Raise to Z +20.
Fresh-block case
Illustrative simulator moves
Individual bore inspection
Previous opening stays inside
Load the drill Ø10. At X 50.5, Y 30, move the tip to Z −24. Raise to Z +20. Load the boring head Ø20.00, move to X 50, Y 30, then bore to Z −21.
The modeled Ø20 bore contains the earlier opening. Its row reports measured Ø20.00 through, with no diameter-too-big, centre-position or CUT TOO FAR failure; the unfinished whole job does not need to pass.
Previous opening extends outside
Load the drill Ø10. At X 52, Y 30, move the tip to Z −24. Raise to Z +20. Load the boring head, enter 18 in Boring Ø and choose Set; bore at X 52, Y 30 to Z −21. Raise, set Ø20, then bore at X 50, Y 30 to Z −21.
CUT TOO FAR — Bore Ø20.00 ±0.05 through reports about Ø20.41, 0.41 too big, with the fitted centre about 0.38 from target. THRU also fails because inspection tests a full allowed diameter around the fitted irregular opening; it does not mean the centered boring-head move stopped short. The centered final pass cannot replace the material removed outside its circle.
In the first case, where is the edge of the Ø10 opening relative to the centered Ø20 removal circle?
In the second case, which individual checks show that the result is not simply a centered Ø20 hole: diameter, position, overcut, or all three?
Why does a final DRO of X 50, Y 30 not undo the earlier off-axis removal?
These coordinates, depths, offsets and fitted/grid inspection numbers belong only to this idealized simulator. They are not acceptable cleanup allowance, safe boring offset, rework instructions or physical gauge results. The model does not predict boring-bar entry or interrupted-cut behavior, rigidity, deflection, chatter, force, finish, alignment uncertainty or workholding. Geometric containment is necessary here, not sufficient for a real process: use the drawing, measured hole, complete setup, tool-maker guidance and responsible process authority.
The top, boss and chamfers remain unfinished in both cases, so the overall feature row or job may still be incomplete. Read the bore's diameter, position and overcut checks for this comparison.
Match the head seat to the fastener drawing
Match the head seat to the fastener drawing
A counterbore has a cylindrical wall and a flat shoulder. A countersink has a conical seat. The screw head must match that seat's included angle; the thread diameter alone does not determine the head angle or the countersink diameter.
A spot face removes enough surface material to create a local flat seat for a head, nut or washer. It is useful on a rough or uneven surface. A spot face and a counterbore may use similar tools, but their required depth and purpose differ.
Read the specified diameters, depths and angle before cutting. A tool used only to break a sharp edge is not necessarily producing a fastener seat to size. Do not substitute a preferred cutter angle for the drawing requirement.
Test the choice before choosing the cutter; Practice
Test the choice before choosing the cutter
A smooth pin hole already on location suggests reaming. A hole whose axis must be corrected suggests boring, if there is enough material. A socket-head screw recessed into a cylindrical pocket suggests counterboring. A conical flat-head seat suggests countersinking.
Decode inch and metric thread names, distinguish thread fit from strength, and choose fastener features by their function.
Read diameter, spacing, series and class separately; Practice
Read diameter, spacing, series and class separately
In 1/4-20 UNC-2B, 1/4 is the nominal major diameter in inches, 20 is the number of threads per inch, UNC is the Unified coarse series, and 2B identifies the internal thread's fit class. The major diameter is the largest thread diameter; it is not the diameter of the hole drilled before tapping.
Read the whole callout. Matching only the nominal diameter is not enough.
UNF identifies the Unified fine series. At a given nominal diameter, fine threads have more threads per inch and therefore a smaller pitch than coarse threads. In M6 × 1, M identifies a metric thread, 6 is the nominal major diameter in millimeters, and 1 is the pitch in millimeters. It does not mean one thread per inch.
Unified external thread classes are 1A, 2A and 3A; internal classes are 1B, 2B and 3B. A means external, as on a screw; B means internal, as in a tapped hole. Class 1 permits a looser fit, class 2 serves general applications, and class 3 uses closer dimensional control.
The class number is not a material grade or a load rating. A class 3 thread does not by itself make a stronger bolt. Read the drawing for the required class and use the appropriate inspection limits. M6 × 1 alone does not specify a metric tolerance class; do not append an inch A/B class to it.
For the general distinction between a nominal dimension, its tolerance and a mating fit, see Tolerances and Fits. Exact thread acceptance limits require the applicable specification and gauges.
Pitch is spacing; lead is travel per revolution
Pitch is spacing; lead is travel per revolution
Pitch is the axial spacing between adjacent thread crests. For an inch thread, pitch in inches = 1/TPI. A 20-TPI thread has a pitch of 0.050 in. Lead is the axial travel in one complete relative revolution.
On a single-start thread, lead equals pitch. On a multiple-start thread, lead equals pitch times the number of starts. Right- and left-hand threads move in opposite axial directions for the same rotation. Look for a left-hand designation rather than forcing a fastener that does not start normally.
The lathe topic owns the process of single-point thread cutting. The tapping topic explains preparing and making internal threads with taps.
Choose the fastener by how it locates and clamps the parts
Choose the fastener by how it locates and clamps the parts
Part
Function and selection question
Bolt or screw
A bolt commonly passes through clearance holes and uses a nut; a screw commonly engages a tapped part. Names overlap in catalogs, so check the actual product specification.
Cap screw
A headed screw, often with a hex or socket drive. Choose the head clearance, bearing seat, thread and specified material properties, not just appearance.
Set screw
Its point bears on a mating part, such as a shaft, to resist relative motion. Point shape and the mating surface matter; it is not simply a small clamping bolt.
Stud
A headless threaded member, often installed in one part with a nut on the exposed end. Check which end engages the part and how much usable thread remains.
Nut
Provides the mating internal thread. Match thread size, pitch and required properties; head shape alone does not establish compatibility.
Washer
Provides a bearing surface beneath a head or nut. Choose its size, hardness and type for the joint rather than assuming every washer also locks it.
Threaded insert
Provides an internal thread in a parent material or repairs a damaged thread. Follow that insert system's hole, tap and installation requirements.
Engagement, grade and locking are separate decisions
Engagement, grade and locking are separate decisions
Engagement length is the axial length of mating threads carrying load. There is no single diameter multiplier that establishes adequate engagement for every combination of screw and parent material. Use the joint design or fastener-system requirements, and ensure the screw does not bottom before it clamps.
Strength identification must come from the specified fastener grade or property class and its traceable markings or documentation. Thread fit class and head style are not substitutes. Do not assign a strength grade to an unidentified fastener from its appearance.
A flat washer is not a locking device. A lock washer or thread-locking compound is not a guarantee against loosening in every joint. Use the specified locking method; for a compound, follow its compatibility, preparation, cure and removal instructions.
Supporting detail: Addendum 242 — Check the entire joint before substituting a fastener.
Machining/Drilling and Threading
Tap Drills and Tapping
Estimate a cutting-tap drill, distinguish thread percentage from engagement length, and plan tap geometry, alignment and depth.
Subtract the pitch to estimate a cutting-tap drill; Practice
Subtract the pitch to estimate a cutting-tap drill
A tap makes an internal thread in a prepared hole. Start by reading the full thread callout. For common straight Unified and metric cutting taps, a useful roughly 75% thread estimate is:
Inch: drill diameter ≈ nominal major diameter − 1/TPI. Both diameters are in inches; TPI means threads per inch.
Metric: drill diameter ≈ nominal major diameter − pitch. Both dimensions are in millimeters.
This is an estimate, not a final hole specification. Use the major diameter, not the minor or pitch diameter. Select the actual drill from the tap maker's chart for the material and required thread. Do not apply this cutting-tap estimate to forming taps, pipe threads or insert-installation taps.
Thread
Estimate
Cutting-tap chart comparison
1/4-20
0.250 − 1/20 = 0.200 in
No. 7, 0.2010 in
M6 × 1
6 − 1 = 5.00 mm
5.00 mm
3/8-16
0.375 − 1/16 = 0.3125 in
5/16 in, 0.3125 in
Supporting detail: Addendum 243 — Chart basis and the approximation's limits.
Thread percentage is not percent of bolt strength; Practice
Thread percentage is not percent of bolt strength
Percent thread describes how much thread height the hole permits relative to a reference profile. With the same cutting tap, a larger prepared hole leaves less thread height; a smaller hole leaves more material for the tap to remove and generally increases tapping torque.
It does not describe how far the screw enters the hole. That is engagement length. Nor does 75% thread mean 75% joint strength. Material, engagement length, thread geometry and loading all affect the joint. More thread height is not automatically a better choice.
Supporting detail: Addendum 244 — Keep percentage and fraction separate.
Taper, plug and bottoming describe the tap's lead-in
Taper, plug and bottoming describe the tap's lead-in
The chamfer is the gradual lead-in where the first teeth progressively cut the thread. A taper tap has a long lead-in that helps starting; a plug tap has a shorter lead-in; a bottoming tap has the shortest of the three and reaches full thread closer to the bottom of a blind hole.
A bottoming tap still has a lead-in. It cannot produce full thread all the way to the physical bottom. For hand tapping, start with a tap that can establish alignment, then use a bottoming tap when the required depth calls for it. Leave room for incomplete threads, chips and the drill point.
Chamfer style is separate from chip direction. A spiral-point cutting tap generally pushes chips ahead and needs exit space; a spiral-flute cutting tap can draw chips back toward the entrance. Select a tap intended for the material and through or blind hole.
Use a guide to start a hand tap square; Checklist
Use a guide to start a hand tap square
Confirm thread size, tap type, drill size, actual hole size and required full-thread depth.
Prepare the hole entrance as specified. Clamp the work or hold it in a vise rather than by hand; see Machine Hazards for why. Choose the tap maker's recommended lubricant for the material.
Align the tap with a suitable tapping guide. With a spindle used as a guide, keep it unpowered and follow the approved hand-tapping setup.
Turn with a suitable tap wrench while maintaining alignment. Follow the tap's chip-breaking instructions; do not force a tap whose resistance rises unexpectedly.
Keep within the planned travel, withdraw appropriately, clean and inspect the thread with the specified gauge or inspection method.
To help prevent broken taps, use the correct tap drill, maintain alignment, clear chips as the tap's instructions specify, use the recommended lubricant and do not force the tap. Reverse-to-break-chip routines depend on tap design; do not apply one hand-tapping rhythm to every tap.
Power tapping needs a machine and holder designed for it
Power tapping needs a machine and holder designed for it
Machine tapping coordinates spindle rotation with axial travel at the thread's lead. Depending on the machine, that may use synchronized rigid tapping or a suitable tapping attachment. The machine, holder, tap, reversal and depth control must work together. An ordinary drill-press setup is not automatically a power-tapping setup.
A cutting tap removes chips. A forming tap displaces suitable ductile material to make the thread without cutting chips. Forming taps require their own, generally larger, prepared-hole sizes and suitable lubrication. A cutting-tap drill can be much too small for a forming tap of the same thread size.
Use the machine's instructions and the approved shop procedure for tapping equipment.
Supporting detail: Addendum 245 — Why the local setup decides what is permitted.
Machining/Turning
Turning Tapers
Calculate taper rate, compound angle and tailstock offset, then choose a method and check both slope and size.
A taper changes diameter at a constant rate
A taper changes diameter at a constant rate
A straight taper is a cone, or part of one. Name the large diameter D, small diameter d and axial length of the tapered portion l. Use the same length unit for all three.
Taper rate = (D − d) / l. With inch dimensions, this is taper per inch, often abbreviated TPI. Here TPI means diameter change per inch of length; in Single-Point Threading, the same abbreviation means threads per inch. Write the units to distinguish them.
TPF = 12 × TPI, and TPI = TPF / 12. Taper per foot describes the diameter change over twelve inches; the actual tapered portion need not be a foot long.
Supporting detail: Addendum 246 — Check the rate with a fresh example.
Set the compound to the half-angle measured from the spindle axis
Set the compound to the half-angle measured from the spindle axis
The tool travels along one side of the cone. Its angle to the spindle axis is the half-angle α; the angle between the two sides is the included angle 2α.
α = atan((D − d) / (2l)) = atan(TPI / 2). Use degree mode for a setting in degrees. A rate of 0.050 in/in gives α = 1.432°, while the included angle is 2.864°.
Swivel the compound so its travel makes that half-angle with the spindle axis, then feed along the compound. The taper length is limited by compound travel. Check how the lathe labels its scale: a scale measured from cross-slide travel uses the complementary angle, 90° − α.
The radius changes by half the diameter change. The drawing exaggerates the slope.
Supporting detail: Addendum 247 — Why the factor of two belongs in the angle formula.
Tailstock offset uses the full supported work length
Tailstock offset uses the full supported work length
For a shallow external taper turned between centers, offsetting the tailstock tilts the work while the carriage still travels parallel to the bed. The usual small-angle setup estimate is offset ≈ TPI × L / 2 = (D − d)L / (2l).
L is the total work length between the effective center support points, approximated by the total part length in elementary problems. It is not just the length l of the tapered portion. Center-hole geometry matters in an actual setup. Use inches for L when the taper rate is in in/in; if given TPF, first divide it by 12.
Plan view: offset is transverse to the spindle axis, not a vertical change in center height.
For a rate of 0.050 in/in and L = 8.000 in, the estimate is 0.200 in even if only 3.000 in is tapered. Machine offset capacity and the center arrangement limit this method. Check a trial cut and restore center alignment before straight turning.
Supporting detail: Addendum 248 — Why this is an estimate rather than an exact setting.
Choose the taper method for length, access and support
Choose the taper method for length, access and support
Compound rest
Useful for short external or internal tapers. The compound guides the tool at the half-angle, but its limited travel restricts length.
Tailstock offset
Useful for shallow external tapers between centers. It changes the work axis and does not provide a method for boring an internal taper.
Taper attachment
A guide coordinates cross-slide motion with carriage travel. It can produce internal or external tapers within its travel and angle limits while the work stays aligned with the spindle. Connection and cross-feed arrangements depend on the attachment.
Form tool
A shaped cutting edge produces a short taper by feeding across the axis. A wide edge engages much of the cut at once, increasing cutting load and the tendency to chatter.
A matching taper needs both the right slope and the right size; Practice
A matching taper needs both the right slope and the right size
Measure diameters at two known axial positions to check the rate. A correct rate can still leave the entire taper too large or too small. A suitable taper plug or ring gauge checks the mating geometry; contact pattern and seating position answer different questions.
Morse tapers are commonly used for centers and tool shanks. Jacobs tapers commonly join a drill chuck to its arbor. They are separate families: identify the exact mating designation before selecting a tool or adapter. No dimensions or angles should be inferred from the family name alone.
No standard taper table is reproduced here. Use the specified component drawing and verified manufacturer or standard dimensions for a real fit; see Tolerances and Fits.
Read thread geometry, distinguish pitch from lead, understand compound infeed and check thread size beyond the outside diameter.
Pitch spaces the teeth; lead sets carriage travel per revolution
Pitch spaces the teeth; lead sets carriage travel per revolution
A thread follows a helix around a cylinder. Pitch P is the axial distance between corresponding points on adjacent teeth. For N threads per inch, P = 1/N inch. A 20-per-inch thread has a pitch of 0.050 in.
Lead is the axial advance along one helix in one complete revolution. A single-start thread has one helix, so lead equals pitch. A two-start thread has two interleaved helices and lead equals 2P. In general, lead = number of starts × pitch. Threading feed follows lead; the examples here use single-start threads.
The crest is the top of a tooth and the root is the bottom of the groove. The sides are flanks. The thread angle is the included angle between flanks in an axial section. This page discusses 60° profiles; other thread forms need other tools and geometry.
Schematic external thread, with only the upper half shown. Diameters span across the axis to the opposite side.
Major diameter alone cannot tell you whether a thread fits
Major diameter alone cannot tell you whether a thread fits
Major diameter
The largest thread diameter: across external crests or internal roots.
Minor diameter
The smallest thread diameter: across external roots or internal crests.
Pitch diameter
The diameter of an imaginary cylinder at which thread tooth width and groove width are equal for the ideal profile. It strongly affects flank clearance and fit.
The outside of a screw can measure correctly while its flanks are still too thick. Use the thread designation and its specified limits, not just nominal outside diameter. Tolerances and Fits explains limits; Lathe Operations explains what the simulator's simplified thread check measures.
The tool stays square while the compound feeds near one flank
The tool stays square while the compound feeds near one flank
For a 60° thread, use a tool with the required 60° profile and the specified tip shape. A center gauge, also called a fishtail gauge, checks a ground tool's angle and helps align its bisector perpendicular to the work axis. Set the cutting edge at spindle center height. Swiveling the compound does not mean turning the tool away from square.
A common manual arrangement sets compound travel about 29–30° from the radial cross-feed direction for this thread form. That is about 60–61° from the spindle axis. Check the scale's zero reference before setting it.
The angle describes the infeed path between passes, not the tool's included angle or the thread helix angle.
Near-flank infeed puts most of the cutting on one edge. Exactly 30° is parallel to a flank in the ideal axial profile; slightly less also gives the other edge a small cut. Tool-maker guidance may call for a different infeed strategy.
Supporting detail: Addendum 249 — Radial depth and compound travel are different quantities.
Keep every pass synchronized with the same helix; Checklist
Keep every pass synchronized with the same helix
The gearbox establishes the relationship between spindle rotation and leadscrew rotation. Closing the half-nuts connects the carriage to the leadscrew so that each spindle revolution advances the tool by the selected lead. An ordinary power-feed setting is not a substitute for a threading setting.
Check the machine's threading-dial chart before re-engaging the half-nuts. On an inch-leadscrew lathe, the engagement pattern depends on how the dial is graduated. With four numbered lines and unnumbered half-lines between them, common on older inch lathes with an 8-TPI leadscrew, an odd number of threads per inch (TPI) can usually be caught on any numbered line, but not on the half-lines (see LeBlond's four-numbered-line chart). On dials numbered 1–8, odd TPI are often restricted to lines of one parity (all odd or all even). Even TPI can usually be caught on any line, numbered or half. Fractional TPI may require returning to the same specified line or keeping the half-nuts engaged. These are examples, not universal dial settings: leadscrew pitch and dial gearing determine which marks work, and the machine's chart controls.
Supporting detail: Addendum 250 — Why only certain threading-dial positions return to the groove.
For some combinations, notably many metric threads on inch-leadscrew lathes, ordinary dial re-engagement will lose synchronization. Such setups commonly keep the half-nuts engaged and use the maker's prescribed return method. Confirm the machine and workholding permit that method; this page supplies no universal reversing procedure.
Identify the thread form, hand, pitch, number of starts and required limits on the drawing.
Check the machine chart for the gearing and permitted half-nut/dial procedure.
Check a light scratch pass with a pitch gauge before deepening the thread.
Plan the end of each pass and the return path before cutting to depth.
Measure as the thread approaches size; use the specified inspection method to decide when it is finished.
Calculate a profile depth only after naming the profile; Practice
Calculate a profile depth only after naming the profile
A 60° angle and a pitch do not, by themselves, specify a finished thread depth. Crest flats, root shape, tip geometry and dimensional limits all matter. Use the actual thread specification and tooling data for a production cut, then measure the result. Total depth is not a per-pass infeed instruction.
For the ideal sharp-V teaching profile used in the practice bank, radial depth is H = P / (2 tan 30°) = (√3 / 2)P ≈ 0.8660254P. This is the full sharp triangle height, not a finished Unified or metric thread depth. Actual truncated or rounded profiles remove less radial material than this sharp triangle.
Supporting detail: Addendum 251 — Verify the formula without a thread-depth table.
A pitch gauge checks spacing; wires help measure pitch diameter
A pitch gauge checks spacing; wires help measure pitch diameter
A pitch gauge has toothed leaves that compare with the thread spacing. It identifies pitch and helps detect a wrong gearbox selection, but it does not certify pitch diameter or fit.
In the three-wire method for an external thread, two calibrated wires sit in grooves on one side and a third on the opposite side. A micrometer measures over them. Because the wires contact the flanks, the measurement can be converted to pitch diameter using the correct relation for the thread form and wire size.
Use calibrated wire sizes and their applicable instructions or a verified table. Wire diameter, thread angle and lead-angle effects matter; this page does not supply an unchecked wire formula. A thread micrometer uses dedicated contacts for a similar purpose. Appropriate thread plug or ring gauges check functional acceptance against the specified gauge limits.
Trying a mating nut may reveal gross interference, but it does not establish conformance to a thread class.
Machining/Sawing and Grinding
Grinding Wheels and Abrasives
Match the abrasive to the material, distinguish grit from grade, and read the five main fields of a conventional wheel specification.
A grinding wheel cuts with many small grains
A grinding wheel cuts with many small grains
A bonded wheel holds abrasive grains in a supporting material called the bond. The grains act as small cutting edges. Spaces between them provide room for removed material and, in wet grinding, fluid. Grains can fracture or pull free as the wheel works; dressing restores a useful cutting surface when that renewal is insufficient.
Choose the complete wheel for the machine, material and operation. Abrasive type alone does not establish suitability: shape, dimensions, bond, speed rating and permitted grinding surfaces also matter. See Offhand Grinding and Precision Grinding.
Match the abrasive to the work material
Match the abrasive to the work material
Abrasive
General starting applications
Aluminum oxide
Steels, including high-speed steel (HSS) tool bits. Different formulations serve different grinding conditions.
Silicon carbide
Cast iron, some nonferrous materials, and brittle nonmetals; also conventional carbide-tool grinding with a suitable wheel.
Cubic boron nitride (CBN)
A superabrasive used for hardened steels and HSS.
Diamond
A superabrasive used for cemented carbide, ceramics and other hard nonferrous materials. It is not the general choice for steel grinding.
These are selection starting points, not permission to use any wheel containing that abrasive. In particular, a standard bench wheel for steel is not a wheel for aluminum. Confirm the manufacturer's application listing.
Supporting detail: Addendum 252 — Manufacturer resources for abrasive selection.
Grit is grain size; grade is how firmly grains are held
Grit is grain size; grade is how firmly grains are held
Grit size: within the same conventional grit-number system, a lower number means coarser grains and a higher number means finer grains. Coarse grit generally provides more space for chips and favors material removal; fine grit generally favors smaller scratches. Finish also depends on dressing, feeds, wheel condition and the work material.
Grade: the wheel's resistance to releasing abrasive grains. A hard grade holds grains more strongly; it does not mean that the abrasive mineral itself is harder. A hard work material may need a softer grade so dull grains can release.
Structure: the spacing of the grains. An open structure provides more space between grains than a dense structure. Do not confuse spacing with grain size.
Bond: vitrified bonds are glasslike; resinoid bonds use resin. Rubber and metal bonds serve other applications. Bond choice affects wheel behavior, dressing and permissible operating conditions; no bond name establishes a universal RPM rating.
Read the conventional marking from abrasive to bond; Practice
Read the conventional marking from abrasive to bond
The usual core sequence is abrasive → grit → grade → structure → bond. Prefixes and suffixes may identify a manufacturer's particular abrasive or bond. Some markings omit a structure field. Superabrasive specifications may include concentration and use a different format.
Read the meaning of each field before interpreting a manufacturer's code.
For a teaching example, suppose a supplier defines A 60 J 7 V as aluminum oxide, grit 60, grade J, structure 7 and vitrified bond. The 60 is not an RPM limit; the J is not the hardness of aluminum oxide. Use that supplier's key to interpret J and 7 rather than assuming all manufacturers' grades behave alike.
Supporting detail: Addendum 253 — A manufacturer's explanation of the marking.
Understand bench and pedestal grinder setup, wheel condition, tool-bit shaping and the difference between rim speed and a wheel's maximum RPM.
Offhand grinding guides the work by hand
Offhand grinding guides the work by hand
A bench grinder mounts on a bench; a pedestal grinder stands on a base. In offhand grinding, the operator guides the work against the wheel, usually supported by a tool rest. This suits shaping and sharpening; it does not provide the controlled workholding and feeds of Precision Grinding.
For a conventional straight bench wheel, the intended grinding surface is usually its outer circumference. Move the work across that surface to distribute wear. Use only the surfaces approved for that wheel and machine; a wheel designed for peripheral grinding is not automatically suitable for side grinding.
Wheel wear changes both rest and tongue-guard clearances
Wheel wear changes both rest and tongue-guard clearances
The tool rest supports the work near the wheel. The tongue guard is the adjustable part of the surrounding guard above the working opening; it is not the transparent eye shield. As the wheel becomes smaller, both clearances need checking and adjustment to the applicable machine instructions and requirements.
Positions only, not a scale drawing or a gap-setting gauge. The eye shield is omitted for clarity.
Make these adjustments with the wheel stopped and the machine secured according to its operating procedure. Recheck after dressing or wheel replacement. Use the specified clearance limits, not the proportions in the drawing.
Supporting detail: Addendum 254 — Where to check the clearance requirements.
Inspection, ring testing and dressing do different jobs
Inspection, ring testing and dressing do different jobs
Inspection checks condition and suitability before mounting. A ring test is an additional pre-mounting check for applicable vitrified wheels: a light nonmetallic tap produces a sound that a trained person evaluates for indications of cracking. Wheel size, shape and composition limit where the test applies. A clear ring does not replace the other checks.
Truing restores the required wheel shape and concentric running. Dressing renews the cutting surface by removing unwanted material and exposing useful abrasive. An appropriate dressing operation may do both. Use the dresser and method specified for the wheel.
Loading means work material fills the wheel's spaces. Glazing means dull abrasive remains at the surface and rubs instead of cutting effectively. Either condition calls for correction, not simply more pressure.
Supporting detail: Addendum 255 — Why a wheel can glaze, and where ring testing applies.
Shape an HSS tool bit without overheating its edge
Shape an HSS tool bit without overheating its edge
Grinding a high-speed steel tool bit creates the faces that meet at the cutting edge. Clearance behind the edge lets it cut without the adjacent tool face rubbing; rake influences chip flow. The required angles come from the intended tool and work material, not one universal sharpening angle.
Use light, controlled contact and check the shape frequently. Periodic dipping of a warm HSS bit in water can control temperature when the tool's instructions permit it. This is cooling during sharpening, not heat-treatment quenching; do not heat the bit severely and then plunge it into water.
Do not transfer that dipping method to a hot cemented-carbide tip. Sudden cooling can crack carbide. Use the specified dry method or a compatible continuous wet-grinding process. Intermittently quenching hot carbide is not equivalent to supplying coolant throughout the cut.
Supporting detail: Addendum 256 — Carbide needs consistent temperature control.
Aluminum and other soft, ductile metals can smear into and load a standard wheel intended for steel. Use equipment and abrasives specifically approved for the material. Changing from aluminum oxide to silicon carbide by itself does not establish that the whole setup is suitable.
Compare RPM ratings directly; calculate rim speed separately; Practice
Compare RPM ratings directly; calculate rim speed separately
The machine's spindle speed must not exceed the wheel's printed maximum operating RPM. A wheel's grade or grit marking is not that rating. Passing the RPM comparison is only one compatibility check; it does not approve the wheel's mounting, dimensions or application.
Rim speed is distance traveled at the wheel's outside diameter. With diameter D in inches and spindle speed N in revolutions per minute:
SFPM = π × D × N / 12, in surface feet per minute. The 12 converts inches to feet. Use diameter, not radius.
For an illustrative 7 in wheel at 1,750 RPM, π × 7 × 1,750 / 12 = 3,207 SFPM, rounded to the nearest whole foot per minute. This calculation is not a recommended operating speed. A smaller worn wheel has a lower rim speed at the same RPM; that does not authorize exceeding its marked maximum RPM.
Follow surface-grinder motions and workholding, plan small downfeed increments, and distinguish surface, cylindrical and centerless grinding.
Controlled motion lets many small cuts produce fine size and finish
Controlled motion lets many small cuts produce fine size and finish
Precision grinding combines an abrasive wheel with controlled workholding and machine feeds. Each active grain removes a small amount. A dressed wheel, stable support, small finishing increments and temperature control can produce accurate dimensions and fine surface texture, including on hardened materials.
A surface grinder separates table travel, crossfeed and downfeed
A surface grinder separates table travel, crossfeed and downfeed
On a horizontal-spindle reciprocating-table surface grinder, the table carries the work back and forth under the wheel. Crossfeed shifts the contact across the width of the work. Downfeed moves the wheel toward the work in small increments to remove thickness. Other surface grinders use different arrangements, including rotary tables.
Separate views keep the three directions distinct. Arrows show motion, not feed amounts.
After the finishing downfeed, sparking out continues passes without adding downfeed. The wheel can still remove a small amount as elastic deflection relaxes. Spark-out is not a substitute for measuring the part, and the number of passes is process-dependent.
A magnetic chuck holds suitable ferromagnetic work
A magnetic chuck holds suitable ferromagnetic work
A magnetic chuck uses magnetic attraction to hold suitable material such as many steels. It does not directly hold aluminum, brass or every stainless steel. Holding depends on material, contact area, thickness and the chuck's pole arrangement, not simply whether a magnet attracts one corner.
Clean mating surfaces and remove burrs that would lift the part. Use an approved fixture for parts that the chuck cannot hold adequately. A thin part can be pulled flat during grinding and spring back after release, so check the finished condition after removing the holding force.
Follow the chuck's release procedure after grinding. Residual magnetism may require demagnetizing so particles do not cling to the work. Demagnetizing is not the act that secures the work for grinding.
Supporting detail: Addendum 257 — Magnetic holding and release are equipment-specific.
Count downfeed increments separately from table strokes; Practice
Count downfeed increments separately from table strokes
For an ideal plan with constant downfeed, number of increments = total thickness to remove / downfeed per increment. One increment may require many table strokes and crossfeed steps to cover the entire face. State what a “pass” means before using the equation.
Example: removing 0.024 in from one face at an assumed 0.002 in per full-face layer takes 12 downfeed increments. These are arithmetic teaching values, not machine settings. If the division is not exact, use a smaller final increment rather than removing extra stock.
Supporting detail: Addendum 258 — Why a real grinding plan needs more than the quotient.
Coolant helps control heat and carry away grinding debris
Coolant helps control heat and carry away grinding debris
Grinding fluid can cool the work, lubricate contact and flush away removed particles. Heat changes dimensions during grinding and can alter the work surface. Delivery into the grinding zone, cleanliness and compatibility with the wheel and work material matter as much as having fluid in the tank.
Cylindrical and centerless grinding control round surfaces differently
Cylindrical and centerless grinding control round surfaces differently
Cylindrical grinding commonly rotates work held between centers or in a chuck while a grinding wheel removes material from an outside diameter. Traverse grinding moves along the length; plunge grinding feeds into a selected width. Internal grinding finishes bores and can use rotating work or other machine arrangements.
Centerless grinding supports the work on a blade between the grinding wheel and a regulating wheel. The regulating wheel controls work rotation and, in through-feed operation, helps advance the work axially. The work does not need center holes. Infeed arrangements serve shapes that cannot pass straight through.
Each process needs its own setup and wheel selection. A fine finish alone does not establish roundness, straightness or size.
Machining/CNC
CNC Control Fundamentals
How a control turns a program into motion, how feedback works, and what changes between milling and turning.
CNC repeats programmed motion; the operator still defines the process
CNC repeats programmed motion; the operator still defines the process
Computer numerical control (CNC) uses a program to command machine motion and functions. On a manual machine, the operator directs each move with handwheels or power-feed controls. On a CNC machine, the operator prepares the tools, workholding and coordinate references, then checks the programmed sequence.
CNC can repeat a complex path consistently. It does not remove variation from tool wear, deflection, temperature or setup errors. Programming and setup take time, so CNC is not automatically faster for every one-off job.
The machine control unit (MCU) reads program blocks, keeps track of active settings, calculates intermediate positions along a path, and sends commands to the axis drives and machine functions. The drives supply power to the motors. The control also presents positions, settings and alarms to the operator.
Feedback distinguishes open-loop and closed-loop motion
Feedback distinguishes open-loop and closed-loop motion
System
How position is controlled
What that means
Open loop
The drive sends motion commands without measuring actual position back into that positioning loop.
The control may not detect a missed step. A displayed commanded position is not proof of actual position.
Closed loop
A sensor reports position or motion; the drive/control compares feedback with the command and corrects error.
Excessive following error can produce an alarm. Feedback does not make the mechanics error-free.
A stepper motor advances through commanded angular steps and is often used in open-loop systems. A servo system uses feedback to regulate motion. Closed-loop stepper systems also exist: motor type alone does not tell you whether feedback is present.
Supporting detail: Addendum 259 — Where the sensor sits matters.
Milling rotates the cutter; turning rotates the work
Milling rotates the cutter; turning rotates the work
Basic machine
Cutting motion
Common programming concerns
Three-axis vertical mill
A rotating cutter moves relative to the work along X, Y and Z.
Tool lengths, cutter radius, XY contours and hole locations.
Two-axis lathe
The work rotates while a cutting tool moves along X and Z.
Diameter/radius convention, tool geometry and wear offsets, tool nose radius and changing work diameter.
These pages describe common Fanuc-style milling usage, with turning differences called out. G- and M-code meanings vary by control, machine type, options and configuration. Check the machine's own manual before applying a code or example. These examples teach interpretation; they are not production programs.
PathPilot is Tormach's machine control. Tormach publishes PathPilot programming documentation and post-processor guidelines. Select documentation for the actual machine and software version. A general description does not establish its installed tools, options or setup.
Identify mill and lathe axes, distinguish machine and work zero, and separate work offsets from tool compensation.
Describe tool motion relative to the work with a right-handed frame
Describe tool motion relative to the work with a right-handed frame
Use your right hand: thumb along +X, index finger along +Y and middle finger along +Z, with all three perpendicular. Equivalently, curling from +X toward +Y makes the thumb point along +Z. Z runs parallel to the principal spindle axis.
On a conventional vertical mill viewed from the front, +X is to the right, +Y is toward the back and +Z raises the tool away from the work. These are tool-relative-to-work directions. If the table moves instead of the tool, its physical motion is opposite the tool-relative motion.
For a basic lathe, Z is along the spindle and +Z is away from the headstock. X is radial; positive X values commonly describe the tool side of the centreline. A slant bed or rear turret changes what this looks like from the operator's position. Do not infer axis signs from screen orientation. Two-axis turning normally uses the XZ plane.
A lathe X value may describe diameter or radius; Practice
A lathe X value may describe diameter or radius
In diameter programming, X24 describes a surface 24 mm in diameter, 12 mm from the spindle centreline. In radius programming, the same surface is X12. Z distances are not halved.
For a change from diameter 30 mm to diameter 26 mm, the X coordinate changes by −4 mm in diameter mode, but the tool moves only 2 mm radially inward. Confirm the control's convention for absolute X, incremental X and arc-centre words separately; do not halve every number in a turning block.
Machine zero belongs to the machine; work zero belongs to the setup
Machine zero belongs to the machine; work zero belongs to the setup
Machine zero is the machine coordinate origin. A reference-return or homing procedure establishes the machine's position reference; the home position need not be the coordinate origin. Work zero is a chosen datum on the part or fixture, such as a corner, hole centre or faced end.
Common milling codes G54 through G59 select stored work coordinate systems. Selecting G54 does not measure the part, write the offset table or redefine machine zero. The setup procedure establishes the stored values.
With only a translation, machine position = work-zero location in machine coordinates + work position. If the work origin is (100,60) and the program point is (20,15), the machine point is (120,75). This example omits rotation, local shifts and tool offsets.
In common Fanuc-style milling, G53 selects machine coordinates for the block containing it. It does not erase G54 or force G54 to become the next active work system. The previously selected work system remains selected afterward. Tool-offset interaction and permitted motion modes are control-specific; check your control's manual. Machine-coordinate zero is not necessarily a clearance position.
Tool length and cutter radius compensate for different dimensions
Tool length and cutter radius compensate for different dimensions
In common Fanuc-style milling, G43 H... applies positive tool-length compensation: it adds the signed value stored in the selected H register to commanded Z positions so Z can refer to the intended tool-tip position. The offset's sign, established by the touch-off convention, determines the direction of that shift. G43 does not mean an unconditional upward move. Check your control's manual for its offset and touch-off conventions.
For example, H03 selects register 3; it does not mean a length of 3 mm. T selects a tool; H selects offset data. Their numbers may match by shop convention, but the programmer must verify that relationship. G49 commonly cancels length compensation.
Supporting detail: Addendum 260 — Why positive compensation can use a negative offset.
G41 offsets a cutter to the left of the programmed path looking in the direction of travel; G42 offsets it to the right. G40 cancels it. These are not clockwise/counterclockwise commands. Moving along +X in XY, left is +Y. On many mills a D word selects cutter compensation data; check whether that register stores radius, diameter or a wear adjustment.
Compensation needs suitable entry and exit moves. Do not add a full radius correction to a CAM path that already includes that correction. Turning tool nose compensation also depends on nose radius and tool orientation; it is not simply a milling H offset.
Convert between positions and signed moves, and trace the endpoint of a program as its distance mode changes.
G90 gives a destination; G91 gives a signed change
G90 gives a destination; G91 gives a signed change
In common milling usage, G90 makes axis values absolute coordinates in the active coordinate system. G91 makes them signed changes from the current position. Neither command moves an axis by itself. Units and work offsets still matter.
Increment = next position − current position. Reverse the calculation with next position = current position + increment. Keep a separate running total for every axis.
For an ordinary G00/G01 move, an omitted axis stays in place. In G90, X0 requests X zero; in G91, X0 requests zero X movement. Do not reuse an omitted incremental value from the preceding block.
These G90/G91 meanings must not be assumed on every lathe. Some turning controls use X/Z for absolute and U/W for incremental coordinates, and use G90 for a turning cycle. Check the control before translating a mill program to a lathe.
One path can be written as points or as moves; Practice
One path can be written as points or as moves
Start at A = (6,4) mm. Visit B = (26,4), C = (26,19), then D = (11,19). Z is unchanged; these are coordinate exercises with no cutting setup implied.
Move
Absolute destination, G90
Increment, G91
A → B
X26 Y4
X20 Y0
B → C
X26 Y19
X0 Y15
C → D
X11 Y19
X−15 Y0
Supporting detail: Addendum 261 — Check the conversion in both directions.
Trace the active mode before evaluating each block; Practice
Trace the active mode before evaluating each block
Assume millimetres, one unchanged work coordinate system, no compensation and an initial position (6,4,12). This is a paper trace, not a machine-ready program. F120 is an arithmetic example.
M30 ends this trace; it is not a command to move to zero. For arcs, the endpoint mode and centre mode are separate questions: see G-code and Toolpaths. For a broader view of modes use CNC Program Structure.
Read program identifiers, startup modes, machine functions, feed modes and drilling cycles in common milling G-code.
A block can combine motion, settings and machine functions
A block can combine motion, settings and machine functions
A word is a letter and value, such as X12 or F100. A block is a line of words. The control applies its execution rules; words are not necessarily executed in left-to-right typing order. N numbers label blocks and are often optional. Many Fanuc-style programs use an O number such as O2468 as the program identifier. File naming, percent delimiters and identifiers vary by control.
A modal command stays active until replaced or cancelled within its group. G01 can remain active while G90 changes to G91, because motion and distance mode are different groups. A startup line sets specific modes; it does not clear every stored setting or offset.
A safe-start line declares assumptions; it does not prove the setup
A safe-start line declares assumptions; it does not prove the setup
A common milling startup example is G17 G21 G90 G94 G40 G49 G80: XY plane, millimetres, absolute endpoints, feed per minute, cutter compensation cancelled, tool-length compensation cancelled and canned cycles cancelled. This is a reading example, not a universal restart line. Cancelling an offset changes the coordinate relationship; startup and restart sequences must match the actual control and tool position.
Identify the program and establish required units, plane and modes.
Select the intended work coordinate system and tool; apply the correct offset data.
Establish spindle, feed and coolant settings for the operation.
Perform positioning and machining blocks, including any cycle cancellation.
Use the machine-approved retract and shutdown sequence, then end the program.
Separate spindle, tool and coolant commands from motion; Practice
Separate spindle, tool and coolant commands from motion
These are common Fanuc-style meanings, not a promise for every machine.
Code
Common meaning
Read with it
M03 / M04 / M05
Spindle clockwise / counterclockwise / stop
S sets the speed value. Direction is conventionally viewed from the spindle toward the work; confirm machine orientation.
M06
Tool change on many mills
T selects a tool. The changer may be manual or automatic; offset activation is a separate issue.
M08 / M09
Flood coolant on / coolant off
Available coolant systems and auxiliary M codes depend on the machine.
M30
End program and commonly reset/rewind
It does not command a return to machine or work zero, and does not mean automatically run another part.
For example, S1800 M03 requests 1800 rpm in a fixed-rpm mode; it is not a cutting recommendation. A lathe using constant surface speed interprets S differently. See Feeds and Speeds.
Units, feed mode and plane answer different questions
Units, feed mode and plane answer different questions
Setting
Common milling interpretation
G20 / G21
Inch / millimetre length units.
G94 / G95
Feed in units per minute / units per spindle revolution, where supported.
G17 / G18 / G19
XY / XZ / YZ plane for plane-dependent operations such as arcs.
G00 / G01
Rapid positioning / straight-line motion at programmed feed.
G02 / G03
Clockwise / counterclockwise arc in the selected plane.
In G21 G94, F90 means 90 mm/min. In G21 G95, F0.15 means 0.15 mm/rev; at 600 rpm that corresponds to 90 mm/min. G20/G21 alone does not choose the time basis. Some lathes use G98/G99 for feed mode, while mills commonly use those codes for drilling return levels.
Rapid path shape depends on the control and can differ from G01. G01 may feed through air as well as cut. Learn the motion and arc geometry in G-code and Toolpaths, including the existing simulator; learn distance modes in Absolute and Incremental Positioning.
G81 and G83 repeat a drilling sequence at hole locations
G81 and G83 repeat a drilling sequence at hole locations
A canned cycle packages repeated motions. In common milling use, G81 feeds a drill to depth then retracts; G83 divides the depth into pecks with retracts for chip clearance. X/Y locate the hole, Z specifies the drill-tip depth, R specifies a return/approach plane, F sets feed, and Q commonly specifies peck depth for G83. Q is not the final hole depth.
With G90 on a conventional mill, Z and R are coordinates in the active work system. Incremental canned-cycle rules need separate study in the manual. G98 commonly returns to the initial level and G99 to R; choose a return level for the actual setup. G80 cancels the cycle. Modal hole cycles can drill again at subsequent position blocks.
Follow the CAD-to-CAM-to-post chain and use graphics, dry run, single block and overrides to check a program against its setup.
CAD describes the shape; CAM plans how to cut it
CAD describes the shape; CAM plans how to cut it
CAD supplies design geometry and drawings. CAM uses geometry plus the programmer's stock, tool, workholding, operation and cutting-data choices to calculate toolpaths. Depending on the operation, CAM may work from 2D profiles or a 3D model; a solid model is not always required.
A post-processor translates CAM output into the syntax and conventions for a particular machine/control combination. Selecting the wrong post can change tool calls, arc format, offsets or startup behavior. Review the posted code as well as the CAM preview.
Supporting detail: Addendum 262 — Other ways to create a program.
Each prove-out aid answers a different question
Each prove-out aid answers a different question
Prove-out compares the intended operation, posted code and actual setup. Follow Equipment Operating Procedure and Machine Hazards and Housekeeping for safety requirements; this page explains program-checking concepts, not a machine operating procedure.
Aid
Useful for
Limit
Graphics or simulation
Inspecting path shape, endpoints, sequence and modeled interference.
A missing clamp, wrong tool model or incorrect offset can make the preview disagree with the machine.
Dry run
Observing a trial cycle under the control's defined test conditions.
It may substitute feed rates; the name does not guarantee no motion or no contact. Use the manual's procedure.
Single block
Advancing through blocks while comparing position and active modes with expectations.
One canned-cycle block may contain several motions. Not every internal action stops separately.
Feed override
Adjusting eligible feed motions during observation.
It need not affect rapids, tool changes or synchronized operations. Rapid override may be a separate control.
Review the program against the setup before a supervised trial; Checklist
Review the program against the setup before a supervised trial
Match the posted file and revision to the intended part, machine and post-processor.
Identify the active units, plane, distance mode and feed mode at each operation.
Compare work offsets, tool numbers and offset registers with the documented setup.
Trace the first approach, tool changes, cycle returns and final retract against the modeled stock and fixtures.
Check that the actual setup matches what the preview includes; resolve any discrepancy with the instructor before proceeding.
Identify the manual's dry-run, single-block and override behavior before using those functions in a supervised trial.
After an edit, repeat the affected checks; compare the first part's measured features with the drawing.
Practise interpretation with G-code and Toolpaths and explore the existing 3D/WebGL milling lab in Milling Operations. A successful simulation only establishes behavior within that model. It does not approve a program for a real machine.
Machining/CNC
CNC Turning Setup and Offsets
Read lathe X and Z coordinates, identify tooling and workholding, and separate part location from tool geometry and wear.
Read X as a size and Z as a position along the spindle; Practice
Read X as a size and Z as a position along the spindle
Start with CNC Control Fundamentals for how CNC works and Lathe Operations for the cuts a lathe makes. Here the work rotates and the ordinary turning tool moves in the XZ plane. Z runs along the spindle; positive Z is away from the headstock in the basic arrangement shown. X moves radially, even when its displayed value is a diameter. A slant bed or rear turret changes the view, so check the machine's axis diagram.
Confirm diameter or radius programming before reading an X value. For a 28 mm diameter, diameter mode uses X28 and radius mode uses X14. Moving from X28 to X24 in diameter mode removes 2 mm radially. Z is not halved. Confirm incremental and arc-centre conventions separately.
Use Absolute and Incremental Positioning for coordinate arithmetic. On many Fanuc-style lathes X/Z are absolute endpoints and U/W are increments; G90 can be a turning cycle. Do not paste a mill's G90/G91 startup into a lathe program.
The tool arrangement determines how the next cutter reaches the work
The tool arrangement determines how the next cutter reaches the work
A turret indexes a selected tool station into working position. Gang tooling mounts several tools on a slide; moving the slide brings the selected tool into position without turret indexing. Each tool still needs the correct offsets and a checked approach path.
Live tooling powers a rotating cutter on the lathe for operations such as drilling or milling. A C axis controls the spindle's angular position, allowing the work to be indexed or rotated under position control. These are options, not features of every CNC lathe. Some machines also add a Y axis. Live-tool and spindle-mode commands belong to the machine's manual.
Supporting detail: Addendum 263 — Why an extra axis changes the work a turning center can do.
Match the workholding and automation to the part
Match the workholding and automation to the part
A chuck grips with jaws. A self-centering chuck moves its jaws together; independent jaws permit individual adjustment. Jaw style and setup determine which shapes can be held.
A collet closes around a matching stock size and shape. Its useful size range depends on the collet design.
A tailstock center supports the free end of suitable work. It does not replace the chuck or collet that drives the work.
A bar feeder advances bar stock for successive parts. A parts catcher receives a separated part. Their timing and interlocks are machine-specific; neither is assumed in an ordinary two-axis program.
Locate the part face once, then locate each tool relative to it
Locate the part face once, then locate each tool relative to it
Use CNC Axes and Offsets for machine zero, work zero and the general offset relationship. On a lathe, a common part datum is Z0 at the finished face and X0 on the spindle centreline. Establish the Z work shift using the control's documented reference-tool, probe or touch-off method. Allow for any material still to be faced away.
For X touch-off, the reference is a measured diameter. In a trial-cut method, a tool cuts a short cylindrical surface and that diameter is measured; the control's measurement function uses the known size to establish that tool's X geometry. Use the manual's procedure for the actual machine, including which table receives the value. Do not enter the measured diameter as though it were automatically the raw geometry-offset value.
Stored information
What it describes
Work shift or work offset
The part datum, especially its Z location.
X and Z tool geometry
The position of each tool's reference tip relative to the established reference system.
X and Z wear
Small dimensional corrections after measurement, separate from the basic tool setup.
Check whether an X wear entry is interpreted radially or diametrally, its sign, and whether the control adds to or replaces the existing value. A work-offset change affects the shared datum; a tool correction addresses one tool. Selecting G54 does not measure or store a new zero. G53 does not erase the offset table.
Supporting detail: Addendum 264 — Control example: separate geometry and wear fields.
Machining/CNC
CNC Turning Spindle and Feed Modes
Calculate constant-surface-speed RPM, apply an RPM ceiling, and distinguish feed per revolution from feed per minute.
G96 changes RPM with diameter; G97 holds a requested RPM; Practice
G96 changes RPM with diameter; G97 holds a requested RPM
In the Fanuc-style lathe convention used here, G96 selects constant surface speed (CSS). S gives cutting speed: surface feet per minute with inch units, or metres per minute with metric units. G97 cancels CSS and makes S an RPM value. Confirm the actual control's units and code meanings.
Use the work diameter at the cutting point, not the insert size. From Feeds and Speeds:
Inch: RPM = SFM × 12 / (π × diameter in inches).
Metric: RPM = cutting speed in m/min × 1000 / (π × diameter in mm).
At 180 SFM on a 1.5 in diameter, RPM = 180 × 12 / (π × 1.5) = 458 RPM, rounded to a whole RPM. At 90 m/min on a 30 mm diameter, the result is 955 RPM. These are arithmetic examples, not recommended cutting data.
Set the maximum RPM before enabling constant surface speed; Interactive; Practice
Set the maximum RPM before enabling constant surface speed
Establish an appropriate spindle-speed ceiling for the actual setup before G96. On the Fanuc-style lathe convention here, G50 S1800 limits requested speed to 1800 RPM. The number is only an illustration; determine the permissible limit from the machine, workholding, tooling and setup documentation. Other controls use different commands or parameters.
As diameter approaches zero during facing, CSS requests increasing RPM. Once the clamp is reached, RPM stays limited and surface speed falls. At the centre, a nonzero surface speed cannot be maintained at any finite RPM. Use CNC Programming and Prove-Out and the Safety collection for the required operating checks.
Supporting detail: Addendum 265 — Calculate where a speed ceiling starts to matter.
Worked example: 240 SFM, 2 in stock outside diameter (OD), and a 1000 RPM clamp. These are teaching values, not cutting recommendations. D* = 240 × 12 / (π × 1000) = 0.917 in.
The dashed horizontal line is the RPM ceiling. The dot shows D = 0.5 in.Below D*, RPM stays at 1000 and surface speed falls linearly toward zero.
One setpoint, three cutting diameters
D (in)
RPM
SFM
Clamped?
2
458.37
240
No
0.5
1000
130.9
Yes
0
1000
0
Yes
At 2 in: 240 × 12 / (π × 2) = 458.37 RPM. At 0.5 in, CSS would request 1833.46 RPM; the clamp gives 1000 RPM and π × 0.5 × 1000 / 12 = 130.90 SFM. At D = 0, the model commands the clamp RPM and surface speed is zero.
This ideal steady-state model uses π without rounding in the calculations. Displays round RPM and surface speed to two decimal places, diameters to three; trailing zeros are omitted. It assumes the commanded RPM is reached immediately and omits acceleration and other machine limits. Unit changes load a fresh teaching preset. For operating checks, see CNC Programming and Prove-Out and the Safety collection.
Read the feed mode before interpreting F; Practice
Read the feed mode before interpreting F
In this common Fanuc-style lathe convention, G99 means feed per spindle revolution and G98 means feed per minute. With inch units, G99 F0.006 means 0.006 in/rev; G98 F0.006 means 0.006 in/min. With metric units, the corresponding lengths are millimetres. Codes vary: the milling return-level meanings of G98/G99 do not apply here.
Feed per minute = feed per revolution × RPM. At 800 RPM, 0.006 in/rev gives 4.8 in/min. If CSS increases RPM while G99 holds F constant, the feed per minute increases too. If G98 holds feed per minute constant, feed per revolution changes with RPM.
Account for a rounded tool nose on tapers and arcs, then distinguish roughing, finishing, grooving and threading cycles.
A rounded tool nose does not cut at the imaginary sharp tip
A rounded tool nose does not cut at the imaginary sharp tip
A turning insert has a rounded corner, called its nose radius. Touching off along X and Z establishes an imaginary tip: the intersection of the two tangent reference lines. There is no cutting material at that intersection. The actual contact point moves around the nose as the direction of the surface changes.
Axis-parallel cuts can reach the measured diameter or face with the corresponding touch-offs. On a taper, chamfer or arc, simply driving the imaginary tip along the desired surface leaves a profile error. Account for the nose radius with a calculated toolpath or the control's tool nose compensation. See Turning Tapers for taper geometry.
Supporting detail: Addendum 267 — Why a good diameter measurement does not prove a taper is correct.
Compensation needs nose radius, tip orientation and a clear entry and exit
Compensation needs nose radius, tip orientation and a clear entry and exit
In common Fanuc-style usage, G41 selects compensation to the left of the programmed direction of travel and G42 to the right; G40 cancels it. Judge the side in the control's XZ-plane convention. Do not choose a code from the screen's apparent left or right, or assume one code means every outside cut.
Enter the actual nose radius and the control's tip orientation, which tells it where the imaginary tip sits relative to the nose centre. Select the correct tool-offset register, use the manual's lead-in and lead-out requirements, and check the resulting path with CNC Programming and Prove-Out. Tip numbers differ by control; there is no universal number table here.
Do not apply full nose-radius compensation again to a path already corrected for that radius. Check whether a CAM post expects full geometry compensation, wear-only compensation or no control compensation.
Supporting detail: Addendum 268 — Where to check the control behavior.
A roughing cycle removes layers while leaving stock for finishing
A roughing cycle removes layers while leaving stock for finishing
A G71-type roughing cycle uses a defined final profile to generate repeated stock-removal passes, commonly along Z for outside or inside turning. The programmer supplies the applicable cut depth, retract and finish allowance. A G70-type finishing cycle follows the defined profile to remove the remaining allowance.
Read the control's cycle definition before entering parameters. One-block and two-block formats differ. A depth word may be radial while an X allowance is diametral; the same letter can mean different things in different blocks. P and Q commonly identify the first and last numbered profile blocks. Check the referenced blocks, permitted profile direction changes, return path and compensation rules.
Supporting detail: Addendum 269 — Why no universal cycle template is shown.
Grooving repeats plunges; threading synchronizes feed with rotation
Grooving repeats plunges; threading synchronizes feed with rotation
A grooving or peck cycle divides a plunge into smaller advances and retracts. Some formats repeat the plunge at different Z positions to make a wider groove. G75 is one common outside/inside grooving family; face-grooving and peck-drilling families may use other codes. Check peck size, final depth, groove width and tool-width convention separately.
A G76-type threading cycle makes repeated synchronized passes with increasing depth. The thread lead determines the axial advance per spindle revolution. The cycle also needs control-specific information about final size, infeed, pass depth and runout. Use Single-Point Threading for pitch, lead and thread form; a threading cycle does not choose those dimensions for you.
Formats differ by control, so no complete parameter syntax is universal. See the Haas G75 reference and the G70/G76 entries in its lathe workbook as examples. CNC Turning Program Walkthrough spells out ordinary moves so the sequence can be read without decoding a cycle.
Machining/CNC
CNC Turning Program Walkthrough
Trace an original facing, outside roughing, chamfering, finishing and cutoff sequence with every block explained.
The invented part is 20 mm in diameter and 25 mm long, with a 1 mm × 45° front chamfer. The chamfer runs from X18 Z0 to X20 Z−1: the 2 mm diameter change is a 1 mm radial change. Stock is 24 mm diameter with its raw face at Z+0.5. G54 has Z0 at the finished face and X0 on the spindle centreline. Stock and clearance extend beyond Z−28; workholding is farther toward negative Z.
Assume diameter programming and absolute X/Z endpoints; this dialect does not need G90 for absolute moves. T0101 selects station 1 and offset 1: a right-hand OD/facing tool with a 0.4 mm nose radius, suitable for the illustrated cuts. Its imaginary tip and radius are set, and G42 is the correct side for this setup's finish contour. T0202 selects a 2 mm wide cutoff tool and offset 2. Its Z reference is the edge toward positive Z, so Z−25 puts the blade in the interval Z−27 to Z−25. The cutoff tool is capable of the illustrated small travel past centre.
The example assumes X60 Z10 is an already-verified tool-change clearance location for both tools and the turret sweep, and starts there with spindle and coolant off. These coordinates are not a general clearance rule. All speeds, feeds and the 1800 RPM ceiling are teaching values, not material recommendations. Verify the real setup, tool calls, compensation entry/exit, centre crossing and file delimiters using CNC Programming and Prove-Out and the Safety collection.
Face the end, then leave a small allowance on the outside diameter
Face the end, then leave a small allowance on the outside diameter
Every parenthesized comment explains its block. G01 remains active until G00 replaces it; X/Z values here are destinations. Facing travels slightly past the centre to account for the rounded nose. Roughing uses two explicit lengthwise passes rather than a control-specific canned-cycle format.
O2460 (IDENTIFY THIS EXAMPLE PROGRAM)
G18 G21 G40 G80 G99 (XZ PLANE, MM, COMP OFF, CYCLES OFF, MM/REV)
G54 (SELECT THE PRESET PART WORK OFFSET)
T0101 (SELECT OD TOOL 1 WITH OFFSET 1 AT VERIFIED CLEARANCE)
G50 S1800 (SET THE EXAMPLE MAXIMUM SPINDLE RPM)
G97 S600 M03 (FIXED 600 RPM, START SPINDLE IN SETUP DIRECTION)
G00 X26.0 (APPROACH OUTSIDE THE 24 MM STOCK AT Z10)
G00 Z0.0 (MOVE TO FINISHED FACE PLANE WHILE OUTSIDE STOCK)
M08 (TURN ON THE ASSUMED FLOOD COOLANT SYSTEM)
G96 S90 (SELECT 90 M/MIN CSS WITH THE RPM CEILING ACTIVE)
G01 X-0.8 F0.10 (FACE THROUGH CENTRE: 0.4 MM RADIAL OVERTRAVEL)
G00 Z2.0 (RETRACT AXIALLY BEYOND THE FACED END)
G00 X22.0 (POSITION FOR THE FIRST OD ROUGHING PASS IN AIR)
G01 Z-28.0 F0.20 (ROUGH LENGTHWISE TO 22 MM DIAMETER)
G00 X26.0 (RETRACT RADIALLY OUTSIDE THE ORIGINAL STOCK)
G00 Z2.0 (RETURN TO THE FRONT AT CLEAR X)
G00 X20.6 (POSITION FOR THE SECOND OD ROUGHING PASS)
G01 Z-28.0 F0.20 (LEAVE 0.6 MM ON DIAMETER FOR FINISHING)
G00 X26.0 (RETRACT OUTSIDE STOCK AGAIN)
G00 Z2.0 (RETURN AHEAD OF THE FACE FOR FINISHING)
Compensate the chamfer and finish, then cut off at fixed RPM
Compensate the chamfer and finish, then cut off at fixed RPM
The finish contour uses the same tool at a smaller feed. Nose compensation is active for the chamfer and OD; it is entered ahead of the face and cancelled after departing the finished contour. See CNC Turning Profiles and Cycles for why a sharp-point assumption would give the wrong chamfer.
G00 X16.0 (POSITION AHEAD OF THE FACE FOR THE COMPENSATED ENTRY)
G01 G42 X18.0 Z0.0 F0.10 (ENGAGE RIGHT COMP ON THE FACE APPROACH)
G01 X20.0 Z-1.0 (CUT THE 1 MM RADIAL BY 1 MM AXIAL CHAMFER)
G01 Z-26.0 (FINISH THE 20 MM OD PAST THE CUTOFF FACE)
G01 X22.0 Z-27.0 (FEED OUT FROM THE OD BEHIND THE FINISHED PART)
G01 G40 X26.0 (CANCEL COMPENSATION ON THE OUTWARD DEPARTURE)
G97 S600 (CANCEL CSS AND REQUEST FIXED 600 RPM)
G00 X60.0 (RETRACT RADIALLY TO THE ASSUMED CLEARANCE X)
G00 Z10.0 (RETURN AXIALLY TO THE VERIFIED TOOL-CHANGE LOCATION)
M09 (COOLANT OFF)
M05 (STOP THE SPINDLE BEFORE THE TOOL CHANGE)
T0202 (SELECT CUTOFF TOOL 2 AND ITS EDGE-REFERENCED OFFSET 2)
G97 S500 M03 (START AT FIXED 500 RPM FOR THIS CUTOFF EXAMPLE)
G00 X26.0 (POSITION OUTSIDE THE STOCK WITH THE NEW TOOL)
G00 Z-25.0 (LOCATE THE POSITIVE-Z BLADE EDGE AT THE REAR FACE)
M08 (COOLANT ON)
G01 X-0.2 F0.05 (PART OFF WITH THE ASSUMED 0.1 MM RADIAL OVERTRAVEL)
G00 X60.0 (WITHDRAW RADIALLY FROM THE CUTOFF SLOT)
G00 Z10.0 (RETURN TO THE ASSUMED CLEARANCE Z)
M09 (COOLANT OFF)
M05 (SPINDLE STOP)
M30 (END AND RESET THE PROGRAM; NO RETURN MOVE IS IMPLIED)
File-start/end percent delimiters, tool-call behavior and supported startup codes must be supplied or adapted as required by the target control. No bar-feeder or parts-catcher sequence is implied.
Trace the modal state and finished dimensions on paper; Checklist; Practice
Trace the modal state and finished dimensions on paper
Mark where S means RPM and where it means metres per minute; locate the preceding RPM clamp.
Confirm that every F value is interpreted in mm/rev under G99.
Calculate the radial depth of each OD pass and the two chamfer endpoints.
Locate the nose-compensation entry and departure, and identify the selected offset register.
Check that the cutoff blade's positive-Z edge leaves the intended 25 mm length.
The syntax conventions can be compared with the Haas lathe programming reference. This original example is not copied from a manufacturer program. A paper trace establishes intended geometry and modal state; actual prove-out still follows CNC Programming and Prove-Out.
Check the first part, watch the process during production, and use suitable measurements to decide whether parts meet requirements.
Inspect before a setup error becomes a batch of parts
Inspect before a setup error becomes a batch of parts
Quality control uses evidence to keep production meeting requirements. Inspection checks what was made; it does not repair a process or make a bad part good.
First-article inspection
Check the first part from a new or changed setup against the required features before releasing continued production. A good first part supports the setup decision; it does not prove that later parts will stay good.
In-process checks
Check selected features while production continues. Record results in production order so tool wear or a shifting setup is visible before many parts are affected.
Final inspection
Check the completed part or lot against the acceptance plan, including requirements that earlier operations could not verify. Keep its identity connected to its results.
If a check fails, identify and hold the affected material, report the result, and investigate before continuing under the applicable procedure. Consider parts made since the last known good check; checking only the next part leaves that interval unresolved.
A gauge gives a decision; a measurement gives a value
A gauge gives a decision; a measurement gives a value
Attribute gauging reports a category such as pass/fail. Variable measurement reports a number, such as 18.012 mm. A number can show how close the process is getting to a limit; a passing gauge alone cannot.
For a plain hole, the GO plug checks the small-hole limit and should enter over the specified inspection length. The NO-GO plug checks the large-hole limit and should not enter as defined by the gauging procedure. Do not force either end. For a plain shaft, a GO ring should pass over the specified length and a NO-GO ring should not pass: the GO ring checks the large-shaft limit.
Conceptual plain plug gauge. The diameter difference is exaggerated; these are not gauge manufacturing dimensions.
A GO plug that will not enter is a failed check, not proof of one particular cause: an undersize hole, burr, dirt, poor alignment or form error can obstruct it. Clean and investigate using the approved method. A NO-GO plug that enters beyond the permitted engagement is also a failed check.
Use the correctly identified gauge with current calibration status. Do not derive gauge sizes directly from workpiece limits. This plain-gauge explanation does not supply the engagement rules for threaded gauges.
Supporting detail: Addendum 271 — Why the gauge itself needs limits and wear checks.
Build a clean, repeatable surface-plate setup; Checklist
Build a clean, repeatable surface-plate setup
A surface plate provides a reference plane. A height gauge measures from that plane; an indicator can compare the part with a reference or show variation as a surface is swept. Neither tool corrects a rocking part or dirt under a support.
Read the required feature and reference surfaces on the drawing; select a suitable instrument and range.
Clean the plate, supports and contact surfaces. Address burrs under the approved preparation method without altering the feature being inspected.
Support the part stably on the intended reference surfaces and allow temperature differences to settle as the measurement procedure requires.
Check the instrument against the appropriate reference, set zero or reference height, and use consistent contact force and alignment.
Repeat the reading, record the value and units, and investigate disagreement before accepting the result.
A CMM relates measured points to the part's references
A CMM relates measured points to the part's references
A coordinate measuring machine (CMM) records positions in three dimensions using a probe or sensor. Software uses sampled points to evaluate features such as a plane, bore or hole location relative to the chosen part alignment.
The operator still needs a suitable setup, probe qualification, measurement strategy and drawing interpretation. A few points cannot reveal every possible surface defect. A CMM is a measurement system, not an automatic guarantee that every requirement has been checked.
Increase checks when the process is new or changing
Increase checks when the process is new or changing
Sampling means inspecting some parts to learn about a larger group or process. It reduces inspection effort but leaves a chance that unmeasured defects will escape. Select samples by a defined plan, not by choosing the nicest-looking parts.
A new setup, tool replacement, unexpected variation or a trend toward a limit calls for closer attention and potentially more frequent checks under the inspection plan. A demonstrated stable process may justify fewer checks; feature consequences and customer requirements still matter. Some features require every part to be inspected.
Keep the readings in order and compare their trend and spread, not just their pass/fail status. Process Capability and Variation explains that distinction. Do not repeatedly adjust a stable process just because its readings differ slightly.
Trust a result only as far as the measurement supports it; Practice
Trust a result only as far as the measurement supports it
Accuracy concerns agreement with a reference or true value; precision concerns agreement among repeated measurements under stated conditions. Readings can cluster tightly and still be consistently wrong.
Calibration compares instrument indications with reference values under specified conditions and establishes their relationship and uncertainty. It is not merely setting zero, and adjustment is a separate action. Traceability belongs to a measurement result supported by a documented chain of calibrations, each contributing uncertainty.
For classroom limit comparisons, treat the stated numbers as exact and include both endpoints. In real inspection, uncertainty matters near a limit: apply the specified acceptance decision rule rather than assuming the last displayed digit is exact.
Compare the allowed tolerance band with the process's centre and spread, without mistaking five good parts for proof of capability.
The drawing sets the limits; the process produces the spread
The drawing sets the limits; the process produces the spread
A tolerance band is the permitted interval from the lower size limit to the upper size limit. Process spread describes how much the manufactured values vary. Changing a machine setting may shift the centre; it does not necessarily reduce the spread.
A capable process consistently fits its variation within the required limits with useful margin. A narrow spread near a limit can still produce rejects if the process drifts. A wide spread cannot be fixed simply by moving its average to the middle.
Illustrative spreads, not probability curves or measured capability results. Both rows use the same size axis.
Consider five invented readings: 24.98, 24.99, 25.00, 25.01 and 25.02 mm, with limits of 24.95 to 25.05 mm.
Mean: add all five readings and divide by five: 125.00 / 5 = 25.00 mm.
Range: subtract the smallest from the largest: 25.02 − 24.98 = 0.04 mm.
Midpoint of the limits: (24.95 + 25.05) / 2 = 25.00 mm. This sample mean is centred on that midpoint, and all five values are inside the limits.
Now add 0.04 mm to every reading. The mean becomes 25.04 mm and the range remains 0.04 mm, but the largest reading becomes 25.06 mm and fails. Centre and spread answer different questions.
Supporting detail: Addendum 272 — Why a small sample range is not the full process spread.
Passing parts are evidence, not proof of a capable process; Interactive; Practice
Passing parts are evidence, not proof of a capable process
Capability concerns a process over time, not a single successful part. First establish that the measurement method is suitable and the process is stable enough to describe meaningfully. Collect representative readings across the conditions the conclusion is meant to cover.
A stable process can still be too wide for the tolerance. An unstable process can happen to produce five passing parts. Neither case is resolved by averaging away the problem. Investigate a trend or sudden change using the inspection plan.
Supporting detail: Addendum 273 — Where capability indices fit.
Capability explorer: assume a stable process with roughly normal output. μ is the process mean; σ (standard deviation) measures spread. These are chosen teaching inputs, not estimates from the five readings above. The five-readings example above explains why passing parts are evidence, not proof of a capable process.
Cp = (USL − LSL) / (6σ) compares tolerance width with spread, ignoring centring. Cpk = min(USL − μ, μ − LSL) / (3σ) uses the nearer limit. Cpk is negative when the mean lies outside the limits. LSL and USL are the lower and upper size limits.
Predict first: which case has the higher Cp? Does it also have fewer parts outside the limits?
Centring makes Cp and Cpk equal. The wide spread still puts parts beyond both limits.
Expected ppm means parts outside the limits per million under this normal model, not a measured reject count. Values are rounded; less than 1 ppm is not a guarantee of zero rejects. Requirements depend on the application; no universal pass threshold is used here.
Locate a part repeatably, clamp it against supports, and distinguish tool-guiding jigs from workholding fixtures.
A jig guides the tool; a fixture locates and holds the work
A jig guides the tool; a fixture locates and holds the work
A drill jig locates and holds the part and guides the drill with a bushing. A fixture locates and holds the part while the machine controls the tool path. A plate with clamps is not automatically a jig: ask whether it guides the cutting tool.
Both reduce the need to recreate the part position for every cycle. Neither removes the need for trained setup, secure restraint and inspection. Follow the approved mounting method; do not infer that a jig may be held by hand.
Three, two and one contacts establish six independent constraints
Three, two and one contacts establish six independent constraints
A free rigid body can translate along X, Y and Z and rotate about X, Y and Z: six degrees of freedom. For an ideal rectangular block seated against perpendicular locating planes, the 3-2-1 arrangement establishes its position without redundant locating contacts.
Contacts
Plane in this example
Additional motions constrained while seated
Three non-collinear supports
Primary, XY underside
Z translation, rotation about X and Y: three
Two separated side locators
Secondary, XZ side
Y translation and rotation about Z: two
One end locator
Tertiary, YZ end
X translation: one
Schematic contact locations, with the hidden contacts shown through the block. A, B and C name the locating planes in this example, not a replacement for the part drawing.
These contacts locate only while the work stays seated. Clamps maintain contact and resist forces that would lift or separate the part. Do not count positive and negative directions as twelve independent degrees of freedom.
Direct clamp force into supports and leave room for chips; Checklist
Direct clamp force into supports and leave room for chips
Place clamp forces toward locators and supported regions, not toward open space where the part can bend. Use enough restraint for the operation without distorting the part. Plan the load path from the cutting force through the work and supports into the machine.
A fourth fixed support under an imperfect surface may make the part rock instead of improving location. Extra supports can be useful for stiffness if they are adjusted to the already located part without shifting it. Avoid redundant locators that fight one another.
Foolproofing (poka-yoke) makes an incorrect loading orientation difficult or impossible—for example, a locating feature that accepts an asymmetric part in only one orientation. Keep chips away from locating contacts with accessible cleaning paths and relief spaces; a trapped chip can relocate every subsequent cut.
Identify the intended locating contacts and check that the part seats without rocking.
Check that clamps press into supports and that loading, cutting and unloading paths are clear.
Check that incorrect orientation is prevented or clearly detectable.
Verify the first part after setup before repeating the cycle.
Modular fixtures trade dedicated tooling for reusable components; Practice
Modular fixtures trade dedicated tooling for reusable components
A modular fixture combines a reusable base with locating pins, supports and clamps. It suits changing work when the arrangement can be documented and rebuilt repeatably. A dedicated fixture may reduce loading time for repeated production, but takes its own design and manufacturing effort.
A tombstone is an upright fixture carrier with mounting faces that can present several setups to a machining centre. It still needs suitable locating, clamping and tool clearance on each face.
Select fixture materials for stiffness, wear, temperature change and the required accuracy. Aluminium can be useful; thermal expansion is a design consideration rather than an automatic ban on close-tolerance work. Wear surfaces may need hardened inserts or replaceable components.
See how programmed machining, tool changes, pallet handling and robots work together—and what must be reliable before unattended production makes sense.
NC and CNC put machining motions under program control
NC and CNC put machining motions under program control
Numerical control (NC) directs machine actions using coded instructions. Computer numerical control (CNC) uses a computer-based controller to execute those instructions. This is a base for automation, not a promise that loading, inspection and fault recovery are automatic too.
Programs still depend on correct tools, work location, offsets and a verified setup. See G-code and Toolpaths and CNC Control Fundamentals for the controls and program details.
Tool changers and pallet changers automate different waits
Tool changers and pallet changers automate different waits
An automatic tool changer exchanges cutting tools so a program can perform several operations. Correct tool identification, dimensions and available tool life remain essential.
A pallet changer exchanges work carriers. In a suitable system, one pallet can be loaded at a designated station while another is being machined. The pallet locates the fixture; the fixture locates the part. Dirt at either interface can undo the expected repeatability.
Repeatable fixturing and planned inspection are part of the automation system, not tasks that disappear after a changer is installed.
A manufacturing cell coordinates machines and handling
A manufacturing cell coordinates machines and handling
A flexible manufacturing cell combines machining and handling resources arranged to produce a planned family of parts. Flexibility comes from suitable programs, tools, fixtures and scheduling; it does not mean any part can be run without preparation.
A loading robot uses a programmed manipulator and a gripping device to transfer parts between defined positions. The cell must confirm conditions such as part presence, clamp state and machine readiness before the next action. A robot's repeatable motion does not compensate for a wrongly seated part.
Supporting detail: Addendum 274 — Cell, system and integration describe different scopes.
Lights-out production requires a plan for faults and variation
Lights-out production requires a plan for faults and variation
Lights-out machining means planned operation without an operator continuously attending the machines. It relies on a validated process, sufficient material and tool life, dependable chip and coolant management, and a defined response to faults.
Monitoring may detect tool breakage, missing parts or measurement trends, but only for conditions the system is designed to detect. Automatic compensation and inspection of every part are options, not universal features of automation. Decide what is measured, what stops production and how affected parts are contained.
Unattended operation is a system-level decision under the applicable equipment and facility procedures. These concepts are not authorization to leave a machine running unattended or enter an automated cell. A stopped cycle alone does not establish safe access.
Machining/Production and Nontraditional Processes
Electrical Discharge Machining
Sinker and wire EDM use controlled sparks to shape conductive work, with a gap between electrode and finished surface.
EDM needs an electrically conductive workpiece
EDM needs an electrically conductive workpiece
Electrical discharge machining (EDM) removes material with repeated electrical discharges across a small gap. Local heating melts and vaporizes tiny amounts of material. The electrode does not cut by rubbing against the work.
Check conductivity before considering EDM. Hardened tool steel is a candidate; ordinary nonconductive glass or ceramic is not. Hardness is less restrictive than in cutting with a conventional tool, but composition and electrical and thermal properties still affect machining behavior.
Supporting detail: Addendum 275 — Why the fluid and the gap matter.
Use sinker EDM for cavities and wire EDM for through profiles
Use sinker EDM for cavities and wire EDM for through profiles
Sinker, ram or die-sinking EDM feeds a shaped electrode toward the work to make a cavity. The cavity is larger than the electrode because removal extends across the spark gap. Mold cavities and hardened dies are typical uses. Electrode wear must be allowed for.
Wire EDM feeds a thin wire through the cutting zone while controlled motion traces a profile. The wire is continuously renewed. An enclosed opening normally needs a start hole for threading; the wire must pass through the work. A blind pocket calls for another approach, such as sinker EDM.
Wire EDM is useful for intricate die openings and thin features with low cutting force. Internal corners still have a radius: the wire radius plus the working gap limits how tight a corner can be. Specify a small radius rather than a mathematically sharp corner.
Offset the wire center by its radius plus the spark gap; Practice
Offset the wire center by its radius plus the spark gap
The wire runs perpendicular to this top view. Gap and wire are enlarged. The dashed line is the wire center path; the solid boundary is the finished wall.
Center-path offset = wire radius + spark gap. Measure this distance from the finished contour toward the material being removed. In a simple straight cut, the full cut width (kerf) is wire diameter plus twice the gap.
For an illustrative radius of 0.120 mm and a one-sided gap of 0.018 mm, the offset is 0.138 mm. These are teaching inputs, not machine settings. A control may apply compensation to a programmed part contour; do not also offset the geometry a second time.
Supporting detail: Addendum 276 — Why one offset does not describe every pass.
Low cutting force does not mean no thermal change
Low cutting force does not mean no thermal change
EDM can hold fine features and produce a fine finish with suitable finishing passes, but its surface contains small discharge craters. Melted material can solidify again as a recast layer. Heat can alter nearby material, so surface integrity and any required finishing belong in process selection.
Supporting detail: Addendum 277 — Further reading on EDM surfaces and wire systems.
ECM dissolves conductive metal through an electrolyte rather than removing it with sparks or a cutting edge.
ECM removes metal by electrochemical dissolution
ECM removes metal by electrochemical dissolution
In electrochemical machining (ECM), the metal workpiece is the positive electrode (anode), and the tool is the negative electrode (cathode). Direct current passes through a flowing, electrically conductive liquid called an electrolyte. Metal dissolves from the work surface while the tool advances without cutting contact.
Consider ECM for conductive metals, including hard alloys and complex contours. The tool shape, gap and electrolyte flow govern the resulting feature. A suitable electrolyte must be matched to the metal; a generic salt solution is not a universal process recipe.
ECM uses a conducting liquid; EDM uses controlled breakdown
ECM uses a conducting liquid; EDM uses controlled breakdown
Two electrically powered processes with different removal mechanisms
Question
ECM
EDM
What removes material?
Electrochemical dissolution
Heat from discharges
What does the liquid do?
Conducts current and carries reaction products away
Insulates between discharges; cools and flushes
Does the tool wear?
No removal-related tool wear in principle; real tooling still needs maintenance
Electrode wear occurs; wire is renewed
What surface results?
Can be smooth and burr-free, without a thermal recast layer
Discharge craters and possible recast material
ECM is not a melting process and normally avoids a heat-affected zone. That does not mean the electrolyte stays cold: current flow heats it. Flow, temperature, chemistry and gap control all matter.
Supporting detail: Addendum 278 — Why hardness alone does not set ECM performance.
Compare focused light, moving water and a plasma arc by material, thickness, edge quality and thermal effects.
Distinguish a thermal cut from an erosive cut
Distinguish a thermal cut from an erosive cut
Laser and plasma use concentrated heat. Waterjet uses mechanical energy. A heat-affected zone (HAZ) is material beside a cut whose properties or structure have changed from heating without being melted away.
Conceptual cross-sections, not a scale comparison of kerf or HAZ widths. Kerf means the width removed by a cut.
Laser cutting concentrates light into a small region
Laser cutting concentrates light into a small region
A focused laser beam supplies thermal energy; cutting gas commonly helps remove material. Laser cutting is a candidate for fine profiles in sheet material. Metals, wood and selected plastics require suitable laser systems; a machine that cuts acrylic is not automatically a metal cutter.
A narrow kerf and fine detail are possible, particularly in thinner material. Edge finish, taper and dimensional accuracy depend on material, thickness, focus, gas and cutting speed. Melting, discoloration or charring may affect the edge. Do not assume the HAZ is zero.
Supporting detail: Addendum 279 — Why the material and laser must be matched.
Waterjet cuts soft materials; added abrasive cuts hard materials
Waterjet cuts soft materials; added abrasive cuts hard materials
Pure waterjet uses a high-speed water stream for materials such as foam, rubber and other soft sheet. Abrasive waterjet adds hard particles to erode metals, stone, non-tempered glass and many ceramics. Electrical conductivity is not required.
Waterjet normally creates no thermal HAZ. It is a candidate for thick stock or a heat-sensitive edge, but thickness still affects speed and cut quality. Taper, where the cut width changes through the thickness, and striations, visible lines down the cut face, can limit accuracy and finish. Slower quality cuts may reduce these effects. Brittle edges may chip and need finishing.
Identify the glass type before choosing a process: tempered glass is not a candidate for ordinary waterjet cutting. A no-HAZ process is not a promise of no mechanical damage.
Supporting detail: Addendum 280 — Further reading on glass and waterjet limits.
Plasma is a thermal cutting candidate for conductive metal
Plasma is a thermal cutting candidate for conductive metal
A plasma cutter uses an electric arc through ionized gas to melt metal; the gas stream expels it. The work must conduct electricity. Steel, stainless steel and aluminum are candidates; ordinary glass and wood are not.
Plasma often suits productive plate cutting where its edge quality meets the drawing or later machining is planned. Compared with a fine laser cut in thin sheet, small details can be harder to hold. Edge bevel, attached solidified metal (dross) and a HAZ may need attention. Equipment and thickness determine actual capability; plasma is not automatically a rough-only process.
Supporting detail: Addendum 281 — Compare capability on the actual thickness.
A vibrating tool drives abrasive particles against hard, brittle work without requiring electrical conductivity.
Ultrasonic impact machining removes material with abrasive particles
Ultrasonic impact machining removes material with abrasive particles
A shaped tool vibrates rapidly with a small stroke, driving abrasive particles in a liquid slurry against the work. The removal energy at the work is mechanical, even though electricity powers the vibration system.
Consider this process for holes or shaped cavities in hard, brittle materials such as glass and ceramics. The work need not conduct electricity. It is generally less effective for soft, ductile materials that deform instead of breaking away under particle impacts.
No thermal HAZ does not mean a perfect surface
No thermal HAZ does not mean a perfect surface
Ultrasonic impact machining normally avoids a thermal heat-affected zone. Abrasive size, tool wear, slurry access and feature depth affect dimensional control and finish. Fine abrasive can improve the surface, but removal may be slow; edge chipping and subsurface damage remain possible in brittle work.
Distinguish this process from ultrasonic-assisted cutting, where vibration is added to another cutting or grinding process. The two names do not imply identical tooling or removal mechanisms.
Supporting detail: Addendum 282 — Why a shaped tool does not give an exact-size copy.
A mask protects selected areas while an etchant dissolves exposed metal; sideways etching limits the detail.
A mask defines where chemical removal occurs
A mask defines where chemical removal occurs
Chemical machining uses a chemical reaction to dissolve exposed material. A protective mask covers areas that should remain. Chemical milling can make shallow recesses or reduce a metal part's weight. Photochemical etching uses a patterned resist and can produce intricate thin-sheet parts, including through openings.
Unlike ECM, ordinary chemical etching does not use an external machining current between a tool and the work. Select an etchant compatible with the particular material; “chemical machining” does not name one chemistry that works on everything.
Allow for sideways etching beneath the mask
Allow for sideways etching beneath the mask
Etching can spread sideways beneath the mask edge as well as into the surface. This undercut limits narrow lands, corner sharpness and dimensional control, especially as etch depth increases. The mask design must compensate for the etching behavior. Surface finish depends on the material and chemistry. Chemical removal avoids a cutting-induced thermal HAZ, but that is not the same as saying the chemical bath has no temperature requirements.
Supporting detail: Addendum 283 — Why thin-sheet patterns are a useful application.
Mark the feature: through profile, blind cavity, shallow recess or finished surface. Identify tool access and any start-hole requirement.
Record thickness, minimum internal radius and the thinnest remaining feature.
Read the drawing's dimensional and surface requirements. Decide whether a thermal HAZ or recast layer is acceptable.
Shortlist processes, then check actual equipment capability, finishing needs and production quantity.
Hardness alone does not select a process. A hard nonconductive ceramic rules out ordinary EDM even though EDM can cut hardened steel. See Tolerances and Fits and Surface Texture and Finish for what the finished part must meet.
Use the feature to narrow the candidates
Use the feature to narrow the candidates
Starting candidates, not guaranteed process approvals
Part requirement
Candidate and reason
Check next
Hardened steel die with a through opening and small inside radii
Wire EDM: conductive work, low cutting force, fine profile
Wire radius plus gap, threading access and surface integrity
Keep conventional machining on the candidate list; Practice
Keep conventional machining on the candidate list
For an accessible flat face, hole or round shaft in a machinable material, conventional cutting may be the simplest route. Use the family map to reach those methods. A part may combine sawing, milling and grinding, or use waterjet for a blank followed by machining of critical faces.
Increasing thickness can increase cutting time, taper or flushing difficulty. A thin remaining wall may deflect or be damaged even when cutting forces are small. Ask for evidence of capability on the actual material and geometry rather than relying on a universal tolerance ranking.
Predict how one unidirectional composite layer stretches and skews when its fibers turn relative to the same applied stress.
Fiber direction changes elastic response
Fiber direction changes elastic response
A fiber-reinforced composite combines a reinforcement with a surrounding matrix. In a unidirectional layer, the reinforcement is continuous and parallel. The layer is much stiffer along the fibers than across them, so its elastic response depends on direction.
Stress is force divided by loaded area. This lesson compares patches under the same uniform axial stress, so each square millimeter carries the same applied force. Strain is deformation divided by original dimension. Elastic stiffness connects stress to strain in the reversible small-strain model.
The illustrative material uses E1 = 40 GPa along the fibers, E2 = 10 GPa across them, G12 = 5 GPa, and ν12 = 0.30. These round teaching values do not describe a named composite and are not design allowables.
Predict the least stretch, then turn the fibers; Interactive
Predict the least stretch, then turn the fibers
Read the directions: the fiber angle is the starting, unloaded direction measured from the horizontal load axis. In this drawing, +45° slopes up to the right and −45° slopes down to the right. Axial means along the load; transverse means across it. The drawn fibers follow the exaggerated deformation, so their visible slope can differ from the starting angle on the control.
Predict first: identical free material patches carry uniform axial stress σx = 10 MPa, with no applied transverse or shear stress. Which orientation stretches least: 0°, 45°, or 90°?
Same illustrative lamina and same 10 MPa stress
Fiber angle
Effective axial stiffness
Axial strain
Transverse strain
Engineering shear strain
0°
40.00 GPa
0.0250%
−0.0075%
0 µε
+45°
12.90 GPa
0.0775%
−0.0225%
−375 µε
−45°
12.90 GPa
0.0775%
−0.0225%
+375 µε
90°
10.00 GPa
0.1000%
−0.0075%
0 µε
Result: 0° stretches least because the stiff fiber direction is aligned with the load. Opposite 45° angles have the same axial stiffness and stretch, but their shear strain has opposite sign.
This is a freely deforming material patch loaded by uniform edge traction. It is not a tensile-test coupon held in rigid grips: grips would restrain the off-axis skew and create another boundary-value problem.
Off-axis extension can also create shear strain
Off-axis extension can also create shear strain
At 0° and 90°, the loading direction matches a principal material direction. The patch stretches and narrows without extension–shear coupling. At an off-axis angle, an axial stress can also make the free patch skew. Turning +45° to −45° mirrors that skew while leaving the axial stiffness unchanged.
The interactive drawing exaggerates every strain by the same factor of 120. A larger drawn change therefore means a larger calculated strain; the display does not secretly rescale each angle to fill the frame.
Supporting detail: Addendum 284 — How the axial stiffness is calculated.
Stiffness does not predict strength; Practice
Stiffness does not predict strength
A smaller strain under the same stress means greater elastic stiffness. It does not say when the material fails, which direction is safest, or which laminate should be built. Strength needs failure data and criteria; a laminate also needs its complete stacking sequence, ply thicknesses, bonding, environment, loading, and boundary conditions.
This lesson models one thin, continuous-fiber lamina in small-strain linear elasticity and plane stress. It omits failure, damage, buckling, bending, temperature, moisture, manufacturing defects, grips, and interaction between multiple plies.
Supporting detail: Addendum 285 — Primary mechanics source and model boundary.
Stack plies into a laminate and find one equally stiff in every direction; Interactive
Stack plies into a laminate and find one equally stiff in every direction
A real part is rarely one ply. A laminate is a stack of bonded plies, each with its own fiber angle. The stacking sequence is written from the top face down: [0/90] is a 0° ply on top of a 90° ply, and a subscript s means the list is mirrored about the midplane, so [0/90]s is [0/90/90/0]. Every ply here is the same illustrative ply as the card above, 0.125 mm thick.
Challenge: using only 0°, +45°, −45° and 90° plies, build a laminate that is equally stiff in every in-plane direction. Then find out why an unsymmetric stack curls when it is pulled.
Same ply, two balanced symmetric stacks. Left, cross-ply [0/90]s: 25.21 GPa along 0° and 90° but only 14.82 GPa at 45°. Right, [0/+45/−45/90]s: 20.74 GPa in every in-plane direction, so the shaded rose is a circle. The dotted outline is one 0° ply on its own (40 GPa along the fibers, 10 GPa across), the same ply as the fiber-orientation lesson above. Radius = modulus; outer ring 40 GPa.
Same illustrative plies, 0.125 mm each. Ex is flat-held (curvature held at zero).
Stack (top first)
Symmetric
Balanced
Quasi-isotropic
Ex at 0° / 45° / 90°, GPa
Largest |Bij|
[0]
yes
yes
no
40.00 / 12.90 / 10.00
0
[0/90]
no
yes
no
25.21 / 14.82 / 25.21
239.8 N
[0/90]s
yes
yes
no
25.21 / 14.82 / 25.21
0
[+45/−45]
no
yes
no
14.82 / 25.21 / 14.82
119.9 N
[±45]s
yes
yes
no
14.82 / 25.21 / 14.82
0
[0/+45/−45/90]s
yes
yes
yes
20.74 / 20.74 / 20.74
0
A single 0° ply gives 40.00 GPa along x and 10.00 GPa along y, the fiber-orientation result for the same ply.
Same pull, Nx = 0.5 N/mm, no applied moment. [0/90] curls: κx −7.87×10⁻⁴ mm⁻¹ · κy 0 mm⁻¹ · κxy 0 mm⁻¹ (principal radius about 1271 mm). [0/90]s stays flat: all curvatures are zero because B = 0. Height exaggerated ×30 in both drawings of a 50 mm square patch; the dashed outline is the unloaded patch and in-plane stretch is not drawn. With no load, both are flat.
The polar plot is a stiffness rose. Its radius in each direction is the laminate's effective in-plane modulus Ex(θ) for a pull in that direction, computed with the laminate held flat. A circle means the same in-plane stiffness every way.
Symmetric, balanced and quasi-isotropic are three different properties
Symmetric, balanced and quasi-isotropic are three different properties
Symmetric: the plies above the midplane are a mirror image of the plies below it. Then the coupling matrix B is zero, so in-plane loads and bending stay separate. [0/90]s is symmetric; [0/90] is not.
Balanced: every +θ ply has a −θ ply of the same thickness somewhere in the stack (0° and 90° plies need no partner). Then A16 = A26 = 0: there is no extension–shear coupling in the flat-held in-plane response, so a pull along x or y held flat does not shear the laminate in its plane. A balanced and symmetric stack also has B = 0, so it does not shear when free either; a balanced unsymmetric stack such as [0/+45/−45/90] can still shear and twist when free to curve.
Quasi-isotropic: the in-plane stiffness matrix A is the same in every direction, so the rose is a circle. Equal numbers of 0°, +45°, −45° and 90° plies do this, and because A ignores the order of the plies, [0/+45/−45/90]s and [+45/0/−45/90]s both qualify. It describes in-plane stiffness only; bending stiffness D still depends on order and direction.
An unsymmetric laminate does not bend just because B is not zero. With no applied force and no applied moment, this model predicts no deformation at all. B only links a load to a response: pull an unsymmetric panel in its plane and it also curls or twists, even though no moment is applied. A symmetric panel under the same pull stays flat: it stretches (and, if unbalanced, also shears in its plane) but does not curl or twist.
Flat-held and free stiffness differ for unsymmetric laminates
Flat-held and free stiffness differ for unsymmetric laminates
The two stiffness numbers for an unsymmetric laminate answer different questions. Flat-held (curvature-constrained) stiffness uses A alone and assumes something stops the panel from curving. Free stiffness lets it curve with zero applied moment and solves the full relation including B and D; it is never higher, and in most directions lower, because the panel can curl as well as stretch. For a symmetric laminate the two are identical.
Real unsymmetric panels can also warp as they cool after curing, because each ply shrinks differently in different directions. That temperature effect is not modeled here, and the curled panel in the interactive is not a picture of it: every curl drawn above is the response to the stated in-plane load.
Supporting detail: Addendum 286 — How the laminate stiffness and the free-panel response are calculated.
This is linear, small-deflection classical laminate theory with perfectly bonded plies. It does not predict strength, first-ply failure, delamination, buckling, temperature or moisture effects, or how a real panel behaves once its deflection is comparable to its thickness.
Supporting detail: Addendum 287 — Primary mechanics source and model boundary.
Engineering Fundamentals/Units and Measurement
Measurement Language
Use quantities, units, symbols, and SI prefixes precisely before a drawing, program, or calculation has a chance to drift.
A measurement is a number and a unit
A measurement is a number and a unit
A dimension on a drawing, a speed in a robot program, and a torque setting are all
quantities: a number paired with a unit. The number tells how many; the unit tells
what kind of thing and how large each part is.
25 mm
A length: twenty-five millimeters. Writing only 25 leaves
the measurement incomplete.
4.25 min
A CNC cycle time. It is not interchangeable with 4.25 seconds or
4.25 hours.
3.0 m/s
A speed or velocity magnitude. The slash means meters per
second.
Carry units through every line of a calculation. They are an error check,
not decoration. If the last line needs a length and the units say seconds, stop before the
wrong number reaches a drawing or controller.
Use the unit symbol exactly as specified: m for meter, s for
second, kg for kilogram. Symbols are not pluralized and do not take a period:
12 mm, not 12 mms.
Two systems you will encounter
Two systems you will encounter
The International System of Units (SI) is the standard system for science and
much technical work. U.S. drawings, hardware, materials, and equipment also use
U.S. customary units. Neither system lets us skip the unit; the job is to state
which one is being used and convert deliberately when they meet.
SI drawing25.0 mmmillimeters
U.S. customary drawing≈ 0.984 ininches
The part does not change. The measurement language does. A value
copied without its unit can make the same feature look like two different sizes.
SI base units used here
meter (m) for length, second
(s) for time, and kilogram (kg) for mass.
U.S. customary units used here
inch (in), foot (ft),
mile (mi), second (s), pound mass (lbm), and U.S.
liquid gallon (U.S. gal).
Coherent BG engineering system
The source slides call the coherent engineering
form BG (British Gravitational): foot, slug, and second. In that system,
slug · ft/s2 = lbf. A pound force and a pound mass are not the
same unit.
A gallon must be named. This unit set uses the U.S. liquid gallon
(U.S. gal), not an Imperial gallon.
Supporting detail: Addendum 288 — Why technical writing cares about the space.
SI prefixes change scale, not quantity
SI prefixes change scale, not quantity
A prefix is a power of ten attached to a unit. It makes a practical-sized number without
changing the physical quantity: 0.025 mm and 25 µm describe the same length.
Common engineering prefix ladderMove right: each unit is 1,000 times smaller, so the number is 1,000 times larger.
kilokm103 m
no prefixm100 m
millimm10−3 m
microµm10−6 m
nanonm10−9 m
1 m=1,000 mm=1,000,000 µm=1,000,000,000 nm
The ladder is a teaching subset; the complete reference follows. It shows why
1 mm = 0.001 m and 1 µm = 0.000001 m: changing a prefix changes the
number used to describe a length, not the length itself.
All current SI prefixes, plus the unprefixed unit used between them.
Name
Symbol
Factor
quetta
Q
1030
ronna
R
1027
yotta
Y
1024
zetta
Z
1021
exa
E
1018
peta
P
1015
tera
T
1012
giga
G
109
mega
M
106
kilo
k
103
hecto
h
102
deca
da
101
none
—
100
deci
d
10−1
centi
c
10−2
milli
m
10−3
micro
µ
10−6
nano
n
10−9
pico
p
10−12
femto
f
10−15
atto
a
10−18
zepto
z
10−21
yocto
y
10−24
ronto
r
10−27
quecto
q
10−30
Case matters.M is mega (106);
m is milli (10−3). A wrong capital letter changes a result by a
billion.
Prefix explorer
Prefix explorer
Choose two prefixes for the same base unit. The calculation compares their powers
of ten; it does not change what is being measured.
Move 3 powers toward larger units. The target unit
is 103 times larger, so the numerical value is divided by 103.
From: µm · 10^−6To: mm · 10^−3
smallest listed unit 10−30no prefix 100largest listed unit 1030
Result:
25 µm = 25 × 10−6 m = 0.025 ×
10−3 m = 0.025 mm.
Practice and sources; Practice
Practice and sources
Use the practice bank to apply this lesson’s prefix-conversion method.
Supporting detail: Addendum 289 — Sources and definitions.
Engineering Fundamentals/Units and Measurement
Dimensional Analysis
Convert quantities by multiplying by named equalities, cancelling units, and treating squared and cubed units as powers.
Convert by multiplying by one; Watch out
Convert by multiplying by one
A conversion factor is a ratio of two exactly equal physical quantities
written as a fraction. For example, 1 ft and 0.3048 m name exactly the same length. Their ratio
therefore has the numerical value 1, so multiplying by it changes the unit expression without
changing the physical quantity.
Either orientation is valid: 1 ft / 0.3048 m and
0.3048 m / 1 ft both equal 1. Choose the orientation that cancels the unwanted unit.
To convert 12 m to feet, put meters on the bottom:
12 m ×
1 ft0.3048 m
= 39.370078740… ft ≈ 39.3701 ft.
For the reverse conversion, turn the same exact equality over so feet cancel:
39.370078740… ft ×
0.3048 m1 ft
= 12 m.
Do not memorize an arrow. Write the desired unit, then arrange the factor so
the unwanted unit cancels. The units tell you whether the fraction is facing the correct way
before you calculate.
Exact, defined
1 in = 0.0254 m, so
1 ft = 0.3048 m and 1 yd = 0.9144 m exactly.
Keep guard digits
Use exact factors or sufficient digits while calculating;
round the displayed result only at the end and only as the task needs.
Match dimensions
Length converts to length, area to area, volume to volume,
and force to force. A calculator cannot make incompatible dimensions meaningful.
Powers apply to the whole conversion
Powers apply to the whole conversion
Area and volume are not lengths with decorative superscripts. The conversion factor itself
must be squared or cubed.
Why a single linear factor is not enough.
Quantity
Exact relationship
Useful result
Length
1 ft = 0.3048 m
1 ft = 0.3048 m
Area
(1 ft)2 = (0.3048 m)2
1 ft2 = 0.09290304 m2
Volume
(1 ft)3 = (0.3048 m)3
1 ft3 = 0.028316846592 m3
Time squared
(1 min)2 = (60 s)2
1 min2 = 3,600 s2
For example, 4 m2 × (1 ft / 0.3048 m)2 =
43.0556 ft2, which is sensibly reported as 43.1 ft2.
For liquid capacity, 1 m3 = 1,000 L and
1 U.S. gal = 3.785411784 L. The converter labels this as a U.S. liquid
gallon so it cannot be mistaken for an Imperial gallon.
Supporting detail: Addendum 290 — Dimensional analysis is also a design check.
Conversion bench
Conversion bench
This tool uses exact internal factors where standards define them. It only converts
within one quantity type; a length cannot become a speed without additional information.
Speed is a nonnegative magnitude and has no direction. A negative signed value
represents a velocity component opposite the chosen positive direction.
Result:
12 m × (1 ft / 0.3048 m) = 39.370078740… ft ≈ 39.3701 ft.
CNC production calculation
CNC production calculation
A CNC program estimates 4 min 15 s per part. The operator uses 30 min of an
8 h shift for setup. How many complete parts fit in the shift?
Convert the cycle: 4 min 15 s = 4.25 min.
Find machine-running time: 8 h × (60 min / 1 h) − 30 min = 450 min.
Divide running time by cycle time: 450 min / 4.25 min per part = 105.882....
105 complete parts. The fractional result is time into the
106th cycle, not a finished part. This assumes one machine, no unplanned stops, and that the
stated cycle time already includes every repeatable operation.
Supporting detail: Addendum 291 — Two more conversion cases from the unit.
Practice and sources; Practice
Practice and sources
Use the practice bank to apply cubic conversion factors to a model volume.
Supporting detail: Addendum 292 — Sources and exact factors.
Engineering Fundamentals/Motion and Rotation
Motion Quantities
Distinguish path length from displacement, and speed from velocity, before using time to describe a machine or vehicle in motion.
Path length and displacement answer different questions
Path length and displacement answer different questions
Distance is how much path was traveled. Displacement
is the directed change from the starting position to the ending position. A return trip can add
distance while leaving displacement at zero.
Distance
A nonnegative scalar path length. A conveyor that moves a tote 12 m
out and 12 m back travels 24 m of distance.
Displacement
A change in position with direction. If the tote returns to its
start, its displacement is 0 m even though it moved.
Coordinate choice
Choose a positive direction before calculating. Along a
straight robot rail, right might be positive and left negative.
Distance tells what the machine did along its path; displacement
tells where it ended up relative to where it began. Do not substitute one for the other
just because both use meters or feet.
Speed and velocity are not synonyms
Speed and velocity are not synonyms
Average speed is total distance divided by elapsed time. Average
velocity is displacement divided by elapsed time. Velocity includes direction; speed
does not.
average speed = total distance / elapsed time average velocity = displacement / elapsed time
Notation bridge: this site uses x for position
and Δx for displacement. Some course materials use s for position
instead. For a stated interval, write average velocity as
vavg = Δx / Δt; the symbols differ, but the physical idea is
the same.
For the 12 m out-and-back path completed in 16 s, average speed is
24 m / 16 s = 1.5 m/s. Average velocity is
0 m / 16 s = 0 m/s. Both statements can be true at the same time.
A production-line example
A mechanism must carry a part 12 m in 8 s. Its required average speed is
12 m / 8 s = 1.5 m/s. Converting with exact factors gives
1.5 m/s × (39.37007874 in / 1 m) = 59.055... in/s, or
59.1 in/s. If the programmed direction is stated, its average velocity is
+59.1 in/s in that direction.
Average and instantaneous readings
Average and instantaneous readings
An average uses a time interval. An instantaneous reading describes one moment: a car
speedometer reports instantaneous speed; a robot controller’s live velocity value is an
instantaneous velocity in its coordinate frame.
Use average speed for throughput, travel-time, and trip planning.
Use average velocity for a net movement over a stated interval.
Use an instantaneous reading when clearance, collision avoidance, or a
machine limit depends on what is happening now.
Supporting detail: Addendum 293 — The calculus idea, after the practical one.
Out-and-back path lab
Out-and-back path lab
Set positions along a straight path and the outbound and return times. The text
results make the distance and displacement distinction visible even when the track is not used.
−3 m15 m
Start: 0 mTurn: 12 mEnd: 0 m
Distance
Displacement
Average speed
Average velocity
Practice and sources; Practice
Practice and sources
Use the practice bank to apply distance, speed, and round-trip rate reasoning.
Calculate change in velocity over time, distinguish average from instantaneous acceleration, and convert squared time units correctly.
Acceleration is change in velocity over time
Acceleration is change in velocity over time
Acceleration is not simply “speeding up.” It is a change in velocity,
so it can describe speeding up, slowing down, or turning.
aavg = Δv / Δt = (vf − vi) / (tf − ti)
Δv
Change in velocity. With one chosen positive direction,
Δv = vf − vi.
m/s2
Meters per second per second. Each second, velocity changes
by the stated number of meters per second.
ft/s2
Feet per second per second. The coherent
foot–slug–second system uses this acceleration unit with slugs for mass.
Write the sign. A final velocity lower than the initial velocity produces
negative acceleration in the selected direction; it is not an error just because the answer is
negative.
Average is an interval; instantaneous is a moment
Average is an interval; instantaneous is a moment
Average acceleration is calculated over stated start and end conditions. An accelerometer or
control system can report instantaneous acceleration at one moment. They match at every moment only when the
acceleration stays constant through the interval.
Machine arm example
A machine arm starts from rest and reaches 3 m/s in 4 s:
aavg = (3 m/s − 0 m/s) / 4 s = 0.75 m/s2.
This is the average acceleration for the four-second move. If the drive ramps gently at the
start and end, its instantaneous acceleration changes during the move even though the average
remains 0.75 m/s2.
Robot gripper example
A SolidWorks motion study programs a gripper from 0 to 5 ft/s in 0.5 s to pick an electronic
component. Its average acceleration is 5 ft/s / 0.5 s = 10 ft/s2. In SI,
10 ft/s2 × (0.3048 m / 1 ft) = 3.048 m/s2.
Squared time needs a squared factor; Watch out
Squared time needs a squared factor
Acceleration has time in the denominator twice. When converting an acceleration unit, convert
the entire squared time relationship, not just one s.
1 min = 60 s means 1 min2 = (60 s)2 = 3,600 s2.
Use the inverse relationship in the correct direction.1 ft/s2 = 0.3048 m/s2, not
0.30482 m/s2. The foot is the only unit being changed in
that expression; seconds are already seconds in both units.
By contrast, converting m/min2 to m/s2
requires the full squared time factor. The unit cancellation shows why:
1 m/min2 × (1 min / 60 s)2 = 1/3,600 m/s2.
Acceleration lab
Acceleration lab
Change the initial and final velocities and the elapsed time. The last result
converts the calculated foot-per-second-squared value to SI.
Change in velocity
Average acceleration
SI equivalent
Practice and sources; Practice
Practice and sources
Use the practice bank to apply average acceleration over a stated interval.
Scale CAD geometry correctly, connect volume and density to mass, and keep force and weight as separate quantities.
Scale changes area and volume by powers; Watch out
Scale changes area and volume by powers
If every linear dimension of a model is multiplied by a scale factor s,
area changes by s2 and volume changes by s3. A
20% larger model is not 20% larger in area or volume.
Length
Lnew = sLold
Area
Anew = s2Aold
Volume
Vnew = s3Vold
For s = 1.2, area factor = 1.22 = 1.44 and volume factor
= 1.23 = 1.728. This is why a modest scale change can matter to material
use, shipping mass, tank capacity, and actuator selection.
Never scale an area with a linear factor or a volume with an area
factor. The exponent belongs to the geometry, not to the number of decimal places.
Volume is capacity only after you name the unit
Volume is capacity only after you name the unit
CAD mass properties often report volume in a model’s document units. Before treating that
number as a tank capacity or a material quantity, state the volume unit and convert it to the
form the drawing or specification requires.
Volume relationships used in this unit.
Relationship
Meaning
1 m3 = 1,000 L
A cubic meter contains one thousand liters.
1 U.S. gal = 3.785411784 L
This is a U.S. liquid gallon, not an Imperial gallon.
1 ft3 = 7.48051948 U.S. gal
Derived from the exact foot and U.S. gallon definitions.
Static solved reservoir example
A SolidWorks model gives a hydraulic reservoir internal volume of 2.5 ft3. Its
capacity is 2.5 ft3 × 7.48051948 U.S. gal/ft3 =
18.7013 U.S. gal, or 18.7 U.S. gal. This assumes the reported CAD volume
is the usable internal volume and no design headspace has yet been subtracted.
Density connects volume to mass
Density connects volume to mass
Density is mass per volume, and its symbol is ρ (rho):
ρ = m/V. Turned around, when material density and CAD volume use compatible
units, m = ρV produces mass.
(kg/m3) × (m3) = kg
Density units in the two systems.
System
Unit
Conversion
SI
kg/m3
1 kg/m3 = 0.00194032 slug/ft3
Foot–slug–second
slug/ft3
1 slug/ft3 = 515.3788 kg/m3
For example, a volume of 0.13824 m3 made of material with a density of
2,700 kg/m3 has mass
m = 2,700 kg/m3 × 0.13824 m3 = 373.248 kg.
Static solved steel example
A steel I-beam has a volume of 0.2 m3 and a density of 7,850 kg/m3. Its
mass is m = 7,850 kg/m3 × 0.2 m3 = 1,570 kg. That is the
same mass the weight example below starts from — a CAD volume and a material card are
usually where a weight calculation actually begins.
Mass does not change merely because an object is moved from one
planet to another. Weight can change because gravitational acceleration changes. CAD
models, material databases, and shipping specifications commonly need mass; lifting and support
calculations commonly need force or weight.
Supporting detail: Addendum 296 — Check the CAD assumptions before trusting mass properties.
Force and weight are separate quantities
Force and weight are separate quantities
Force is a push or pull. For constant mass, Newton’s second law is
Fnet = ma. Weight is one particular force: the force due
to gravity, written W = mg.
Fnet
Net force, in newtons (N) or pound force
(lbf). It is the combined force that produces acceleration.
W
Weight, a gravitational force. Near Earth’s standard gravity,
g0 = 9.80665 m/s2; local gravity can differ slightly.
m
Mass, in kilograms, pound mass, or slugs. It is not measured in newtons or
pound force.
In coherent SI, 1 N = 1 kg · m/s2. In the coherent
foot–slug–second system, 1 lbf = 1 slug · ft/s2. Do not
silently replace lbm with lbf.
Static solved weight example
For a 1,570 kg mass at standard gravity, W = mg = 1,570 kg ×
9.80665 m/s2 = 15,396.44 N, or 15.4 kN. This is a weight
calculation at standard gravity, not a claim that the mass is 15.4 kN.
CAD scale, mass, and weight lab
CAD scale, mass, and weight lab
This model begins with an area and volume in SI units, scales them, then uses
density and gravitational acceleration to show the separate mass and weight results.
Area factor
Volume factor
Scaled area
Scaled volume
Mass
Weight force (N)
Weight force (lbf)
Practice and sources; Practice
Practice and sources
Use the practice bank to apply squared-area conversion and complete-count reasoning.
Supporting detail: Addendum 297 — Sources and engineering context.
Engineering Fundamentals/Motion and Rotation
Angular Motion
Measure rotation in degrees, radians, and revolutions, then use angular velocity and angular acceleration to describe a turning shaft.
Rotation is measured three ways
Rotation is measured three ways
Angular displacement is how far something has turned. Its symbol is
θ (theta), and there are three units in everyday use for it. They measure
the same rotation; they differ only in how much turning counts as one unit.
Revolution (r)
One complete turn. This is what a machine nameplate counts.
Degree (°)
One revolution cut into 360 parts. This is what a drawing and a
protractor use.
Radian (rad)
The angle whose arc is exactly as long as the radius. This is the
SI unit, and it is the one formulas such as v = ωr expect.
A radian is defined by the circle itself, not by a count somebody picked. Swing the
radius around the rim until the arc it traces is as long as the radius, and the angle you have
opened is one radian.
The three units, describing one and the same rotation.
In revolutions
In degrees
In radians
1 r
360°
2π rad = 6.283185 rad
0.5 r
180°
π rad = 3.141593 rad
0.25 r
90°
π/2 rad = 1.570796 rad
≈ 0.159 r
≈ 57.29578°
1 rad
The two factors worth keeping to hand: 1° = 0.01745329 rad and
1 rad = 180°/π = 57.29578°.
The degree sign sits tight against the number —
90°, not 90 °. Every other unit symbol takes a space:
1.57 rad, 45 r/min. The degree, minute, and second of plane angle are
the only exceptions to that rule.
Supporting detail: Addendum 298 — Why a radian is barely a unit at all.
Angular velocity is how fast it turns; Watch out
Angular velocity is how fast it turns
Angular velocity uses the symbol ω (omega), and it is
directed angle change per time interval for rotation about a fixed axis:
ωavg = Δθ / Δt. Instantaneous angular
velocity is the rate at one moment; it equals this average throughout the interval only for
constant angular velocity.
Supporting detail: Addendum 299 — Where 0.1047198 comes from.
Angular acceleration is how fast the turning changes
Angular acceleration is how fast the turning changes
Angular acceleration uses the symbol α (alpha), and it
is change in angular velocity divided by the time it took:
αavg = Δω / Δt
Its SI unit is rad/s2. Everything true of straight-line acceleration on
Acceleration and Squared Time is true here as well: it is a change, so a shaft
slowing down has angular acceleration opposite its angular velocity (negative if it is turning
in the positive direction), and
the squared second means a squared factor whenever the time unit changes.
Worked example: a motor speeding up
A motor shaft is turning at 17 rpm. Power to the motor is increased, and 1.1 s later it is
turning 8 rpm faster. What is the angular acceleration in rad/s2?
Only the change matters, so convert the 8 rpm increase:
8 r/min × 0.1047198 rad/s per r/min = 0.837758 rad/s.
Divide by the time: 0.837758 rad/s ÷ 1.1 s = 0.7616 rad/s2.
0.76 rad/s2, as an average over those 1.1 s. The
starting 17 rpm never enters the calculation — acceleration is built out of the change, not
out of the speed.
Worked example: a spindle running up
A machining-centre spindle goes from rest to 8,000 rpm in 2.5 s.
8,000 r/min × 0.1047198 rad/s per r/min = 837.758 rad/s.
That is the average over the run-up. A drive that ramps gently at each end has
a changing instantaneous angular acceleration inside the same interval, exactly as a linear drive
does.
Sources
Sources
Supporting detail: Addendum 300 — Where these values were checked.
Engineering Fundamentals/Motion and Rotation
Rotation and Linear Speed
Turn a shaft speed into the speed of what it drives, and back again, using the radius - belts, rollers, wheels, and grinding wheels.
The radius is what links turning to travelling; Watch out
The radius is what links turning to travelling
A roller turns; the belt on it travels. A wheel turns; the vehicle moves. The two
speeds are not the same number, and the thing that converts one into the other is the
radius.
v = ωr · a = αr
Here a is the tangential acceleration, not the rim point’s total
acceleration: it also has an inward component ω2r. Belt and
vehicle speeds match rim speed only when there is no slipping.
v
The straight-line speed of a point on the rim — the speed of the belt,
the sheet, the vehicle.
ω
Angular velocity, in radians per second. See
Angular Motion for the conversion from rpm.
r
The radius, in the same length unit you want the answer in.
Rollers and wheels are almost always specified by diameter, so halve it first.
Both of these formulas are only true when the angle is in radians. Feed
them rpm and the answer is wrong by a factor of about 9.55; feed them degrees per second and it
is wrong by a factor of about 57.3. Convert to rad/s first, every time.
Two mistakes account for nearly every wrong answer here: using the diameter where
the radius belongs, and leaving the speed in rpm. Both are worth a deliberate check before the
arithmetic starts.
Supporting detail: Addendum 301 — Why the radian is the only angle unit that works.
Worked example: a conveyor drive roller
Worked example: a conveyor drive roller
A conveyor belt runs over a drive roller 200 mm in diameter, turning at 45 rpm. What is the
belt speed, and how long does a package take to travel 15 m?
Halve the diameter: r = 100 mm = 0.100 m.
Convert the speed: 45 r/min × 0.1047198 rad/s per r/min = 4.712389 rad/s.
Multiply: v = 4.712389 rad/s × 0.100 m = 0.4712 m/s.
Divide the distance by the speed:
15 m ÷ 0.4712389 m/s = 31.83 s.
0.47 m/s, and about 32 s for 15 m. That assumes the belt
does not slip on the roller, which is the assumption a real drive is designed to make true.
Worked example: a roll-forming feed rate
Worked example: a roll-forming feed rate
Forming rolls 150 mm in diameter rotate at 25 rpm. What is the feed rate of the sheet in
m/min, and how long does 20 m of sheet take?
r = 75 mm = 0.075 m.
25 r/min × 0.1047198 rad/s per r/min = 2.617994 rad/s.
v = 2.617994 rad/s × 0.075 m = 0.19635 m/s.
The question asks for metres per minute, so convert the time unit:
0.19635 m/s × 60 s/min = 11.78 m/min.
20 m ÷ 11.78 m/min = 1.70 min, which is about 1 min 42 s.
Note what step 4 did and did not do. Changing seconds to minutes in a speed takes one
factor of 60. If the quantity had been an acceleration, the same change would take
602 — see Acceleration and Squared Time.
Worked example: running the conversion backwards
Worked example: running the conversion backwards
Sometimes the linear quantity is what you know. The formulas simply rearrange:
ω = v/r and α = a/r.
A wheel, from angular to linear
A tyre 28 in in diameter turns at 3.5 rad/s. How fast is the vehicle moving, in miles per hour?
r = 14 in × 0.0254 m/in = 0.3556 m.
v = 3.5 rad/s × 0.3556 m = 1.2446 m/s.
1.2446 m/s ÷ 0.44704 m/s per mph = 2.78 mph.
A wheel, from linear to angular
A vehicle accelerates at 5 m/s2 on tyres 78 cm in diameter. What is the angular
acceleration of a wheel?
r = 39 cm = 0.39 m.
α = 5 m/s2 ÷ 0.39 m = 12.8 rad/s2.
Check the unit on the answer, not just the number. Dividing
m/s2 by m leaves 1/s2, and because
the radian is a ratio of two lengths, rad/s2 is the same thing named for
what it describes.
Rim speed is why wheel size changes the safe rpm; Stop
Rim speed is why wheel size changes the safe rpm
A grinding wheel is limited by how fast its rim moves, not by how fast its centre
turns. Put a bigger wheel on the same spindle at the same rpm and the rim goes faster, because
every point on it travels a longer circle in the same time.
Take a wheel whose rim speed must stay at or below 35 m/s:
Same 35 m/s rim-speed limit, two wheel sizes.
Wheel diameter
Radius
ω = v/r
Same speed in rpm
200 mm
0.100 m
350 rad/s
3,342 rpm
250 mm
0.125 m
280 rad/s
2,674 rpm
The larger wheel has to run slower, by about 670 rpm, to keep the same rim
speed. Nothing about the machine changed; only the radius did.
Do not calculate your way to a grinding-wheel speed. The number that governs
is the maximum operating speed marked on the wheel, and OSHA requires that the
spindle speed of the machine be checked before a wheel is mounted, to be certain it
does not exceed that marking (29 CFR 1910.215(d)(1)). The arithmetic
above explains why a bigger wheel is marked slower. It does not authorise a wheel, and
it is not a substitute for reading the wheel. See Machine Hazards and Housekeeping.
Sources
Sources
Supporting detail: Addendum 302 — Where these values were checked.
Engineering Fundamentals/Force and Power
Torque
Turning effort is force times radius - how to calculate it, which unit belongs to it, and why the order of the two words is not decoration.
Torque is force applied at a radius; Watch out
Torque is force applied at a radius
A force pushes. A torque turns. The same force produces more
torque the further it acts from the axis of rotation, which is why a longer wrench loosens a
tighter nut with the same pull.
The force acts at right angles to the radius. Everything below assumes that; a force
pointing partly along the radius contributes only the part of it that is perpendicular.
r is the radius, measured from the axis of rotation to where the force acts.
Pulleys, rollers, and wheels are specified by diameter, so halve the number on the drawing
before it goes into this formula.
Note: when a turning effort is described about an axis rather
than about a shaft, it is often called a moment and given the symbol
M. It is the same calculation.
The unit, and the word order that identifies it
The unit, and the word order that identifies it
Torque units and rounded conversion factors between them.
System
Unit
Symbol
Conversion
SI
newton metre
N·m
1 N·m = 0.7375621 lbf·ft
Foot–slug–second
pound-force foot
lbf·ft
1 lbf·ft = 1.355818 N·m
Case matters, and this one bites. The SI torque unit is
N·m with a lower-case m. Written N·M it is not a valid SI torque unit: M is the
prefix for 106, but a prefix cannot stand alone as a unit. The same trap catches Kg for kg and S for
s. See Measurement Language.
Here torque is written lbf·ft; energy is written ft·lbf.
The same two units, the same numerical factor, written in the opposite order — and NIST
prints them that way round on purpose: pound-force foot converts to the newton metre, foot
pound-force converts to the joule. They are different physical quantities that happen to share
a unit combination. Word order is a convention, not a mathematical distinction; use the
quantity and context to tell them apart. SI avoids the ambiguity by giving energy its own name, the joule; a torque is never
written in joules. See Work and Energy.
Worked example: can the motor hold the arm up?
Worked example: can the motor hold the arm up?
A robot-arm joint motor produces 15 N·m. The arm segment is 0.35 m long and carries a
25 N load at its end. Will the motor hold the arm horizontal?
The load acts straight down, at right angles to a horizontal arm, at the full 0.35 m:
τ = 0.35 m × 25 N = 8.75 N·m.
Compare with what the motor produces:
8.75 N·m < 15 N·m.
Yes, with 6.25 N·m to spare — for the load
alone. The weight of the arm segment itself also produces a torque about the joint, and no
mass was given for it, so this answer is a partial one. In a real selection you would add the arm
weight acting at its own centre of mass, then keep margin on top of that.
This is the shape of most torque questions: work out what the load demands, then check it
against what the drive can supply, and be explicit about what you have left out.
Worked example: torque from a tangential force
Worked example: torque from a tangential force
A wheel 250 mm in diameter needs 3.5 kN of tangential force to overcome resistance. What torque
must the motor supply to the axle?
r = 125 mm = 0.125 m.
3.5 kN = 3,500 N.
τ = 0.125 m × 3,500 N = 437.5 N·m.
The same formula, rearranged
When the torque is what you know and the force is what you want,
F = τ/r. That single rearrangement explains a family of everyday machines: a
longer wrench, a bigger steering wheel, and a larger pulley all trade radius against force. Double
the radius and the same torque delivers half the force — and, at the same rotational speed,
the rim travels twice as far, which is why Power and Efficiency comes out unchanged.
Sources
Sources
Supporting detail: Addendum 303 — Where these values were checked.
Engineering Fundamentals/Force and Power
Work and Energy
Force moving through a distance is work - the joule, the foot pound-force, and why an energy unit reads backwards from a torque unit.
Work is a force moving something through a distance
Work is a force moving something through a distance
Holding a heavy box still is exhausting, and in this sense it is zero work. Work
needs a component of force along the displacement; work is negative when that component
opposes the movement.
W = Fs — work equals force times displacement for a constant force parallel to the motion.
Work is one of the ways energy moves from one place to another, so it is measured in energy
units and is often written E when what matters is the energy delivered rather than
the act of delivering it.
The two systems, for work and every other form of energy.
System
Unit
Symbol
Built from
SI
joule
J
1 J = 1 N·m
Foot–slug–second
foot pound-force
ft·lbf
1 ft·lbf = 1.355818 J
Worked example: lifting a load
How much work is required to lift a 2,000 lb load to a height of 10 ft?
The force needed to lift steadily is the load’s weight, 2,000 lbf, and it acts
straight up along the 10 ft of travel.
W = 2,000 lbf × 10 ft = 20,000 ft·lbf.
In SI: 20,000 ft·lbf × 1.355818 J per ft·lbf = 27,116 J, or
27.1 kJ.
Two things this calculation assumes, both worth saying out loud: the load is
raised at a steady speed, so no extra force goes into accelerating it, and the 2,000 lb figure is
a weight in pound-force, not a mass in pound-mass. On
Geometry, Mass, and Force those are separate quantities, and here it is the force that belongs
in the formula.
Work and torque share dimensions - word order is a convention; Watch out
Work and torque share dimensions - word order is a convention
Multiply a constant force by displacement along that force and you get work. Multiply a force by a radius and you get
torque. Both are a force times a length, so in the foot–pound system both come out as some
arrangement of feet and pounds-force.
Here torque is written lbf·ft. Energy is written
ft·lbf. The numerical factor is identical — 1.355818 of
either — but word order alone does not establish the physical quantity. Torque describes turning
effort; work describes energy transferred through displacement.
SI removes the ambiguity by naming the energy unit separately. A torque stays
N·m; energy becomes the joule. Numerically
1 J = 1 N·m, but a torque is never reported in joules. See Torque.
Supporting detail: Addendum 304 — Turning a torque into work, and where the radian goes.
The energy units you will actually meet
The energy units you will actually meet
Energy is billed, rated, and specified in a lot of different units. They all convert; the only
work is knowing which one a number is in.
Common energy units, expressed in joules.
Unit
Symbol
In joules
Where it turns up
joule
J
1 J
The SI unit. Everything else converts to it.
foot pound-force
ft·lbf
1.355818 J
U.S. mechanical work and energy.
watt hour
W·h
3,600 J (exact)
Battery capacity.
kilowatt hour
kW·h
3,600,000 J (exact)
The line on an electricity bill.
British thermal unit (IT)
BtuIT
1,055.056 J
Heating, cooling, and fuel ratings.
horsepower hour
hp·h
≈ 2,684,520 J
Engine and drive energy.
calorie (IT)
calIT
4.1868 J (exact)
Thermal work and material data.
A kilowatt hour is a power multiplied by a time, and that is all it is. One
kilowatt sustained for one hour. It is not an SI unit — NIST lists it among the units to
be converted into SI — but it is exactly 3.6 MJ, and it is the unit an electricity
meter counts in.
“Btu” on its own is ambiguous. NIST lists six
different British thermal units, from 1,054.35 J to 1,059.67 J depending on which definition is
meant. The spread is about half a percent, which is small until it is multiplied by a fuel bill.
Use BtuIT unless a specification names another one.
Sources
Sources
Supporting detail: Addendum 305 — Where these values were checked.
Engineering Fundamentals/Force and Power
Power and Efficiency
Power is work per unit time - three equivalent ways to calculate it, the horsepower conversions, and what an efficiency figure can and cannot be.
Power is how fast work gets done
Power is how fast work gets done
Two hoists that lift the same load to the same height do the same
work. The one that does it in half the time needs twice the power.
P = W / t — average power equals work divided by elapsed time.
The two power units and the factors between them.
System
Unit
Symbol
Definition and conversion
SI
watt
W
1 W = 1 J/s; 1 W = 0.001341022 hp
Foot–slug–second
horsepower
hp
1 hp = 550 ft·lbf/s; 1 hp = 745.6999 W
The symbol W does double duty: upright W after a number
is the watt, while W standing in a formula for a quantity is usually work. Context
separates them: P = W/t uses W for work, while
1 W = 1 J/s uses it for the watt.
Worked example: powering the lift
On Work and Energy, lifting 2,000 lbf through 10 ft took 20,000 ft·lbf, or 27.1 kJ.
How much power does doing it in 4 s require?
In U.S. units: 20,000 ft·lbf ÷ 4 s = 5,000 ft·lbf/s, and
5,000 ÷ 550 = 9.09 hp.
In SI: 27,116 J ÷ 4 s = 6,779 W, or 6.78 kW.
Cross-check the two: 9.0909 hp × 745.6999 W/hp = 6,779 W. They agree,
which is the point of doing both.
That is the power delivered to the load. A motor sized for this job needs more than that,
because no drive is perfectly efficient.
The same power, three ways to reach it; Watch out
The same power, three ways to reach it
Which form you use depends on what you have been given, not on which is more correct. All three
produce watts in SI. In P = Fv, force and velocity must be parallel;
otherwise use the force component along the velocity.
Three routes to a power, in each system.
Form
SI
Foot–pound
Work over time P = W/t
J/s = W
(ft·lbf/s) ÷ 550 = hp
Force times speed P = Fv
N × (m/s) = W
(lbf × ft/s) ÷ 550 = hp
Torque times angular velocity P = τω
(N·m) × (rad/s) = W
(lbf·ft × rad/s) ÷ 550 = hp
In the third form the angular velocity must be in rad/s. An rpm figure
substituted directly is wrong by a factor of about 9.55. Convert it first —
Angular Motion.
The divisor 550 is not a fudge factor. One horsepower is defined as 550 pound-force
feet of work per second, so dividing by 550 is simply converting the unit.
Two shortcut formulas, and the conditions attached to them
Two shortcut formulas, and the conditions attached to them
These two save a lot of arithmetic in practice. Both are unit conversions with an assumption
hidden inside.
From volts and amps
hp = (volts × amps) ÷ 746
The 746 is exact: NIST defines a separate unit, horsepower (electric), as 746 W. So
the formula is really two steps — find the electrical power in watts, then convert watts to
horsepower.
The hidden condition is in the first step. Volts times amps gives real power
in watts for a direct-current circuit or a purely resistive load. For single-phase AC, RMS volts times RMS amps
gives apparent power, in volt-amperes; the real power in watts is that multiplied by
the power factor, the ratio of real power to apparent power. Use the shortcut
on an AC motor without its power factor and the answer comes out high. See
Current, Voltage, and Resistance.
From torque and rpm
hp = (torque in lbf·in × speed in rpm) ÷ 63,025
This one is the P = τω row above, with the rpm-to-rad/s conversion and
the inch-to-foot conversion already folded into the constant. It only works with the torque in
pound-force inches and the speed in rpm; feed it
lbf·ft and the answer is twelve times too small.
Supporting detail: Addendum 306 — Where 63,025 comes from.
Efficiency is the fraction that makes it through; Watch out
Efficiency is the fraction that makes it through
The efficiency of a machine is the ratio of useful output to total input. Its
symbol is η (eta), and it can be written with either power or work as long as
both sides of the ratio use the same one:
η = Pout / Pin ·
η = Wout / Win
It is a ratio of two like quantities, so the units cancel: efficiency is a plain number, usually
quoted as a percentage.
For a real machine in steady operation, η < 1; the ideal lossless limit is 1. You cannot get more power out than you
put in, and some of every input always leaves as heat, noise, or friction rather than as useful
output. A calculated efficiency above 1 means an error in the numbers, not a remarkable
machine.
Worked example: an electric hoist motor
A motor consumes 500 W and applies 1,000 N of force to lift an object at 0.45 m/s. What is the
efficiency of the system?
Useful output, using P = Fv:
1,000 N × 0.45 m/s = 450 W.
η = 450 W ÷ 500 W = 0.90, or 90%.
The missing 50 W has not vanished. It is power lost rather than delivered to the load, typically as heat in the motor and drive.
Worked example: follow power through two stages
A hypothetical steady system receives 100 W. Stage 1 is given as 80% efficient, and Stage 2
is given as 90% efficient. Each percentage applies to the power entering that stage.
Useful power continues across the top. Each loss branches at the boundary where it occurs.
Stage 1 output: 100 W × 0.80 = 80 W. Stage 1 loss:
100 W − 80 W = 20 W.
Stage 2 receives 80 W, not the original 100 W. Its output is
80 W × 0.90 = 72 W. Its loss is 80 W − 72 W = 8 W.
Overall efficiency: 72 W / 100 W = 0.72, or 72%. Equivalently,
0.80 × 0.90 = 0.72.
Total accounted loss: 20 W + 8 W = 28 W. Check the boundary:
72 W useful + 28 W loss = 100 W input.
Do not add 20% + 10% and call the system 70% efficient. The 20% loss is
measured from 100 W, while the 10% loss is measured from the 80 W that reaches Stage 2. Watts may be added here
because 20 W and 8 W are amounts of power accounted across the same overall boundary.
Work backward when the required output is known: Stage 2 needs 72 W / 0.90 = 80 W at its input,
and Stage 1 needs 80 W / 0.80 = 100 W. The same result comes from
72 W / 0.72 = 100 W. Use Gear Ratios to explore the same multiplication idea for
stated per-mesh losses.
These are given, illustrative constant efficiencies at steady operation with no changing stored
energy. They are not a motor performance prediction. The accounted losses leave the useful-flow path rather than
disappearing; this example does not predict their temperature or physical mechanism.
Efficiency figures are only comparable when the boundary is the same. A
motor efficiency, a drive efficiency, and a system efficiency measured
from the wall socket to the load are three different numbers for the same machine, and the largest
of them is the one a datasheet prefers to print. Say which one you mean.
Sources
Sources
Supporting detail: Addendum 307 — Where these values were checked.
Engineering Fundamentals/Power Transmission
Belt, Chain and Gear Drives
Choose a drive by shaft spacing, timing, speed and environment, then check its load rating and maintenance needs.
Three ways to carry rotation from one shaft to another
Three ways to carry rotation from one shaft to another
A drive transfers motion and turning effort from a driver to a driven shaft. Belts and chains bridge a gap. Gears engage directly and fit into a compact housing. Start with the job the drive must do, then choose the parts.
Three transmission paths, drawn schematically. A belt or chain lets the shafts sit farther apart without adding an intermediate shaft.
Gears, chains and timing belts are positive drives: engagement maintains a tooth-count ratio without ordinary frictional slip. Flat and V-belts are friction drives: their grip depends on friction and tension, so slip can change the speed ratio.
Positive engagement does not mean perfect positioning. Tooth clearance, elastic deflection and chain speed ripple still matter. For ratios, compound trains and losses, use Gear Ratios. For turning effort and power, use Torque and Power and Efficiency.
Choose a shaft arrangement, a timing requirement, a speed range and an environment. Change one requirement at a time and watch which reason changes. “Close” allows a compact gear mesh; “separated” needs a flexible span. These are qualitative screening rules, not a component sizing tool.
Try this on paper: two separated parallel shafts must stay synchronized in a clean, lubricant-sensitive area. A timing belt is a useful starting candidate: its teeth maintain timing and the belt mesh needs no oil. Flat and V-belts cannot guarantee timing. An ordinary chain needs lubrication; a single gear pair cannot bridge the chosen gap without making the gears much larger.
Now remove the timing requirement: flat or V-belts become candidates. Bring the shafts close together inside a lubricated housing: gears become candidates. Each change removes a different constraint.
Compare timing, space and upkeep side by side
Compare timing, space and upkeep side by side
Typical tendencies for correctly selected industrial drives; actual ratings come from the chosen product.
Question
Flat / V-belt
Timing belt
Roller chain
Gear pair
Center distance
Useful across separated shafts
Useful across separated shafts; check available lengths
Useful across separated shafts; manage slack
Close shafts; size and mesh set spacing
Slip and timing
Can slip; unsuitable for fixed timing
Positive; matched teeth engage
Positive average ratio; clearance and speed ripple remain
Positive ratio; backlash matters on reversal
Noise
Usually quiet; absorbs vibration
Often quiet, but tooth engagement can make noise
Link engagement becomes noisier at speed
Spur teeth can whine; helical engagement is smoother
Lubrication
Belt contact runs dry
Belt contact runs dry
Ordinary chain needs lubricant at its joints
Most loaded metal gears need lubrication
Cost
Often low initial cost
Matched toothed parts usually cost more than basic friction belts
Include sprockets, lubrication and replacement
Precision gears, bearings and housing can raise initial cost
Check oil/grease, seals, tooth condition and alignment
Belt contact running dry does not mean the shaft bearings need no lubrication. A sealed gearbox can keep lubricant away from a product; an exposed chain generally cannot. Special materials and lubrication-free products need their own ratings.
Turn a shortlist into a rated drive; Checklist; Practice
Turn a shortlist into a rated drive
Record shaft directions, center distance, available space and adjustment travel.
Specify input speed, required output speed, power and torque, including starts and shock loads.
Decide whether the job needs synchronized motion, low noise or accurate reversal.
Check temperature, abrasive dust, water and chemicals against the material and lubricant ratings.
Use the manufacturer's selection procedure to check size, service factor, wrap or tooth engagement, shaft loads and bearings.
Plan inspection access, replacement parts, lubrication and the total cost over the drive's life.
A bigger pitch is not a complete strength rating. Width, material, speed, tooth count and duty also matter. A drive that fits the space can still fail the load check.
Supporting detail: Addendum 308 — What the explorer assumes, and where to check a selection.
Engineering Fundamentals/Power Transmission
Belt Drives
Distinguish friction belts from timing belts, read belt and pulley terminology, and recognize common wear patterns.
Flat and V-belts grip; timing belts engage teeth
Flat and V-belts grip; timing belts engage teeth
Flat belt
A broad, flat band transmits force through friction against a pulley. Useful for smooth, quiet motion and long spans when the drive is designed for them. Tracking and tension matter.
V-belt
A trapezoidal section runs in a matching V-groove. Contact at the sides gives a wedging action that increases grip. The belt should not rely on rubbing the bottom of the groove.
Timing / synchronous belt
Teeth on the belt engage matching grooves in the pulleys. Load is carried by this engagement, so the drive keeps its tooth-count ratio without frictional slip in normal operation.
Contact shape determines how force crosses from pulley to belt. Sketches show the principle, not a manufacturing profile.
Timing does not come from extra tension. It comes from matching teeth. An undertensioned or overloaded timing belt can jump teeth or strip them; that is a fault, not its normal way of transmitting power. A notched V-belt remains a friction belt: relief notches for bending do not make it a timing belt.
Belt contact transfers load at the pulley rim; the pulley still needs a connection to its shaft. For a keyed pulley, follow the torque path through the key and hub. Other pulley mountings use different connections.
Read length, tension and wrap before ordering
Read length, tension and wrap before ordering
Pulley / sheave
The wheel that carries a belt. “Sheave” is commonly used for a grooved belt pulley. A timing pulley has matching tooth grooves.
Pitch and pitch length
Timing-belt pitch is the spacing between adjacent tooth centers along the pitch line. Pitch length is the loop length along that reference line, near the tensile cords. It is not the outside circumference. Match pitch and tooth profile to the pulley.
Tension
The pulling force along the belt. The difference between the loaded and return spans transmits torque. Installation tension keeps the belt seated; too little encourages slip or tooth jumping, and too much loads belts and bearings.
Wrap angle
The angle through which the belt contacts a pulley. Less wrap gives a friction belt less contact and a timing belt fewer teeth in engagement. Check the smaller pulley in particular.
Catalogs may specify inside, outside, datum, effective or pitch lengths. Use the length convention and measuring method for that belt family; do not substitute a tape measurement of the outside for the catalog value.
One-stage reminder: nout = nin × Ddriver / Ddriven using matching effective/pitch diameters and assuming no slip. For timing belts, use tooth counts N in place of diameters. Write the reduction as i:1, where i = input speed / output speed. Follow Gear Ratios for the ratio method and Rotation and Linear Speed for belt linear speed.
Here N means teeth and n means rotational speed. Some class slides use n for teeth and ω for angular speed; check the quantity, not just the letter.
Choose a belt for the load and environment
Choose a belt for the load and environment
Belts can span separated shafts, soften vibration and avoid oil at the transmission contact. Flat and V-belts suit jobs where a small speed variation is acceptable. Choose a timing belt when the shafts must stay synchronized. Compare the alternatives in Belt, Chain and Gear Drives.
Check belt section or tooth profile, width, minimum pulley size, available length, wrap, power rating, temperature and chemical compatibility. There is no single maximum speed or temperature range for every belt. Reinforcement cords limit stretch, but the belt still needs correct alignment and installation tension.
Some specially designed flat-belt layouts connect nonparallel shafts. That does not make misalignment acceptable in an ordinary V-belt or timing-belt installation. Frictional slip may soften an overload, but it can also generate heat and destroy the belt; it is not a guaranteed overload-protection device.
Use the wear pattern to find the cause; Practice
Use the wear pattern to find the cause
Fault clues to investigate with the drive safely isolated.
Symptom
Possible cause to check
Squeal, glazing or excess heat on a friction belt
Low tension, overload, contamination or worn pulley grooves can reduce grip.
Frayed edges or the belt tracking to one side
Pulley alignment, damaged flanges and shaft movement.
Cracks or hardening
Age, heat, chemical attack or repeated bending around an unsuitable pulley.
Missing timing-belt teeth or lost timing
Overload, inadequate tension, poor engagement, debris or worn pulleys.
Inspect the pulleys as well as the belt. Replacing the worn part without fixing its cause often repeats the failure. Follow the product's tension and inspection instructions; use Equipment Operating Procedure before touching the drive.
Supporting detail: Addendum 309 — Manufacturer references for belt geometry and faults.
Explore how pulley size and spacing change belt length and wrap; Interactive; Practice
Explore how pulley size and spacing change belt length and wrap
Use pitch diameters D (large) and d (small), and center distance C in one length unit. For an open belt, the approximate pitch length is L ≈ 2C + π(D + d)/2 + (D − d)²/(4C). The last term is the correction for unequal pulleys. Increasing C increases length and brings small-pulley wrap closer to 180°; the no-slip speed ratio stays D/d.
Real belts come in standard lengths from the manufacturer's catalog. Pick the nearest stock length in the correct length convention, then use “Enter L → find C” to estimate the required shaft spacing. These calculations do not set installation tension or replace the manufacturer's selection procedure.
Open belt: D = 200, d = 100 mm; n_small = 1200 r/min
Belt pitch length L (approx., mm)
1277.49
Center distance C (mm)
400
Speed ratio n_small / n_large
2
Large-pulley speed (r/min)
600
Belt speed (m/min)
376.991
Small-pulley wrap (degrees)
165.638
Unequal-pulley correction (mm)
6.25
Less wrap means less grip for a friction belt and fewer teeth engaged for a timing belt. This geometry model does not rate load capacity.
Worked example: D = 200 mm, d = 100 mm, C = 400 mm and n_small = 1200 r/min. L ≈ 800 + 150π + 6.25 = 1277.49 mm. The inverse returns C ≈ 400 mm. Ratio = 2; n_large = 600 r/min; v = π × 100 × 1200 / 1000 ≈ 376.99 m/min; wrap ≈ 165.64°.
Supporting detail: Addendum 310 — Derive the inverse and check speed and wrap.
Recognize chain components, decode ANSI pitch numbers, and distinguish ISO chain series before choosing sprockets.
Sprocket teeth engage a chain of moving joints
Sprocket teeth engage a chain of moving joints
A chain drive is a positive drive: sprocket teeth engage the chain instead of relying on frictional grip. It can bridge separated shafts and carry substantial load, but its joints and sprockets need attention.
Pitch, p
The center-to-center distance between adjacent chain pins. A chain's pitch must match its sprocket.
Roller
A sleeve that turns around a bush as it contacts a sprocket tooth. Some small chains are bush chains and have no separate roller.
Link
A connecting unit of the chain. Ordinary roller chain alternates inner links, carrying bushes and rollers, with outer links, carrying pins and side plates.
Sprocket
The toothed wheel that engages the chain. Tooth count sets the speed relationship; tooth shape and width must suit the chain series.
Master / connecting link
The link used to join the ends into a loop. Use the specified type and installation method; retention and strength depend on the product.
Pitch measures joint spacing, not roller diameter or the length of two links together. Side view is simplified; the pin sits inside the bush and roller.
The chain engages the sprocket teeth, but torque must also pass between each driven or driving sprocket and its shaft. A keyed sprocket uses a key between the shaft and hub; tooth engagement alone does not explain that connection.
Read #25, #35 and #40 as pitch codes
Read #25, #35 and #40 as pitch codes
For the common ANSI short-pitch chain numbers here, remove the final digit of the base number and divide the remaining number by 8 to get pitch in inches. Thus #40 uses 4/8 in, not 40/8 in. #100 uses 10/8 in.
Common ANSI designation examples, checked against Tsubaki's chain guide and sprocket catalog.
Base number
Pitch calculation
Pitch
Construction clue
#25
2/8 in
0.250 in = 6.35 mm
Final 5: bush chain, no separate rollers
#35
3/8 in
0.375 in = 9.525 mm
Final 5: bush chain, no separate rollers
#40
4/8 in
0.500 in = 12.70 mm
Final 0: roller chain
#41
4/8 in
0.500 in = 12.70 mm
Narrow variation; not identical to #40
#100
10/8 in
1.250 in = 31.75 mm
Two digits remain before dividing by 8
A suffix such as -1 or -2 counts parallel strands: simplex or duplex. #40-2 still has a 0.500 in pitch. Heavy-series suffixes and manufacturer prefixes carry other information; do not apply the pitch shortcut to every chain product code.
Supporting detail: Addendum 311 — Checked public wording behind the ANSI numbers.
“Metric chain” still needs a series and a pitch
“Metric chain” still needs a series and a pitch
ISO chain data are commonly tabulated in millimeters. That does not make every pitch a whole number of millimeters. ISO 606 covers both A-series chains derived from American practice and B-series chains derived from European practice.
Selected B-series simplex chains from Renold's public tables.
Designation
Pitch
05B-1
8.000 mm
06B-1
9.525 mm
08B-1
12.700 mm
10B-1
15.875 mm
The common 06B, 08B and 10B sizes correspond to 6/16, 8/16 and 10/16 in pitch. Use the table for the exact designation: small sizes such as 05B do not follow that shortcut. B identifies the series; -1 identifies one strand.
Same pitch does not mean interchangeable. #40 and 08B both have 12.7 mm pitch, but roller diameter and inner width differ. Check series, pitch, width, roller diameter and strand count when matching a sprocket or replacement link.
Supporting detail: Addendum 312 — ISO scope and the source of the millimeter dimensions.
Positive engagement still permits wear and speed ripple; Practice
Positive engagement still permits wear and speed ripple
Chain is worth considering when separated shafts need a fixed average ratio and lubricant and noise are acceptable. Select it for the actual power, speed, starts, shock loads and environment. Tensile breaking strength is not an allowable continuous working load.
One-stage reminder: nout = nin × Ndriver / Ndriven; reduction i = Ndriven / Ndriver, written i:1. N counts teeth and n is rotational speed. For the reasoning and further stages, use Gear Ratios.
The chain wraps a sprocket as a series of straight links, forming a polygon rather than a perfectly smooth circle. This chordal action produces speed ripple, especially with small sprockets. Backlash and elastic stretch also limit precise positioning, even without ordinary slip.
Wear elongation: pin/bush wear increases joint clearance and measured chain length. The worn chain rides poorly on sprocket teeth and can jump. Take-up removes slack; it does not restore worn joints.
Stiff or seized joints: check lubrication reaching the joints, contamination and corrosion.
Fractured plates or pins: investigate fatigue, overload, misalignment and connecting-link installation.
Hooked or uneven sprocket teeth: inspect the chain and sprockets together and follow replacement limits for that drive.
Use the specified lubricant, alignment and slack. A chain is not installed taut like a belt. Set inspection intervals and wear limits from the maker's guide; isolate the drive before measuring or servicing it. See Equipment Operating Procedure.
Supporting detail: Addendum 313 — Chain selection and maintenance reference.
Few sprocket teeth make the chain surge and bob; Interactive
Few sprocket teeth make the chain surge and bob
A chain can bend only at its pins, so it wraps a sprocket as a polygon with one side per tooth. Even at a perfectly steady sprocket speed, the chain leaving that polygon speeds up and slows down once per tooth, and the span rises and falls with it. Predict how much, then turn the sprocket and watch.
Pin at the top: the leaving span sits at the full pitch radius R and moves at ωR, its fastest.Two pins straddle the top: the span leaves from a flat of the polygon at R cos(180°/N) and moves at ωR cos(180°/N), its slowest.
Pitch radiusR = p / (2 sin(180°/N))
Speed rangeωR cos(180°/N) ≤ v ≤ ωR
Ripple(vmax − vmin) / vmax = 1 − cos(180°/N)
Span riseR (1 − cos(180°/N))
Worked example: #40 chain (p = 12.7 mm) on a 9-tooth sprocket at 120 r/min. R = 12.7 / (2 sin 20°) = 18.57 mm. ω = 120 × 2π / 60 = 12.57 rad/s, so vmax = ωR = 0.233 m/s and vmin = ωR cos 20° = 0.219 m/s. Ripple = 1 − cos 20° = 6.03 %; the span rises and falls 1.12 mm, once per tooth: 18 times a second. With 21 teeth the same chain and speed give 1.12 % and 0.476 mm.
Three teeth of rotation. Each pulse is one tooth: the speed peaks when a pin passes the top and dips at the hand-over between pins. More teeth make a shallower, more frequent pulse.
Chordal speed variation by tooth count. Rise is for p = 12.7 mm (#40); ripple percentages do not depend on pitch or speed.
Teeth N
R / p
Ripple (vmax − vmin) / vmax
Same spread ÷ average speed
Span rise (mm)
6
1
13.40 %
14.03 %
1.7
8
1.307
7.61 %
7.81 %
1.26
9
1.462
6.03 %
6.15 %
1.12
10
1.618
4.89 %
4.98 %
1.01
12
1.932
3.41 %
3.45 %
0.836
15
2.405
2.19 %
2.20 %
0.667
17
2.721
1.70 %
1.71 %
0.588
19
3.038
1.36 %
1.37 %
0.526
21
3.355
1.12 %
1.12 %
0.476
25
3.989
0.79 %
0.79 %
0.4
30
4.783
0.55 %
0.55 %
0.333
Read the trace: the speed peaks each time a pin passes the top of the sprocket and dips at the hand-over between pins. Chain speed as a fraction of ωR and span height as a fraction of R follow the same curve, cos θ, where θ is the leaving pin's angle from the top. The ripple percentage depends only on the tooth count. Speed and pitch change the size of the numbers, not the percentage.
Supporting detail: Addendum 314 — Where the formulas come from, and what this model leaves out.
Engineering Fundamentals/Power Transmission
Gear Drives and Tooth Geometry
Compare spur and helical gears, identify tooth dimensions, and match pitch and pressure angle before choosing a gear pair.
Gears transmit rotation by direct tooth contact. They make a compact positive drive, but accurate mounting, tooth compatibility and lubrication matter. This page compares external spur and helical gears on parallel shafts.
Spur gear
Teeth run parallel to the shaft. It is comparatively simple to make and produces no axial thrust from the ideal tooth mesh. Engagement can be noisy at higher speed.
Helical gear
Teeth run at a helix angle around the gear. Contact enters progressively across the face and overlapping teeth share load. This generally gives smoother, quieter operation, with added manufacturing cost.
The inclined helical tooth force also pushes along the shaft. That axial thrust needs a suitable bearing arrangement. A spur gear still loads its bearings radially; “no axial thrust” does not mean “no bearing force.”
The driver supplies power. The pinion is the smaller gear in a pair; it can be the driver or the driven member. An idler passes motion between gears and still needs a shaft or other bearing support. Follow Gear Ratios for direction, tooth-count ratios and compound trains.
Tooth contact and shaft attachment are separate connections. Where a gear hub is keyed to its shaft, the key transfers torque at the hub. Check axial retention separately, especially when the tooth mesh produces thrust.
Measure teeth from the pitch circle
Measure teeth from the pitch circle
The pitch circle is a reference, not the outside edge of the gear. The enlarged sector flattens the arcs for clarity; it is not a cutting profile.
Pitch diameter, d
The diameter of the reference pitch circle. In a standard unshifted pair at its standard center distance, the pitch circles roll together without slipping.
Module, m
Metric tooth size: m = d/N, with d in millimeters and N teeth. Larger module means larger teeth.
Diametral pitch, Pd
Inch-based tooth size: Pd = N/d, with d in inches. More teeth per inch of pitch diameter means smaller teeth. Do not confuse it with circular pitch, the distance along the pitch circle between successive teeth.
Pressure angle, α
The angle between the line of action (the contact-force direction, neglecting friction) and the common tangent to the pitch circles at the pitch point. It describes tooth geometry, not the helix angle.
Addendum / dedendum
Radial tooth height from pitch circle to tip / radial depth from pitch circle to root. Neither is a diameter difference by itself.
Backlash
Clearance between mating tooth flanks. It allows clearance in the mesh but creates lost motion when the load reverses.
Supporting detail: Addendum 315 — Check the size definitions with one gear.
Matching pitch is necessary, but not sufficient
Matching pitch is necessary, but not sufficient
Ordinary spur gears intended to mesh must share module or diametral pitch and pressure angle. Matching outside diameter or tooth count does not establish compatibility. Check the tooth system, center distance, clearance and manufacturer's mating information too.
For external helical gears on parallel shafts, match tooth size, pressure angle and helix angle. Use one right-hand and one left-hand gear (teeth slanting in opposite directions), and confirm the manufacturer's mating specification. Equal tooth counts are not required.
Supporting detail: Addendum 316 — Normal and transverse measurements use different planes.
A larger tooth size can support more load when other conditions are comparable, but pitch alone cannot determine capacity, backlash or achievable reduction. Material, face width, heat treatment, alignment and speed remain part of the design.
Supporting detail: Addendum 317 — Primary references for the geometry and helical mesh.
Gear damage tells you where the load went
Gear damage tells you where the load went
Choose gears for compact packaging, a positive ratio and a supported shaft arrangement. Choose helical teeth when smoothness and noise justify their cost and thrust bearings. Check tooth bending strength, surface durability, speed, lubricant, seals and bearing loads before approving a pair.
Common gear faults and conditions to investigate.
Damage
What to check
Scoring or scuffing: streaked, torn tooth surfaces
Lubricant supply and type, excess temperature, contamination and load.
Broken tooth or root crack
Overload, repeated bending fatigue, impact and material condition.
Pitting / spalling: small pits or flakes leaving the surface
Repeated contact stress, lubrication and local load concentration.
Wear concentrated at one edge
Shaft/bearing alignment, deflection and tooth contact pattern.
A symptom is a clue, not a unique diagnosis. Correct the cause before replacing parts. Most loaded metal gear sets need a controlled lubricant supply; some specially selected materials can run dry. Follow the product data and Equipment Operating Procedure for access.
Choose a thread form for the load, read an inch or metric callout, and identify which way a screw advances.
A fastener holds parts together; a power screw moves a load
A fastener holds parts together; a power screw moves a load
A thread is a ridge wrapped around a cylinder. A matching internal thread in a nut follows that ridge. Relative rotation can produce straight-line travel along the screw's axis.
A machine screw usually holds parts together. A lead screw uses the thread to position or drive a load: a slide, a vise jaw, or a linear actuator. Belts, chains and gears commonly transfer rotation between shafts; a lead screw converts rotation into linear motion. See Lead Screws for the calculations.
Keep four descriptions separate: form is the thread's cross-sectional shape; series selects diameter and pitch combinations; hand determines direction; starts count the separate helices. A helix is the spiral path around the cylinder.
Match the thread form to fastening, repeated travel, or one-way thrust
Match the thread form to fastening, repeated travel, or one-way thrust
Profiles cut through the screw axis. These drawings compare shapes, not manufacturing dimensions. The load-bearing side of a thread is its flank.
Thread-form trade-offs for sliding screw-and-nut contact.
Form and use
What it offers
What it costs
Square: power screws and jacks
High efficiency relative to angled flanks under otherwise comparable conditions.
Difficult, expensive machining; wear adjustment is difficult.
V / machine-screw thread: bolts and fastening screws
Widely available fasteners; mass production by rolling makes standard parts economical.
Flank wedging increases friction, so it is a poor choice for efficient repeated power transmission.
ACME / metric trapezoidal: vises, clamps and linear actuators
Easier machining than square; a broader thread root provides a sturdier profile than a comparable square thread. Split-nut (an adjustable, divided nut) arrangements can take up clearance.
Flank wedging increases friction relative to square. A precision drive screw can cost more than an ordinary stock fastener.
Buttress: heavy axial thrust (push along the screw) predominantly in one axial direction, such as a screw press
A nearly perpendicular working flank limits wedging in the intended load direction; the sloping back supports the thread.
Its strength and efficiency advantages are directional. A special asymmetric profile and matching nut affect manufacturing and cost.
No thread form wins every comparison. Actual strength also depends on diameter, pitch, engaged length, material and the failure being checked. ACME is not automatically stronger than every V thread. Nor does its name guarantee a larger lead. ACME and metric trapezoidal are related forms, not interchangeable parts.
Supporting detail: Addendum 318 — Why the efficiency and strength comparisons need conditions.
No radial wedging (outward force on the nut) does not mean no wear
No radial wedging (outward force on the nut) does not mean no wear
In the ideal square-thread geometry, axial load does not create the outward wedging associated with angled flanks. That reduces a source of radial loading on the nut. The loaded surfaces still slide against each other. Friction, lubrication, materials, load and speed still affect wear.
Wear can increase backlash: clearance that must be taken up after reversing direction before the load moves. An adjustable nut can reduce that clearance; adjustment does not restore lost material or guarantee longer life. Do not infer nut life from the thread profile alone.
Supporting detail: Addendum 319 — Where wear and operating limits enter the selection.
Inch callouts count threads; metric callouts state pitch; Practice
Inch callouts count threads; metric callouts state pitch
Pitch is the axial distance between adjacent thread crests. Inch fastener callouts commonly give threads per inch (TPI), so pitch = 1 / TPI in inches. Metric callouts give pitch directly in millimetres.
Selected callouts transcribed from checked public standard sources; pitches in the last column are calculated.
Callout
Read it as
Pitch
1/4-20 UNC
Nominal diameter 1/4 in; 20 threads per inch; Unified coarse series
1/20 = 0.050 in
1/4-28 UNF
Nominal diameter 1/4 in; 28 threads per inch; Unified fine series
1/28 ≈ 0.03571 in
M6 × 1.0
Metric thread; nominal diameter 6 mm; pitch 1.0 mm
1.0 mm
Fine means a smaller pitch at the same nominal diameter. It does not mean a better-quality thread. Metric threads also have coarse and fine pitch choices. The 6 in M6 is a diameter, not a pitch; the 20 in 1/4-20 is a count per inch, not a lead.
These are basic size-and-pitch callouts, not complete manufacturing specifications. Fit and tolerance information may follow them. A fastener-series label does not tell you the efficiency of a lead screw; for a multiple-start drive, obtain both pitch and starts, or the lead directly.
Supporting detail: Addendum 320 — The exact standard entries used here.
Right-hand and left-hand threads advance in opposite directions
Right-hand and left-hand threads advance in opposite directions
Fix the nut and look along the screw from the end you turn. Clockwise turns a right-hand screw away from you into the nut. The same clockwise rotation moves a left-hand screw toward you. Reverse the rotation and the travel reverses.
Same observer, same rotating member, same clockwise rotation. State all three before assigning a travel direction.
If the screw is held against axial motion and the nut travels instead, the nut moves opposite to the screw travel just described. Handedness changes the direction, not the magnitude of travel per revolution.
Supporting detail: Addendum 321 — Direction reference.
Pitch times starts gives lead. Use lead to convert rpm into travel speed and torque into force, with efficiency applied only to the force conversion.
Pitch is thread spacing; lead is travel per revolution
Pitch is thread spacing; lead is travel per revolution
Lead = pitch × number of starts. This is the distinction to get right before calculating either speed or force.
A start is one continuous helical ridge. A single-start screw has one ridge, so its lead equals its pitch. A triple-start screw has three interleaved ridges: follow one ridge through a full turn and it advances three pitch distances.
Imagine unwrapping the cylindrical surface. Top and bottom are the same angular position one full turn apart. Pitch is measured along the axis between adjacent ridges; lead follows the same ridge through a turn.
At the same pitch, adding starts increases travel per turn. At the same torque it reduces theoretical force. The thread's cross-sectional form and its number of starts are separate choices; see Screw Threads.
Supporting detail: Addendum 322 — Check the definition, not just the label on a catalog.
Multiply rpm by lead to find linear speed
Multiply rpm by lead to find linear speed
For an engaged screw and nut, with the nut restrained from rotating, v = nL. Here n is screw speed in revolutions per minute and L is lead in distance per revolution. The result is distance per minute. Divide by 60 for distance per second.
A triple-start screw with 1.5 mm pitch has L = 1.5 × 3 = 4.5 mm/rev. At 480 rpm, v = 480 × 4.5 = 2,160 mm/min = 36 mm/s.
Do not multiply that speed by efficiency. The teaching rule is: “RPM → velocity is 100% efficient unless the screw is malfunctioning; all efficiency losses are found in the torque → force conversion.” This describes a positive-drive motion relationship, not 100% energy efficiency. It is the same tooth-count principle used in Gear Ratios.
Use the actual screw rpm. If the motor slows under load, the lower rpm gives a lower travel speed. Backlash at reversal and elastic deflection can affect positioning without being an efficiency factor on speed. These calculations describe steady engaged travel, after clearance is taken up. See Rotation and Linear Speed for the general rotation-to-travel connection.
Divide torque times 2π by lead, then apply efficiency
Divide torque times 2π by lead, then apply efficiency
For steady motion driving a resisting axial load, Ftheoretical = 2πT / L and Factual = η × Ftheoretical. Here T is input torque and η (eta) is efficiency written as a decimal: 40% is 0.40.
Make the length in torque match the length in lead.
Torque
Lead for force calculation
Force
N·m
metres per revolution (mm ÷ 1,000)
N
lbf·in (often written lb-in)
inches per revolution
lbf
To find the torque required for a target actual force, rearrange: T = FL / (2πη). For the same load and lead, lower efficiency requires more torque. Keep the efficiency boundary consistent: a whole screw assembly efficiency includes losses in the bearings or collar (a supporting thrust-contact surface) as well as the threads.
Supporting detail: Addendum 323 — Derive the 2π from equal power, or one revolution of work.
Experiment: more starts change speed and force in opposite ways; Interactive
Experiment: more starts change speed and force in opposite ways
Predict first: keep pitch, rpm, torque and efficiency fixed, then change from one start to three. Lead and speed triple; theoretical force falls to one third. The same force ratio holds when efficiency is held fixed.
Static comparison / print example: pitch 2 mm, 300 rpm, torque 1.2 N·m, given efficiency 40%.
Same pitch and input, different starts.
Starts
Lead
Speed
Ideal force
Actual force
1
2 mm/rev
10 mm/s
3,770 N
1,508 N
3
6 mm/rev
30 mm/s
1,257 N
503 N
Changing efficiency to 20% halves each actual force; both speeds stay the same. Real efficiency can change with lead, lubrication and load. Here it is an independent input so the two effects can be studied separately.
Worked actuator: keep inch torque and inch lead together; Practice
Worked actuator: keep inch torque and inch lead together
A single-start ACME actuator has 0.20 in pitch, runs at 900 rpm and receives 12 lbf·in of torque. Its assembly efficiency is given as 60%. Find travel speed and useful axial force.
L = 0.20 × 1 = 0.20 in/rev.
v = 900 × 0.20 = 180 in/min = 3 in/s.
Ftheoretical = 2π × 12 / 0.20 = 376.99 lbf.
Factual = 376.99 × 0.60 ≈ 226 lbf.
The 60% belongs in step 4, not step 2. It is an example input, not an efficiency assigned to every ACME screw.
Worked vise: turn hand force into torque before finding clamp force; Practice
Worked vise: turn hand force into torque before finding clamp force
For an illustrative square-thread vise, a 120 N hand force acts perpendicular to the handle at a radius of 0.18 m from the screw axis. Pitch is 4 mm with one start. Assume a given overall tightening efficiency of 30%; this is not a measured or universal vise efficiency.
Use torque = radius × perpendicular force: T = 0.18 × 120 = 21.6 N·m. Radius is the distance from the axis to the hand, not necessarily the full handle length.
This is a tightening estimate using the supplied efficiency. It is not a vise rating or a prediction of residual force after the hand stops turning. A separate free-travel calculation at 24 rpm gives 24 × 4 / 60 = 1.6 mm/s; the jaws do not continue at that speed through a rigid clamped part.
Choose the motion to allow, identify the load, then compare plain and rolling-element bearings.
A bearing allows useful motion and restrains unwanted motion
A bearing allows useful motion and restrains unwanted motion
A loose rigid part can move in six independent ways: translate along three axes and rotate about those three axes. These are its degrees of freedom. A bearing transfers load to a support while allowing the motion the machine needs, with low friction.
For a rotating shaft, the goal is usually one remaining freedom: rotation about its own axis. Two spaced radial supports resist sideways movement and tilting; axial location stops the shaft walking lengthwise. A single short bearing does not automatically provide that whole constraint system.
Let x run along the shaft. Translation T means movement along an axis; rotation R means turning about it. This is an ideal rigid-body model; real supports deflect and have clearance.
Bearings guide motion; motors and drives supply it. Belt, chain and gear drives load their supporting shafts. See Torque for turning effort and Shaft Support and Axial Adjustment for the complete support arrangement.
Radial load crosses the shaft; thrust acts along it
Radial load crosses the shaft; thrust acts along it
Radial load acts perpendicular to the shaft axis. Axial load, or thrust, acts parallel to it. Combined load has both components. A bearing's orientation and internal geometry determine which it can carry.
Load direction is relative to the shaft, not to the room: a vertical shaft can have a horizontal radial load.
First selection filter, not a load rating. Check the exact catalog design.
Type
Radial load
Axial load
Combined load
Plain journal, without thrust faces
Yes
No intended capacity
Needs a thrust bearing
Plain footstep or thrust collar face
Needs a journal guide
Yes, against the loaded face
With a radial guide
Deep-groove ball
Yes
Both directions, within rating
Yes, within rating
Angular-contact ball or tapered roller, single row
Yes
Primarily one direction
Yes; opposing bearing needed for reverse thrust
Cylindrical roller, NU or N design
Yes
No intended locating duty
Use another bearing for thrust
Pure thrust ball or cylindrical thrust roller
No
Yes; direction depends on arrangement
No
Do not turn “roller” into “radial only,” or “thrust” into a rule for every product bearing that name. Tapered rollers carry combined loads; some spherical roller thrust designs also accept radial load under specified conditions.
Plain and rolling bearings trade friction, upkeep and cost
Plain and rolling bearings trade friction, upkeep and cost
A plain bearing supports sliding surfaces, often with a replaceable sleeve called a bushing. A rolling-element bearing places balls or rollers between rings. “Anti-friction” is a traditional name, not a promise of zero friction.
Compare the operating conditions as well as the purchase price.
Question
Plain bearing
Rolling-element bearing
Starting versus running resistance?
Breakaway friction can exceed running friction. A hydrodynamic film is not fully established at rest.
Often low starting resistance and a smaller start/run difference; seals, grease and preload still matter.
Lubrication and maintenance?
Dry grades may need no added lubricant; oil-fed designs require the specified supply and cleanliness.
Usually grease or oil lubricated. A sealed, prelubricated bearing still has a finite service life.
Speed?
Dry bushings have material-specific speed and pressure limits. Fluid-film bearings can serve high-speed machinery.
Many suit moderate to high speeds; type, size, lubrication and heat limit speed.
Load and cost?
Simple bushings often cost little initially. Capacity depends on size, material, speed and heat removal.
Precision rings and elements add cost. Roller designs often carry more load than ball designs of similar overall size.
Rolling contact generally reduces resistance compared with sliding contact. It does not guarantee higher efficiency than every fluid-film bearing, nor does a cheap bushing guarantee lower lifetime cost. Include lubrication equipment, replacement, downtime and power loss. Bearing losses contribute to Power and Efficiency and the stage efficiencies discussed in Gear Ratios.
Plain bearings differ in both lubrication and load direction
Plain bearings differ in both lubrication and load direction
Dry or self-lubricating
A suitable polymer, composite or lubricant-containing material supplies a low-friction sliding surface. Follow that material's instructions; adding grease is not automatically an improvement.
Hydrodynamic
Relative motion draws lubricant into a converging gap, forming a pressure-supported film. Starts and stops require attention because the running film depends on motion.
Hydrostatic
An external pressure supply supports the load on a fluid film, including at rest while the supply operates. The pump, flow control and loss-of-pressure behavior are part of the system.
Those are lubrication descriptions. Shape answers a different question: a journal surrounds a shaft to carry radial load; a footstep supports axial load at a shaft end; a thrust collar presents an annular face to carry axial load. An assembly can combine a journal and a collar to handle both components.
Rings carry the load; the cage spaces the rolling elements; Practice
Rings carry the load; the cage spaces the rolling elements
Schematic with seals omitted. A raceway is the track on a ring that the rolling elements contact; ring and raceway are not quite the same thing.
The inner ring fits around the shaft; the outer ring fits in the housing. The rolling elements transfer load between their raceways. The cage maintains spacing and guides the elements.
In a common arrangement the inner ring turns with the shaft while the outer ring stays still. The balls spin about their own axes and orbit around the shaft. The rings do not have to rotate in opposite directions.
Balls have idealized point contact; rollers have idealized line contact. Under load these become finite contact patches. The longer roller contact generally supports more load in a similar overall size. Contact angle, not just element shape, determines thrust capability. Thrust ball and roller bearings place their contact geometry to support axial force.
Supporting detail: Addendum 324 — Manufacturer reading for bearing selection.
Recognize the bearing family by its contact geometry; Interactive
Recognize the bearing family by its contact geometry
Choose a family and compare its section with its end view. A radial bearing surrounds the shaft; a thrust bearing places its load-carrying faces across the shaft axis. Ball, straight roller, tapered roller and barrel roller shapes lead to different contact paths.
Fᵣ is radial load; Fₐ is axial load. Arrows show directions, not ratings. Sections omit the cage; end views expose the elements.
Plain journal / bushing
A sleeve supports a sliding shaft surface. Radial load crosses the sleeve. This unflanged journal does not locate the shaft axially. Manufacturer guide.
Plain thrust face
A collar slides against an annular thrust face. The loaded face reacts axial force in one direction. A journal guide supplies the separate radial support. Manufacturer guide.
Deep-groove ball
Deep, nearly circular grooves surround one row of balls. Primarily radial duty, with axial capacity in either direction within the catalog limits. Manufacturer guide.
Angular-contact ball
Offset shoulders give an inclined contact line. A single row carries radial load and thrust in the shown direction. Opposed bearings handle reverse thrust; this is not a preload-setting drawing. Manufacturer guide.
Self-aligning ball
Two ball rows share one spherical outer raceway. The inner assembly can tilt about the bearing centre. Axial capacity is relatively small; allowable misalignment depends on the product and surrounding parts. Manufacturer guide.
Thrust ball
Balls run between grooved washers facing each other. The single-direction arrangement shown carries axial load only. It still needs separate radial guidance. Manufacturer guide.
Cylindrical roller · NU
Straight rollers run parallel to the shaft axis. The NU example has guiding ribs on the outer ring and no inner-ring ribs, allowing axial displacement. Other rib arrangements have different axial duties. Manufacturer guide.
Needle roller · radial
Long, slender rollers give a shallow radial section. This radial example includes both rings. Some needle assemblies run directly on a suitably prepared shaft; a separate thrust-needle arrangement is a different geometry. Manufacturer guide.
Tapered roller
Conical rollers sit between conical raceways. Raceways and roller axes have a common cone apex on the shaft axis. A single row takes radial load plus thrust toward its small end, as drawn; an opposed bearing takes reverse thrust. Manufacturer guide.
Spherical roller
Two rows of barrel rollers share a spherical outer raceway. The curved outer track permits limited self-alignment. The bearing carries radial and bidirectional axial loads within its ratings. Manufacturer guide.
Cylindrical roller thrust
Roller axes point radially across flat washer faces. The single-direction arrangement shown carries axial load, not radial guidance. Compare its radial roller orientation with the shaft-parallel rollers in the NU bearing. Manufacturer guide.
Spherical roller thrust
Inclined barrel rollers meet a spherical housing raceway. Primarily thrust in one direction, with some radial capacity while axial load is present. The spherical raceway permits limited self-alignment; consult the exact design. Manufacturer guide.
These are original schematic sections, not interchangeable catalog parts. Cage details and seals are omitted from the sections to expose the contact geometry. A self-aligning raceway allows a limited tilt; it does not excuse arbitrary misalignment or eliminate the need for a correctly designed support arrangement.
Read the type, dimensions and suffixes in Bearing Designations and Sizes. The type tells you which catalog to consult; the complete designation and catalog row tell you what fits.
A pillow block is a housing arrangement, not another rolling-element shape
A pillow block is a housing arrangement, not another rolling-element shape
The outside casting provides mounting points. Identify the bearing or insert inside it separately.
A pillow or plummer block supports a shaft from a base. A flange-mounted housing attaches around the shaft to a facing support. Different housings can contain different bearing families. For example, NSK Self-Lube units combine a sealed ball-bearing insert with a pillow-block or flanged housing.
Double a ball bearing's load and its basic rating life falls to one eighth; Interactive; Practice
Double a ball bearing's load and its basic rating life falls to one eighth
L10 is the life that 90% of a large group of identical bearings are expected to reach or exceed. It is neither a guaranteed life nor an average. Change one input below and watch the life curve.
Example bearing: C = 14.0 kN, given for this exercise. A real bearing's C comes from its manufacturer's catalog; this example does not represent a catalog part.
Basic rating life: L10 = (C/P)p in millions of revolutions, with p = 3 for balls and p = 10/3 for rollers. C is the basic dynamic load rating; P is the equivalent dynamic load, taken as given here (for pure radial loading in this exercise, P = Fr). Use the same force units for C and P.
At constant speed n in r/min, L10h = L10 × 10⁶/(60 × n) hours. The years conversion assumes a duty schedule you can change; it does not predict calendar aging.
Static worked example (also used for printing).
Example ball bearing: C = 14 kN (given), P = 2 kN, n = 1500 r/min
L10h versus P: logarithmic vertical scale. Equal vertical steps represent equal life ratios. C and speed stay fixed.
Marked points: current 2 kN → 3811 h; double load 4 kN → 476.4 h. Double the load → 1/8 the life.
C/P = 14/2 = 7; L10 = 7³ = 343 million revolutions. L10h = 343 × 10⁶/(60 × 1500) = 3811 h, or 1.906 years at 2000 h/year. At P = 4 kN, L10 = 42.875 million revolutions and L10h = 476.4 h.
Adjusted life factors (a1, aISO), contamination, lubrication and combined-load X/Y factors are beyond this page.
Read a supported bearing code, then use the manufacturer's catalog for its outside diameter, width and full specification.
Read the basic designation before the extra letters
Read the basic designation before the extra letters
A bearing number is a compact description, not a universal sizing formula. Start with the maker and the bearing family. A basic designation identifies a series and bore; prefixes and suffixes add details. The same letters can mean different things in different families or manufacturers' catalogs.
For the ordinary metric deep-groove example 6205, read 6 | (0)2 | 05: type 6 is deep-groove ball; 02 is the dimension series, with width-series 0 omitted in the written number; bore code 05 means 25 mm. The diameter-series digit 2 is not an outside diameter in millimetres.
Width-series digits can be omitted differently: NSK lists 6005 as 6 | (1)0 | 05, and 6305 as 6 | (0)3 | 05. Parentheses here explain the omitted digit; they are not characters to add to an order. See NSK's bearing-series table.
Recognize the geometry first in Bearing Types and Loads. A matching bore alone does not make two bearings interchangeable.
The same bore can come with a different outside diameter and width; Interactive
The same bore can come with a different outside diameter and width
Compare the three catalog rows below. d is the bore, D the outside diameter and B the width. Their 25 mm bores are equal, while their housing and axial-space requirements differ. The picture keeps one scale so that this difference is visible.
All three are single-row deep-groove ball bearings. The bore code is 05 → 25 mm; the other dimensions below are catalog values, not digit arithmetic.
Same 25 mm bore; different NSK catalog envelopes (mm)
NSK 6005: 25 × 47 × 12 mm. The drawing shows only the mounting envelope; it is not an internal construction drawing.NSK 6205: 25 × 52 × 15 mm. The drawing shows only the mounting envelope; it is not an internal construction drawing.NSK 6305: 25 × 62 × 17 mm. The drawing shows only the mounting envelope; it is not an internal construction drawing.
These are nominal boundary dimensions. Shaft and housing fits, shoulder dimensions, corner radii, internal clearance and tolerances still require the complete catalog entry and the application design.
00, 01, 02 and 03 are the bore-code exceptions
00, 01, 02 and 03 are the bore-code exceptions
Ordinary coded metric bores in the system illustrated here
Bore code
Bore d
How it is read
00
10 mm
Special code
01
12 mm
Special code
02
15 mm
Special code
03
17 mm
Special code
04–96
20–480 mm
Code × 5 mm, where this coding system applies
Thus 6202 has a 15 mm bore, not 10 mm; 6205 has a 25 mm bore. This rule supplies only the bore. It does not calculate D or B.
Do not apply it blindly to miniature, inch, letter-coded or special bearings. Slash forms can state the bore directly: NSK gives 63/22 as 22 mm and 230/560 as 560 mm. Its miniature 688 example has an 8 mm bore. NSK excludes double-direction thrust ball bearings from its general 04–96 rule.
Supporting detail: Addendum 325 — Primary references for the bore-code scope.
Series identify a family; the catalog supplies the envelope
Series identify a family; the catalog supplies the envelope
Examples of NSK metric series, not a universal first-digit decoder
A dimension series selects a standardized size family; it is a table key, not a digit-to-millimetres formula. Series examples follow NSK's designation guide. Different types also use different dimension letters. A tapered bearing distinguishes inner-ring width B, outer-ring width C and assembled width T. Thrust catalogs may label axial height T or H: use that manufacturer's diagram rather than substituting B automatically.
Why the axial dimension letter matters: two separately checked catalog examples (mm)
The 15 mm inner-ring width of HR30205J is not its 16.25 mm assembled width. These examples are not added to the three-row deep-groove viewer above. NSK's boundary-dimension diagrams also distinguish radial width from thrust height.
C3 means internal clearance, not accuracy or a loose shaft fit
C3 means internal clearance, not accuracy or a loose shaft fit
Internal clearance is movement between a bearing's rings under the specified measuring conditions. A fit is the relationship between a ring and its shaft or housing seat. A precision class specifies dimensional and running accuracy. These are different quantities; see NSK's explanation of fits and clearance.
Selected NSK suffix meanings in the cited families
Suffix
Meaning
What it does not tell you
ZZ
Shields on both sides of the ball bearing
Not a load rating
DDU
Contact rubber seals on both sides
Not a universal seal code for every maker
VV
Non-contact rubber seals on both sides
Not the same sealing arrangement as DDU
C3
Radial internal clearance greater than CN, for the radial-bearing context shown
Neither a precision class nor a shaft/housing fit
P6
ISO tolerance class 6
Not an internal-clearance group
Prefixes matter too: NSK uses HR for its high-capacity tapered roller series. Read the complete maker-specific designation, including cage and lubrication details where required. Seals and shields affect exclusion of contaminants, friction and speed limits; they do not replace the catalog's load ratings. Sources: NSK TI/E/0111, auxiliary-symbol tables; NSK Bearing Designation Systems, sections 2 and 3.
Locate one end, allow thermal movement at the other, and distinguish end play from preload.
Locate the shaft at one end and allow growth at the other
Locate the shaft at one end and allow growth at the other
In a locating/non-locating arrangement, also called fixed/floating here, both supports carry radial load. The locating support also carries the applied axial load and establishes the shaft's axial position. The non-locating support allows axial movement as the shaft expands relative to the housing.
“Fixed” means axially located, not prevented from rotating. “Floating” means axial travel, not loose radial support.
Location needs a load path from shaft to bearing to housing: shoulders, suitable spacers, nuts, retaining rings or covers can retain the rings. Which end is fixed follows the required position of the driven parts; it is not automatically the left end or the motor end.
The floating end can accommodate movement inside a suitable bearing, such as an NU cylindrical roller bearing, or by controlled sliding of a ring in its seat. Do not loosen an arbitrary fit: see Tolerances and Fits and the bearing maker's mounting guidance.
Supporting detail: Addendum 326 — Why two locating supports can create unwanted load.
Keep shaft support separate from torque transmission. Bearings support the shaft relative to the housing; a keyed shaft-hub connection transfers torque to or from a pulley, sprocket or gear. Securing a hub against sliding along the shaft is a separate assembly requirement.
Heat the shaft and compare free travel with restraint; Interactive
Heat the shaft and compare free travel with restraint
Static comparison: at half the heating range, the shaft wants half the model's maximum free growth. A floating support with sufficient travel accommodates all of it. Two locating supports prevent it. With travel limited to 40%, half-range heating leaves 10% of maximum growth unaccommodated.
The drawing exaggerates growth. Heating level is a relative teaching scale, not a temperature or a material property. The left support and housing stay in place; only the shaft is heated. The dashed outline shows the length the shaft would reach if free. The solid outline shows the ideal constrained length. This model shows incompatible motion, not a binding force, stress or safe operating limit.
End play is free movement; preload is an initial internal load
End play is free movement; preload is an initial internal load
End play is the axial free movement available before the bearing arrangement takes up its clearance. Preload is a deliberately applied internal load before the external working load arrives. Reducing end play to a specified value and applying preload are different adjustments.
Do not tighten a bearing until it merely “feels solid.” Excess preload increases friction and temperature. Some arrangements require positive operating clearance; others use specified preload for stiffness or running accuracy. Temperature and fits change the operating condition.
A shim is a thin, accurately sized spacer. Changing its thickness sets a position in a rigid stack. Whether adding a shim increases or decreases end play depends on where the shim sits and which faces it separates.
Avoid burrs and rubbing contact that could release debris. Use the material and placement specified for the assembly.
A spring maintains force over travel; a shim sets distance; Checklist; Practice
A spring maintains force over travel; a shim sets distance
A shim sets distance and a spring maintains force.
A Belleville washer is a conical disc spring. A wave washer has an undulating shape that compresses axially. Both can apply preload when selected for the required force and working deflection.
A spring can accommodate small dimensional changes while maintaining load. “Very light load” is not a universal specification. Use the bearing's required preload and the spring's load-deflection data; an ordinary lock washer is not a calibrated preload spring.
Supporting detail: Addendum 327 — Position preload versus spring preload.
Identify which support locates the shaft and trace its axial load path.
Find where the other support permits thermal movement and check available travel.
Read the specified end play or preload and its measurement conditions.
Choose the prescribed shim or spring arrangement and verify the final measured setting.
Supporting detail: Addendum 328 — Manufacturer reading and open material questions.
Use the same degrees-of-freedom model to compare round shafts, profile rails and V-wheel carriages.
A linear guide leaves travel along one axis
A linear guide leaves travel along one axis
A linear bearing guides sliding motion just as a rotary bearing guides turning. Let x point along the travel. The guide supports transverse loads and, where its geometry allows, resists moments that would tilt or twist the carriage. A screw, belt or other actuator supplies travel force; the guide does not drive itself.
In the ideal model, translation along x is free. The desired constraints depend on whether rotation about x is acceptable. Real guide selection also checks load, moment capacity, stiffness, clearance, lubrication and alignment.
T means translation; R means rotation. “Restrained” assumes adequate bearing length or block spacing, engagement and rated loads. It does not mean infinite stiffness.
A round shaft does not provide an anti-rotation key
A round shaft does not provide an anti-rotation key
A plain round sleeve or linear ball bushing guides motion along a cylindrical shaft. In the ideal geometry it leaves two freedoms: Tx and Rx. The four other motions are restrained by the support's length or spaced bearings. A second parallel guide can stop the carriage rotating.
Geometric freedom is not a rotary service rating. A recirculating ball bushing may resist or wear under rotation even though its round shaft provides no positive anti-rotation feature. Use a product explicitly rated for combined linear and rotary motion when both are required.
LMU is a common catalog family label associated with round-shaft linear ball bushings. Treat it as a catalog name, not a universal standard or proof of rotary capability. Check the supplier's construction, dimensions and limits.
A profile rail constrains twist as well as sideways motion
A profile rail constrains twist as well as sideways motion
A shaped rail and matching carriage have separated contact paths that resist twisting and tipping. Within their moment ratings, they leave one degree of freedom: Tx. Mounting surfaces must keep the rail aligned; adding constraints can also make an assembly sensitive to misalignment.
MGN commonly identifies a miniature, narrow-block profile-guide family. For example, HIWIN uses MGN within its miniature MG series, with recirculating balls. The label does not make every supplier's product interchangeable, and does not describe every plain or roller guide.
Opposed V-wheels guide a carriage; one wheel does not; Practice
Opposed V-wheels guide a carriage; one wheel does not
A V-groove wheel runs on a matching edge or rail. A stable carriage commonly uses three or more wheels with contacts opposed across the rail and spaced along it. A triangular three-wheel arrangement can use an adjustable wheel to take up clearance.
The assembled carriage should leave only travel along the rail. Three wheels placed arbitrarily do not guarantee that result: orientation, spacing, contact retention and adjustment determine which loads and moments it can resist. A carriage that can lift away from its track has not constrained that motion.
Supporting detail: Addendum 329 — Manufacturer reading and the rotary-motion qualification.
The three quantities every schematic and nameplate uses, the units they are measured in, and the two equations that connect them.
Three quantities, three units
Three quantities, three units
Almost every electrical number you will read off a nameplate, a meter, or a
schematic is one of three quantities. Each has a name, a quantity symbol used in formulas, and a
unit symbol written after a value.
Current, I
The rate at which electric charge flows past a point.
Its unit is the ampere, symbol A — one of the seven SI base
units. One ampere is one coulomb of charge per second.
Voltage, V
Also called electric potential difference: the
difference in electric potential between two points. Its unit is the volt,
symbol V, defined as power per unit of current.
Resistance, R
How strongly something opposes the flow of current.
Its unit is the ohm, symbol Ω, defined as voltage per unit
of current.
How each unit is built out of the others.
Quantity
Unit
Symbol
In other units
Electric current
ampere
A
SI base unit; 1 A = 1 C/s
Electric charge
coulomb
C
s·A
Potential difference
volt
V
W/A, and so (N·m)/(A·s)
Resistance
ohm
Ω
V/A, and so W/A2
Say “amp” if you like; write A. The unit
name is the ampere, and the symbol is a capital A because the unit is named after a person. So is
the volt (V) and the watt (W). Lower case changes the meaning of a
prefix, not just the look of it: mA is a milliampere and MA is a
megaampere, a billion times larger. See Measurement Language.
Supporting detail: Addendum 330 — Why voltage and resistance are called derived units.
Two equations, and everything else follows
Two equations, and everything else follows
For an ohmic resistor (constant resistance under the stated conditions), the set is generated
by Ohm’s law and the power relationship:
V = IR — P = VI
Rearranging and substituting gives three expressions for each of the four quantities. There is
nothing to memorise beyond the two above; the table is a lookup, not a list of new facts.
Resistive-load magnitudes: steady DC, or RMS voltage and current for AC.
To find
From V and I or R
Using power
Using power
Voltage, V
V = IR
V = P/I
V = √(PR)
Current, I
I = V/R
I = P/V
I = √(P/R)
Resistance, R
R = V/I
R = V2/P
R = P/I2
Power, P
P = VI
P = I2R
P = V2/R
P = VI gives real power in watts on direct current or a purely
resistive load. For single-phase AC, RMS volts times RMS amps is apparent power in
volt-amperes, and the real power is that multiplied by the power factor — see
Power and Efficiency.
Worked example: what a lamp draws
Worked example: what a lamp draws
How much current does a 100 W resistive lamp draw on a 120 V supply (RMS for AC)?
Pick the form with the two quantities you have: I = P/V.
I = 100 W ÷ 120 V = 0.833 A.
Check the units rather than trusting the arithmetic. A volt is a watt per ampere, so watts
divided by volts leaves amperes — which is what was asked for.
Worked example: voltage drop along a cord
Worked example: voltage drop along a cord
A 100 ft extension cord has a total out-and-back conductor resistance of 0.1588 Ω.
What is the resistive voltage drop across that path when 10 A flows through it?
V = IR = 10 A × 0.1588 Ω = 1.588 V.
About 1.6 V. That is 1.6 V that never reaches the tool: for DC or an AC resistive load,
the supply voltage equals the cord drop plus the load voltage.
Supporting detail: Addendum 331 — The dropped voltage does not disappear.
The same method keeps working
The same method keeps working
These are not the last units you will meet. Each new quantity arrives the same way: it is
defined as a combination of quantities you already have, and its unit is that same combination.
A few more, and where each one comes from.
Quantity
Defined as
SI unit
Pressure or stress
Force per unit area
pascal, Pa = N/m2
Volumetric flow rate
Volume per unit time
m3/s
Specific weight
Weight per unit volume
N/m3
Capacitance
Charge per unit voltage
farad, F = C/V
Read the middle column and the right-hand column together and the pattern is the whole point:
the unit is the definition, written in symbols. Once that clicks, a unit you have
never seen tells you what the quantity is.
Sources
Sources
Supporting detail: Addendum 332 — Where these values were checked.
Engineering Fundamentals/Electrical Systems
AC and DC
Current direction, sine-wave voltage, transmission losses, and conversion between AC and DC.
DC flows one way; AC reverses direction
DC flows one way; AC reverses direction
Direct current (DC) flows in one direction. Its magnitude can change without making it AC. Alternating current (AC) reverses direction repeatedly. A battery supplies DC; a wall receptacle supplies AC.
Electronics generally run from a DC supply. That does not mean a transistor cannot handle an AC signal: transistors can amplify changing signals and act as switches. The supply and the signal are different parts of the story.
A 120 V sine wave peaks near positive and negative 170 V
A 120 V sine wave peaks near positive and negative 170 V
The nominal 120 V of a US receptacle is an RMS value: root mean square. For a sine wave, Vpeak = VRMS × √2, and VRMS = Vpeak / √2. Thus 120 × √2 = 169.7 V. The instantaneous voltage swings between about +170 V and −170 V, or about 340 V peak to peak.
Frequency counts complete cycles per second, in hertz (Hz). A 60 Hz waveform completes 60 whole cycles per second; a 50 Hz waveform completes 50. A cycle returns to the same phase, rather than ending at the opposite peak. US household mains is 60 Hz; many other countries use 50 Hz (DOE, Electricity 101).
Supporting detail: Addendum 333 — Why use RMS instead of the average voltage?.
Compare signed mean, RMS, and ideal-resistor heating; Interactive; Practice
Compare signed mean, RMS, and ideal-resistor heating
A sine can have a signed average of zero over one cycle and still produce heating. Add a DC offset and the
signed mean moves with the waveform, while total RMS combines the offset and the changing component. Predict
first, then compare the same sine centered on zero, shifted by an offset, kept above zero, or reduced to pure DC.
Print / static comparison: use the analytic waveform
v(t) = offset + amplitude × sin(2πft) over one complete cycle. The resistor is ideal and fixed at
100 Ω. These are low illustrative voltages, not mains or wiring examples.
The same 2 V sine amplitude with different DC offsets
Waveform
Signed mean
AC-component RMS
Total RMS
Minimum / maximum
Average resistor power
0 V offset
0 V
1.414 V
1.414 V
−2 / +2 V
20 mW
+1 V offset
+1 V
1.414 V
1.732 V
−1 / +3 V
30 mW
+3 V offset
+3 V
1.414 V
3.317 V
+1 / +5 V
110 mW
The centered sine has zero signed mean but nonzero RMS and average power. The +3 V offset keeps the total
waveform positive even though it still contains a sine component. A constant pure-DC value has RMS equal to
its magnitude and has no unique oscillation period.
The live explorer evaluates one complete ideal sine cycle analytically; the drawn points only illustrate the
equation. For v(t) = VDC + A sin(2πft), the signed mean is
VDC, the sine component has RMS A/√2, and total RMS is
√(VDC² + A²/2). In one ideal resistor, average power is
VRMS²/R; “RMS power” is not the quantity being calculated.
Higher transmission voltage reduces current and line loss
Higher transmission voltage reduces current and line loss
For the same transmitted power, a higher voltage allows a lower current. The line's resistive heating is Ploss = I2Rline. Halve the current and the loss becomes one quarter, if line resistance stays the same. Here Rline includes the complete current path.
Transformers made it practical to step AC voltage up for transmission and down for use. That advantage helped the AC systems associated with Westinghouse and Tesla prevail over Edison's early DC distribution system in the “war of the currents.” It was not one inventor winning every part of electrical engineering.
Supporting detail: Addendum 335 — A comparison with the same power and the same line.
A rectifier is one stage of an AC-to-DC power supply
A rectifier is one stage of an AC-to-DC power supply
A rectifier makes current flow in one direction from an AC input. Its output can still pulsate. Filtering smooths the output, and regulation controls the output voltage. A complete power supply may include all these functions as well as isolation.
Linear supply: commonly uses a line-frequency transformer, rectifier, filter, and linear regulator. The regulator dissipates excess voltage as heat.
Switch-mode supply: switches current rapidly and uses energy-storage components to convert voltage efficiently. An AC-input version also rectifies its input. Not every switch-mode converter provides isolation.
Both lose some input energy as heat. Efficiency depends on the design, input voltage and load; compare published efficiency curves at the intended operating point rather than assuming one percentage for a whole category. See Power and Efficiency for the input/output calculation.
An inverter makes AC from DC; the waveform matters
An inverter makes AC from DC; the waveform matters
A pure-sine inverter produces an output close to a sine wave. A modified-sine inverter produces a stepped approximation. Equipment may run differently, make more noise or heat, or fail to operate on a stepped waveform. Check the equipment manufacturer's compatibility guidance; equal RMS voltages do not make the waveforms interchangeable.
For grid-tied PV inverters, efficiency is typically above 95% under most operating conditions, according to Sandia PVPMC’s CEC Inverter Test Protocol. Efficiency depends on AC output power, DC voltage and sometimes temperature.
Every real conversion loses some energy. Several conversions in a row multiply their efficiencies rather than adding them. Much of what we use today runs on DC internally, even when it plugs into AC. Phones, computers, and microcontroller electronics bring the instructor's closing question into focus: who gets the last laugh?
Motors, generation, and energy storage make use of both forms of electrical power.
Engineering Fundamentals/Electrical Systems
Wire and Wire Gauge
Separate the conductor from its insulation, and understand what a wire gauge does and does not tell you.
The conductor carries current; insulation separates conductors
The conductor carries current; insulation separates conductors
The metal inside a wire is the conductor. Its resistance depends on material, length, cross-sectional area and temperature. The covering is insulation: it keeps the conductor from contacting other conductors or surrounding objects. The outside diameter includes that covering and does not by itself tell you how much metal is inside.
Solid wire has one solid conductor; stranded wire has several smaller strands forming a conductor. Insulation type and condition matter separately from the metal size. See Electrical Safety for use and inspection guidance.
A smaller AWG number means a thicker conductor
A smaller AWG number means a thicker conductor
American Wire Gauge (AWG) uses smaller numbers for larger conductor cross sections. For the same material, length and temperature, a thicker conductor has less resistance. See Adafruit’s wire-gauge explanation. Under comparable installation and temperature conditions, it can carry more current without exceeding its temperature limit.
Ampacity means the allowable current under specified conditions. Gauge alone is not an ampacity rating: material, insulation temperature rating, ambient temperature, bundling and installation all matter. Use the applicable manufacturer data and installation requirements for a real selection; this page is not a wire-sizing table. IEWC explains these ampacity factors. Choosing a wire involves voltage drop as well as allowable current.
Supporting detail: Addendum 336 — Why a long wire can matter even below its current limit.
Count the return wire: explore voltage drop and heating; Interactive; Practice
Count the return wire: explore voltage drop and heating
A two-conductor circuit carries current out and back. Use twice the one-way run for its wire resistance. At the same current, longer or thinner wire drops more voltage and wastes more power as heat. Voltage drop is a separate check from ampacity: get the current rating from the applicable code table or manufacturer for the insulation and installation.
AWG 18, 50 ft one way, 5 A, 24 V source
Single wire: Ω / 1000 ft
6.385
Single wire: Ω / km
20.95
Loop resistance (Ω)
0.6385
Voltage drop (V)
3.192
Source voltage lost (%)
13.3
Load voltage (V)
20.81
Wire heating loss (W)
15.96
Worked example: 50 ft out + 50 ft back = 30.48 m of copper. R = ρL/A = 0.6385 Ω. At 5 A, IR = 3.192 V and I²R = 15.96 W.
Voltage drop: baseline 3.192 V; now 6.385 VWire heating loss: baseline 15.96 W; now 63.85 W
Outline = baseline; filled = now. Each pair shares its own scale; compare within a pair. Loss is heating power, not wire temperature.
Doubling only current doubles the drop and quadruples heating loss. Doubling only length doubles both; a smaller AWG number lowers both at the same current.
This model assumes solid copper at 20 °C, equal outgoing and return wires, and DC/resistive behavior. Current is an input, not a prediction of how a particular load responds. Heating loss is not a temperature prediction; copper resistance rises with temperature (approx. 0.393%/°C near 20 °C). Connections and AC reactance are omitted.
Supporting detail: Addendum 337 — Definitions used to calculate every result.
Trace current paths, combine resistances, and explore how opening a switch changes voltage, current and power.
Series has one path; parallel has separate branches
Series has one path; parallel has separate branches
In a series circuit, the same current passes through every element. The voltage drops around the loop add up to the source voltage. One break stops current everywhere in that loop.
In a parallel circuit, each branch connects to the same two supply nodes (a node is an electrically connected junction), so each complete branch has the same voltage. The branch currents add up to the supply current. A break in one branch leaves the other branches working, provided the source and shared wiring remain intact.
Equal resistance gives equal drops in series and equal currents in parallel. Different resistances make the drops or currents different. The formulas for each individual resistor are on Current, Voltage, and Resistance.
Add resistances in series; add their reciprocals in parallel
Add resistances in series; add their reciprocals in parallel
Equivalent resistance is the single resistance that would draw the same total current at the supply terminals.
Series: Req = R1 + R2 + R3.
Parallel: 1/Req = 1/R1 + 1/R2 + 1/R3. A reciprocal is 1 ÷ R: one divided by the resistance. Include only connected branches.
Two parallel resistors: Req = R1R2 / (R1 + R2).
Check the result: series resistance is greater than any one positive resistor; parallel resistance is smaller than the smallest connected resistor when two or more branches are connected. An open circuit has no conducting path and is represented by infinite equivalent resistance.
Supporting detail: Addendum 338 — Why the parallel formula uses reciprocals.
Change a resistor or open a switch and predict what changes; Interactive
Change a resistor or open a switch and predict what changes
Use this ideal DC model to compare two or three fixed resistors. Before moving a control, predict which current, voltage and power will change. Switches are ideal, wires have zero resistance and the source holds its set voltage.
Static example: a 15 V source and 30 Ω and 60 Ω resistors, with both switches closed.
The same resistors in two connections
Connection
Equivalent resistance
Total current
R1: current / voltage / power
R2: current / voltage / power
Series
90 Ω
0.1667 A
0.1667 A / 5 V / 0.8333 W
0.1667 A / 10 V / 1.667 W
Parallel
20 Ω
0.75 A
0.5 A / 15 V / 7.5 W
0.25 A / 15 V / 3.75 W
Opening either series switch makes both resistor currents and both resistor voltage drops zero. Opening the R1 parallel switch makes R1 current and power zero while R2 still draws 0.25 A. The voltage across the whole open branch remains 15 V; it falls across the open switch, not the resistor.
The live table reports voltage across each resistor, excluding its switch. In an open series loop the source voltage is across the break or breaks. With several open switches, this ideal model does not determine how that voltage divides between the breaks.
Power explains the bulb comparison, within the model; Practice
Power explains the bulb comparison, within the model
For fixed resistors in series, the larger resistance dissipates more power because both carry the same current. In parallel, the smaller resistance dissipates more power because both have the same voltage. Check the power column rather than assuming the same bulb wins in both arrangements.
Greater electrical power is a useful brightness comparison for otherwise comparable incandescent bulbs. Real filaments change resistance as they heat, and LED lamps contain additional circuitry. The fixed-resistor model is not a universal lamp-brightness predictor.
Connect voltage, current, resistance and continuity measurements to the part of the circuit they describe.
Voltage is measured across; current is measured through
Voltage is measured across; current is measured through
A voltmeter measures the potential difference between two points. Connect it across the component, in parallel. A series ammeter becomes part of the current path: open the path and insert it in series with the element whose current you want.
A meter set for current has a low-resistance input; connecting that input across a source makes a short circuit. Read Electrical Safety before making physical measurements. The diagrams here explain connections, not a procedure for working on mains wiring.
Supporting detail: Addendum 339 — Real meters change the circuit a little.
Place both voltage probes, predict the sign, then reveal; Interactive; Practice
Place both voltage probes, predict the sign, then reveal
A DC voltmeter reports an ordered difference: V(red) − V(black). The two probes must touch the two named points you want to compare. Reversing them reverses the sign; putting both on the same conductor gives zero.
Static example: an ideal 12 V source supplies 30 Ω and 60 Ω resistors in series. Each resistor has an ideal switch immediately before it.
Signed readings from the same ideal circuit
Circuit state
Red point
Black point
Reading
Why
S1 open
Supply +
After S1
+12 V
The single open switch takes the source voltage; no current flows.
Both closed
After S1
After R1
+4 V
Current is 12/(30+60) = 0.1333 A; R1 drops 4 V.
Both closed, probes reversed
After R1
After S1
−4 V
The two point potentials are unchanged; only the ordered subtraction reverses.
S2 open
After R1
After S2
+12 V
The upstream side stays at +12 V and the downstream side returns to 0 V.
Any supported state
One named point
The same point
0 V
A point cannot have a potential difference from itself.
With two open switches, the conductor between them floats in this ideal model. Its voltage is not assigned. The interactive intentionally offers no two-open state.
This is a low-voltage ideal-circuit model with an infinite-impedance voltmeter. It does not authorize live work, mains measurements, or current-mode probing. Fluke's DC-voltage guide explains the V and COM inputs and the negative sign from reversed DC probes; its 381 meter manual shows that voltage probes touch the two desired test points.
A shunt or clamp lets you measure current indirectly
A shunt or clamp lets you measure current indirectly
A shunt is a known small resistance in the current path. Measure the voltage across it and use the relationship in Current, Voltage, and Resistance to find current. The shunt is in series; the voltage measurement across it is in parallel. Many ammeters contain a shunt internally. An installed shunt avoids opening the circuit each time you read it; adding one still requires changing the path.
A clamp meter senses the magnetic field around a conductor without breaking the circuit. Clamp around one conductor, not the outgoing and returning conductors together: their fields can cancel. The instrument must support the type of current being measured; an AC-only clamp does not measure steady DC.
Resistance and continuity are measured with the circuit unpowered
Resistance and continuity are measured with the circuit unpowered
An ohmmeter applies its own small test signal. Use it on an unpowered circuit, with stored energy discharged as described in Electrical Safety. Other connected paths can change the result; isolating the component lets you measure its resistance instead of the whole network.
Continuity is a resistance-threshold test. The beep means the measured resistance is below that meter's threshold. It does not prove exactly zero resistance, identify the intended path, or establish that a connection can carry its working current. The threshold comes from the meter's manual.
A multimeter combines voltage, current and resistance functions, often with continuity too. Select the function, AC or DC mode, range and lead sockets for the measurement. In a schematic, follow the actual connection points rather than the physical positions of the symbols.
Engineering Fundamentals/Electrical Systems
Electrical Diagram Types
Choose a drawing by the question it answers: appearance, connections, function, control logic, or physical location.
Choose the drawing for the job
Choose the drawing for the job
One electrical system can need several drawings. Start with the question: What does the part look like? Where does this wire go? How does the circuit work? Where does the equipment fit?
Choose the drawing for the question you need to answer.
Type
Shows
Usually leaves out
Who uses it, and when
Pictorial
Recognizable appearances of parts.
Exact electrical behavior and hidden connections may be omitted.
A beginner or assembler identifying parts before tracing connections.
Block
Functions and the direction of signal or power flow.
Individual terminals, component values, and return wires.
A designer explaining a system before working out its circuits.
Wiring
Connections between terminals; wire identifiers and routing where specified.
The reason the circuit behaves as it does; scale may be omitted.
An assembler or service technician connecting or tracing wires.
Schematic
Electrical function and connections using component symbols.
Actual component positions, wire lengths, and enclosure geometry.
A circuit designer or technician analyzing how a circuit works.
IC / PCB layout
Physical geometry: a PCB has footprints, pads and copper traces; an IC layout describes structures and interconnect on a chip.
A convenient explanation of circuit operation.
A board or chip designer checking placement and routing before manufacture.
Ladder
Relay or PLC control logic arranged in rungs between rails.
Exact equipment placement and wire routing.
A controls technician tracing the conditions for an output.
Logic
Gates and the relationships between logical inputs and outputs.
Power wiring, package pin locations, and physical placement unless added.
A digital designer following Boolean decisions through a circuit.
Electrical floor plan
Locations of outlets, switches and fixtures on a building plan, interpreted with its legend.
Internal circuit operation; complete routing may be on other drawings.
An installer or building designer locating devices within rooms.
Riser
Distribution between building levels and the equipment serving them.
Detailed room layouts and exact conduit paths unless specified.
A building electrical designer or installer coordinating distribution across floors.
Read the drawing title, legend, revision, and notes before treating a line or mark as an instruction. The same habit applies to mechanical drawings; see Choosing Drawing Views and The Alphabet of Lines.
Compare one circuit in pictorial, wiring, and schematic views; Interactive
Compare one circuit in pictorial, wiring, and schematic views
This teaching example connects a battery, switch, resistor, and LED in one loop. The resistor is in series with the LED. The drawings explain identity and connections; they do not specify a buildable parts list, resistor value, battery rating, or package pinout.
Choose a view. Choose a component to keep it marked when you change views.
Pictorial view
Recognize the parts. These simplified silhouettes are not package dimensions or a lead-identification guide.
Wiring view
Follow terminals: B1+ → S1.1; S1.2 → R1.1; R1.2 → D1.A; D1.K → B1−. A means anode; K means cathode. Terminal names here belong to this example.
Schematic view
Common symbols preserve the wiring connections. S1 is shown open. The LED cathode is the bar on the battery-negative side; the outward arrows identify light emission.
Block view
Arrows show functional order, not individual conductors. The return conductor is omitted.
The wiring view retains every terminal connection. The block view deliberately removes that detail to explain each part's job. The schematic retains those connections while replacing part pictures with common symbols. Compare the three drawings together, or select one view to trace a part. On narrow screens the comparison stacks vertically.
A layout, floor plan, and riser answer different location questions
A layout, floor plan, and riser answer different location questions
A PCB footprint is the land pattern where a component attaches to a board. Traces are the board's conductive paths. An IC is a chip; its internal layout is not the same drawing as the board that holds it.
A floor plan places devices in rooms. Its legend tells you what each mark means. A riser makes the relationship between building levels easier to follow. Neither should be treated as a complete installation instruction by itself.
Read control logic without assuming physical placement
Read control logic without assuming physical placement
A ladder diagram arranges control conditions and outputs in horizontal rungs between two vertical rails. A relay drawing and a PLC program may use a similar ladder shape, but a PLC instruction tests a stored state; it is not a picture of a physical contact.
Common relay forms, shown with S1 open and K1 de-energized. Closing S1 energizes K1; its normally open contact closes and H1 lights. Opening S1 releases K1 and turns H1 off. The shared K1 label links the coil and its contact; it is not a wire between rungs. This is a functional example, not an installation drawing.
A logic diagram emphasizes operations such as AND, OR, and NOT. It helps answer which combinations of inputs produce an output. The diagram may omit supply connections and package pin numbers, so it does not replace a wiring drawing.
Continue with Reading Electrical Connections to recognize common component symbols, distinguish a joined wire from a crossing, and count electrical nodes.
Engineering Fundamentals/Electrical Systems
Reading Electrical Connections
Follow conductors and node labels instead of judging connections by where components sit on the page.
Read the connection convention before tracing a wire
Read the connection convention before tracing a wire
A schematic organizes electrical relationships, not the positions of parts on a bench. Stretching or bending a drawn wire does not change its connections. Moving a line onto a different terminal does.
For the examples on this page, a filled dot at a crossing means the wires join. A crossing with no dot means they do not join. Other drawings may use a bridge or different conventions. Check the legend; an unclear or damaged junction mark is a reason to consult the drawing source.
Count connected conductors, not corners or dots
Count connected conductors, not corners or dots
A node is a set of points joined by ideal conductors. Every point along an uninterrupted wire belongs to the same node, including its bends and branches. A dot marks a connection; it is not a separate component or an extra node.
In the figure, the dotted cross is one node. The undotted cross is two nodes: the horizontal conductor and the vertical conductor. This count concerns the wires drawn in the figure; no connection elsewhere is implied.
Do not trace through a resistor, diode, or open switch as if it were wire. If an ideal switch closes, its two sides become connected; state the switch position before counting nodes. Matching net labels can also indicate a connection without a continuous line across the page. Check the label scope and drawing notes before joining similarly named nets.
Read component identity separately from its value
Read component identity separately from its value
A reference such as R1 identifies a particular part; a value such as 1 kΩ describes its resistance. D1 can identify a diode or LED, so its symbol and parts information still matter. A ground label identifies a reference or connection according to the drawing; it does not by itself establish a connection to protective earth.
US practice (IEEE 315 / ANSI Y32.2) and international practice (IEC 60617) draw some symbols differently. Use the drawing legend; the forms below are teaching examples, not a claim of compliance with a standard.
Trace a connection one terminal at a time; Checklist; Practice
Trace a connection one terminal at a time
Read the legend, notes, revision, and stated switch positions.
Find the source and the named return or reference node.
Follow each conductor to a component terminal, junction, or net label.
Mark each uninterrupted group of conductors as one node.
Check crossings and similarly named labels before assuming they join.
Use the wiring drawing and parts documentation when physical terminal locations matter.
Recognize common symbols before tracing their connections; Practice
Recognize common symbols before tracing their connections
Use the symbol to identify the kind of component, then read its reference and value. The sheet includes both resistor forms and an unpolarized capacitor. A battery is one kind of DC source; other DC supplies may use a circle marked with polarity.
Common teaching forms, panel 1 of 2.
Common teaching forms, panel 2 of 2. Buzzer and fuse shapes vary, so check the legend. The ground mark's meaning depends on the drawing; it does not establish protective earth by itself. The diode bar marks its cathode; the LED adds outward arrows for light.
Find the stator and rotor, then follow the changing magnetic field that keeps a motor turning.
The stator stays still; the rotor turns
The stator stays still; the rotor turns
An electric motor turns electrical input into mechanical motion. In a rotary motor, the stator is the stationary part and the rotor is the rotating part. An air gap separates them. Bearings support the rotating assembly; the shaft carries motion to the load.
The stator is often outside the rotor, but it does not have to be. The names describe motion, not inside versus outside. See Electric Motor Types for both arrangements.
Keep the magnetic target moving: carrot on a stick
Keep the magnetic target moving: carrot on a stick
Picture the rotor turning to align its magnetic field with the stator's field. If the fields simply settled into alignment, that turning effect would disappear. To keep turning, the motor switches a field or keeps the stator field rotating. Think carrot on a stick: keep moving the target ahead.
Commutation means switching current between windings at the right time. Brushes and a commutator can do it mechanically, or a drive can do it electronically. A winding is a coil of wire that creates a magnetic field when current flows through it.
Supporting detail: Addendum 341 — Where the alignment picture needs care.
Why a DC motor keeps turning: coil, field and commutator; Interactive
Why a DC motor keeps turning: coil, field and commutator
The simplest brushed DC motor is one rectangular coil on a shaft between two magnet poles. Turn the coil, find where the field stops pushing it, and see how a split-ring commutator keeps the push going one way.
Predict first: a coil carrying current sits between a north and a south pole. At which angles does the field give it no turning push at all, and where is the push largest?
Torque on the coil. For an ideal rectangular coil in a uniform field, the torque about the shaft is τ = N·B·I·A·sin θ. N is the number of turns, B the field (T), I the current (A) and A the coil's area (m²), so τ is in N·m. θ is the angle from the field B to the coil's normal n, the line perpendicular to the coil's face. The coil's magnetic moment lies along n or against it, depending on which way the current circulates. That sets the direction of the torque, not its size.
One coil at θ = 30°. Left, a cutaway side view: the N pole in front is cut away, the S pole is behind the coil, and B points away from you. Right, the end view from the commutator end, with the top brush positive. In the end view, current runs away from you along side 1 (⊗) and back toward you along side 2 (⊙). F = BIL pushes side 1 down and side 2 up. The two forces are equal and opposite, so there is no net force, but they form a couple. Each acts at a lever arm of r·sin 30° = 0.5r from the shaft, where r is half the coil width. So τ = 0.5·NBIA, counter-clockwise as seen from the commutator end.
Why the angle matters. Whenever current flows, each long side of the coil feels a force F = BIL, the same size at every angle. What changes is its lever arm about the shaft, r·sin θ, where r is half the coil's width. As the coil approaches θ = 0° or 180°, with its face across the field in the neutral plane, the forces point almost straight through the shaft. The lever arm shrinks to zero, and so does the torque. With slip rings the current still flows at those angles and the forces point straight through the shaft. With an ideal split ring the brushes sit on the gaps at that instant, so there is momentarily no current and no force at all. Either way the torque there is zero. At θ = 90° and 270° the lever arm, and the torque, are largest.
Why a commutator. If the coil were fed through slip rings, its current would never reverse. With the polarity drawn here, past 180° the torque would reverse too, pushing the coil back toward that neutral-plane position, and over a whole turn it would average zero. Reverse the supply or the magnets and the coil's resting position moves half a turn. A split-ring commutator turns with the coil. Its brushes change segments exactly as the coil crosses the neutral plane, which reverses the coil current. The torque becomes N·B·I·A·|sin θ|: it never points backward, but it still falls to zero twice a turn.
Torque against θ for one turn, as a fraction of one coil’s peak NBIA. Slip rings (dashed): the torque reverses every half turn and averages zero. Split-ring commutator (solid): the current reverses at the neutral plane, so the torque is |sin θ|, never negative, averaging 2/π ≈ 0.64; it is still zero at 0° and 180°. Two commutated coils 90° apart (thick): the sum runs from 1 to √2 ≈ 1.41, so the smallest torque is 0.71 of the largest and never zero.
Two coils. Add a second coil 90° ahead of the first, each with its own split ring. When one coil is in the neutral plane, the other is at its peak. The total, |sin θ| + |cos θ| in units of one coil's peak, runs from 1 to √2. Its smallest value is 1/√2 ≈ 0.71 of its largest, so the ripple shrinks and the zero-torque dead spot disappears.
Worked example, with illustrative numbers rather than a real motor rating: N = 50 turns, B = 0.20 T, I = 2.0 A, and a coil 40 mm × 30 mm, so A = 1.2 × 10⁻³ m². The peak torque is N·B·I·A = 50 × 0.20 × 2.0 × 0.0012 = 0.024 N·m. At θ = 30°, τ = 0.024 × sin 30° = 0.012 N·m.
Direction. Reversing the current reverses every force (F = I L × B), so the motor turns the other way. Swapping the magnets reverses B and does the same. Reversing both restores the original direction.
Model limits. This is an ideal teaching model: one or two rectangular coils, a uniform field, and current switched exactly at the neutral plane. Torque is shown as a fraction of one coil's peak, N·B·I·A. It does not model back EMF, speed, magnetic saturation or brush sparking.
Supporting detail: Addendum 342 — Sources for the torque formula and the commutator.
Separate turning effort, speed, and power
Separate turning effort, speed, and power
Torque is turning effort. Angular speed tells how fast the shaft turns. Mechanical power combines the two. A stopped shaft can have torque and still deliver zero mechanical power.
Compare how motors switch their fields, what wears, and how they control motion.
Brushed DC: simple supply, wearing contacts
Brushed DC: simple supply, wearing contacts
A small permanent-magnet brushed DC motor has stationary magnets and rotating electromagnets. Carbon brushes press against a segmented copper commutator. As the segments rotate past the brushes, the connections change and reverse current in rotor windings. The torque keeps acting in the intended direction.
Strength: inexpensive and simple to run from DC, useful in small toys, pumps, and actuators. Weak points: brushes wear through contact and electrical arcing; the commutator and spring contact system can also deteriorate. Switching current at the contacts can cause sparks and electrical noise. Permanent-magnet construction is common in small motors; some brushed motors use field windings instead.
A microcontroller can command a power driver with pulse-width modulation (PWM), switching the supply on and off rapidly to control the motor. The driver handles motor current; a logic output is not a motor power supply.
AC induction: the rotor follows a rotating field with slip
AC induction: the rotor follows a rotating field with slip
Stator windings arranged around the motor produce a rotating magnetic field. In a three-phase motor, the currents reach their peaks at different times, moving the combined field around the stator. That moving field induces current in conducting rotor bars. The rotor current and stator field interact to produce torque.
The rotor runs slightly slower than the field during normal motoring. The difference is called slip. If the rotor caught the field exactly, there would be no relative motion to induce the rotor current needed for torque. For example, a field at 1,800 rpm and a rotor at 1,740 rpm differ by 60 rpm, or 3.33% of field speed.
Strength: a squirrel-cage induction rotor needs neither brushes nor permanent magnets, making it useful for pumps, fans, and conveyors. Weak points: speed changes with load and slip; a variable-frequency drive is normally used when adjustable speed is needed.
Supporting detail: Addendum 343 — Why alternating current alone is not the full explanation.
Brushless permanent-magnet motors: switch the stator current
Brushless permanent-magnet motors: switch the stator current
Here the rotor carries permanent magnets and the stator carries windings. A drive switches the stator currents in sequence so the magnetic field turns. There are no commutator brushes to wear.
BLDC means brushless DC; PMSM means permanent-magnet synchronous motor. A DC supply can feed an inverter, an electronic circuit that creates changing phase currents. Most BLDC/PMSM drive systems use this electronic switching. The labels often distinguish waveform and control choices; they do not mean one rotor needs AC magnets and the other needs DC magnets.
A suitably designed line-fed synchronous motor instead follows a rotating field set by the AC supply frequency and pole count. It needs an appropriate starting arrangement. Do not assume an arbitrary BLDC motor can connect directly to an AC line.
Strengths: no brush contact wear and controllable speed; common uses include cooling fans, drones, and controlled machine drives. Weak points: drive electronics and correctly timed switching are needed; bearings still wear and winding temperature still limits output.
Inner-rotor and outer-rotor describe what rotates
Inner-rotor and outer-rotor describe what rotates
An inner-rotor motor, also called an inrunner, rotates inside the stator. An outer-rotor motor, or outrunner, rotates around the stator. These are the arrangements sometimes called “inboard” and “outboard.” Use inner-/outer-rotor when describing the construction.
An inner rotor can have low rotational inertia, useful for rapid speed changes. An outer rotor puts magnetic force at a larger radius, useful for producing torque in fan and propeller drives, but its rotating shell contributes inertia. Dimensions and design still decide the actual performance.
Stepper: count commanded steps, but allow for missed motion; Practice
Stepper: count commanded steps, but allow for missed motion
A stepper drive energizes stator phases in a sequence of magnetic positions. As a first approximation, picture an inner-rotor brushless motor with many magnetic poles or teeth. That helps explain the small steps; it is a simplification, since stepper constructions differ.
Open loop means the controller sends a move without measuring whether it happened. A stepper can position and hold without feedback while energized and within its torque capability. It is useful for printer axes and small indexing mechanisms. Holding position still uses current and produces heat.
The weak point is missed steps. Excessive load or acceleration can prevent commanded motion. Without feedback, the controller keeps counting commands and does not know the shaft fell behind. Step count is not a guarantee of exact position, and holding torque is not a guarantee against any load.
A servo is a motor used with feedback and closed-loop control, not one particular magnetic construction. A sensor such as an encoder measures motion. The controller compares measured position or speed with the command and adjusts the drive to reduce the error.
Strength: responds to a load disturbance and detects position error, useful for robot joints and machine axes. Weak points: adds sensor, controller, tuning, and cost. Feedback does not create extra torque; a servo can still reach its limits. A brushed, brushless, or other suitable motor can be part of a servo system.
Linear motors move directly along a track
Linear motors move directly along a track
Think of the magnetic layout of a rotary motor opened out into a straight line. A traveling field pushes or pulls a moving member along a track, producing linear force instead of shaft torque. One permanent-magnet arrangement uses a magnet track and a moving coil assembly. Linear induction designs also exist; a magnetized rail is not universal.
Strength: direct linear motion without a rotary-to-linear screw or belt, useful for positioning stages and transport systems. Weak points: the magnetic track, drive, cooling, and position measurement can add cost. Separate guides support and constrain the moving assembly; a motor does not replace the guide system.
Use an ideal linear torque-speed curve to find a load point and see why peak output power occurs halfway to no-load speed.
More load torque means less speed on this curve
More load torque means less speed on this curve
This model approximates a permanent-magnet DC motor at a fixed supply voltage with a straight line between two endpoints. Stall torque is the torque at zero speed. No-load speed is the speed at zero external shaft load. It is not a universal curve for induction motors, steppers, or regulated drives.
Let Ts be stall torque, n0 no-load speed, and T the constant resisting load torque. The steady operating point is where motor torque equals load torque:
n = n0(1 − T/Ts).
This is an assumed linear approximation, not a measured motor rating. It omits acceleration, current limiting, temperature changes, and supply voltage drop. At stall it predicts zero shaft power, not zero electrical input. A stall rating is not a continuous operating rating.
Supporting detail: Addendum 344 — Manufacturer basis for the straight line.
Explore the load point and the peak-power point; Interactive
Explore the load point and the peak-power point
Predict first: a model motor has 0.8 N·m stall torque and 3,000 rpm no-load speed. A constant load asks for 0.2 N·m. Does the motor run above or below half speed?
Static example: n = 3,000(1 − 0.2/0.8) = 2,250 rpm. Angular speed is 2,250 × 2π/60 = 235.6 rad/s, so output power is 47.12 W. Peak power is 62.83 W at 1,500 rpm and 0.4 N·m.
The solid line is torque / stall torque; the dashed curve is power / peak power. The circle marks load torque; the diamond marks output power. The square marks peak power.
Peak power is halfway, not at either endpoint; Practice
Peak power is halfway, not at either endpoint
Use P = Tω, with torque in N·m and angular speed in rad/s. Convert rpm using ω = 2πn/60. The definitions and units are on Power and Efficiency and Angular Motion.
At stall there is torque but no speed. At no load there is speed but no external load torque. Both endpoints therefore have zero shaft output power. Between them, torque times speed reaches a maximum.
Supporting detail: Addendum 345 — Derive the halfway result from the straight line.
Supporting detail: Addendum 346 — Manufacturer check on peak power.
Peak efficiency needs electrical input as well as shaft output
Peak efficiency needs electrical input as well as shaft output
Efficiency is output power divided by input power. Peak output power and peak efficiency answer different questions. The torque-speed line alone does not give electrical input or losses, so this explorer deliberately does not calculate efficiency.
For the brushed coreless DC motors described by Portescap, peak efficiency occurs at a lighter load and higher speed than peak output power. Its exact position needs loss or current data. No external load means no useful shaft output, even though a real motor draws current to overcome its internal losses. Consult the actual motor's efficiency and continuous-operation data before selecting a load point.
Supporting detail: Addendum 347 — Manufacturer basis for the efficiency comparison.
Match the motor, reduction, and the same output load; Interactive; Practice
Match the motor, reduction, and the same output load
A gearbox changes the torque demanded at the motor shaft for the same output load. That can move the motor to a different point on its torque–speed curve. Predict both operating points before revealing them.
Static example: a motor has 0.8 N·m stall torque and 120 rpm no-load speed. The output load resists with 0.6 N·m. Compare direct drive with a 20-tooth driver, 40-tooth driven gear, and a stated 90% running mesh efficiency.
The same motor and output load, two connections
Connection
Torque required at motor
Motor speed
Output speed
Motor shaft power
Modeled output power
Direct
0.600 N·m
30.0 rpm
30.0 rpm
1.885 W
1.885 W
2:1 reduction, 90%
0.3333 N·m
70.0 rpm
35.0 rpm
2.443 W
2.199 W
Result: the reduction runs the output faster under this load, even though it divides motor speed. It reflects less load torque to the motor, so the motor reaches a higher speed. The gearbox did not create power: motor shaft power changed before the 10% modeled mesh loss.
This is a fixed-voltage steady-running comparison with a constant resisting torque. It does not establish starting ability, acceleration, thermal or continuous rating, back-driving, electrical input, or gear strength. At stall, speed and shaft output power are zero; if required motor torque exceeds stall torque, the model reports no forward steady operating point instead of assigning a fictitious speed.
Supporting detail: Addendum 348 — Source and the standstill boundary.
Real loads may demand different torque at different speeds. Their operating point is an intersection of a load curve and a motor curve. Practice reflected loadPractice output power
Engineering Fundamentals/Electrical Systems
Microcontroller Basics
Read inputs, make decisions in a program, and control outputs using a classic Arduino Uno R3.
A microcontroller reads inputs and controls outputs
A microcontroller reads inputs and controls outputs
A microcontroller is a small computer on a chip, with a processor, memory and connections to the outside world. Its program can read a switch, decide what that input means, and turn an output on or off. The Arduino Uno is a board that supplies the chip with power connections, a USB interface and accessible pins.
This topic uses the classic Uno R3 with an ATmega328P, operating with 5 V logic. Other Arduino boards, including newer Uno models, can have different converters and electrical limits.
An Arduino program is called a sketch. It uses C/C++ syntax: rules for names, parentheses, braces and statements. It is a programming language, not ordinary English. Capitalization matters: digitalRead and digitalread are different names.
setup() runs once after startup or reset. loop() repeats while the program runs. This original example turns the built-in LED on for half a second and off for half a second.
delay uses milliseconds and pauses normal progress through the sketch. The braces group the statements belonging to each function.
Choose the pin mode before using the pin
Choose the pin mode before using the pin
Three pin modes
Mode
What it does
Typical use
INPUT
Reads a voltage level without enabling the internal pull-up.
A sensor that actively drives a compatible signal; do not leave the input floating.
OUTPUT
Drives the pin HIGH or LOW.
An LED through a current-limiting resistor, or a control signal to a driver.
INPUT_PULLUP
Reads an input with an internal resistor pulling it toward the logic supply.
A button connecting the input to ground.
pinMode(pin, mode) configures the pin. digitalRead(pin) returns HIGH or LOW. On an OUTPUT pin, digitalWrite(pin, HIGH) drives it toward the logic supply; LOW drives it toward ground. These are limited-current signals, not ideal power supplies. On an INPUT pin, digitalWrite instead controls the pull-up.
A button to ground reads LOW when pressed
A button to ground reads LOW when pressed
With INPUT_PULLUP, an open switch reads HIGH. Closing the switch to ground reads LOW. This is called active-low: the action happens when the signal is low.
The pull-up supplies a small current through the closed switch to ground. The switch sinks that current. A physical switch can bounce between states briefly; counting presses reliably needs debouncing beyond this simple state display.
Supporting detail: Addendum 349 — Pull-up resistance and current.
Use the official IDE and function reference; Checklist; Practice
Confirm the board model and choose its matching board entry in the IDE.
Select the port belonging to the connected board.
Verify the sketch to catch syntax errors, then upload it.
Check that the observed input and output match the program.
Disconnect power before changing wiring. Keep signals within the board's ratings and use a suitable driver for a motor. See Electrical Safety for electrical precautions.
Decide whether a sensor communicates with two logic states, a changing voltage, or the timing of pulses.
Digital uses two states; analog uses a range
Digital uses two states; analog uses a range
A digital input interprets two states: LOW/HIGH, or 0/1. The wire still carries a physical voltage; the receiving circuit decides which logic state it represents. A voltage in the undefined region between valid LOW and HIGH levels is not a useful third state.
An analog signal represents a quantity by a continuous range of values. A potentiometer wired between ground and 5 V can provide a changing voltage at its middle terminal. On a classic Uno R3, the usual analog measurement range is nominally 0–5 V with the default reference. That is not a universal sensor range.
Classify the sensor's output circuit, not just its name
Classify the sensor's output circuit, not just its name
Common examples
Device and connection
Signal at the input
Button or switch with a pull-up
Digital open/closed state.
Quadrature encoder with compatible logic outputs
Two digital pulse trains; their order gives direction.
HC-SR04 ultrasonic module, Echo pin
A timed digital pulse. Its duration represents distance; its voltage height does not.
Potentiometer connected as a voltage divider
Analog voltage from its wiper (middle terminal).
Photoresistor in a voltage divider
Analog voltage as resistance changes with light.
Phototransistor with a load resistor
Analog response to light unless a threshold circuit converts it to digital.
Pressure or proximity sensor
Depends on the model: analog voltage, switching output, or digital data. Read its documentation.
A bare resistive sensor does not generate a usable voltage by itself: its surrounding circuit matters. A module may offer both analog and thresholded digital outputs.
Supporting detail: Addendum 350 — Phototransistor circuits can measure light or switch at a threshold.
Supporting detail: Addendum 351 — Why an ultrasonic measurement can be digital.
The ADC reads voltage; PWM controls time; Practice
The ADC reads voltage; PWM controls time
Analog-to-Digital Conversion turns an analog input into a number the program can use. Pulse-Width Modulation switches a digital output on and off for a controlled fraction of each cycle. Neither operation changes the fact that the processor stores and works with digital data.
Relate an Uno R3's 10-bit ADC reading to its reference voltage, step size and approximate sampling time.
Ten bits give 1024 codes, numbered 0 through 1023
Ten bits give 1024 codes, numbered 0 through 1023
An analog-to-digital converter (ADC) samples a voltage and reports a number. The classic Uno R3 has a 10-bit ADC: 210 = 1024 possible codes. analogRead(A0) reads analog input A0 and returns an integer from 0 to 1023.
The reference voltage sets the scale. With an assumed exact 5.000 V reference, one nominal step is 5/1024 = 0.0048828125 V = 4.883 mV, or about 4.9 mV. Resolution describes the step size; it does not guarantee that a real voltage measurement is accurate to that amount.
Supporting detail: Addendum 352 — Arduino's resolution and timing figures.
Use 1024 for the nominal voltage step
Use 1024 for the nominal voltage step
For these exercises, use a clearly defined ideal bin model: divide the 0–5 V span into 1024 equal bins, round down to the bin number, and limit the top code to 1023.
code = min(1023, floor(Vin × 1024 / Vref)). Here floor means round down. At 3.000 V with a 5.000 V reference: floor(614.4) = 614.
To report the nominal voltage represented by a code, use its lower bin edge: V = code × Vref/1024. Code 800 represents 800 × 5/1024 = 3.90625 V. In this model its bin extends up to, but not including, 3.9111328125 V.
Supporting detail: Addendum 353 — Why dividing by 1023 answers a different question.
Explore the steps and check the units; Practice
Explore the steps and check the units
The two-way ADC controls in the PWM and ADC explorer let you enter a voltage or a code. Try nearby voltages within one bin, then cross its boundary. In reverse, code 1023 gives 4.9951171875 V as its lower edge, not proof that the input equals that value.
The same explorer also separates when a voltage is sampled from how its code is calculated. It shows instantaneous raw PWM or settled RC values, the finite mean of the selected point samples, and the mean of their reconstructed lower-edge voltages. Those are different from the waveform's complete-cycle time mean. A held code is the latest point result, not a window average.
Supporting detail: Addendum 354 — Quantize first or average first?.
Explore duty cycle, frequency, average voltage and RC smoothing, then compare PWM output with ADC input.
Duty cycle is the fraction of each cycle spent HIGH
Duty cycle is the fraction of each cycle spent HIGH
Pulse-width modulation (PWM) repeats a rectangular waveform. The period T is the time for one cycle; frequency f is cycles per second. Duty cycle D is the fraction of the period spent HIGH.
T = 1/f, ton = D × T, and for ideal switching between 0 V and a supply Vs, Vaverage = D × Vs. Convert a percentage to a fraction: 25% means D = 0.25.
At 500 Hz, T = 0.002 s = 2 ms = 2000 µs. At 25% duty, the on-time is 500 µs and the average of a 0–5 V output is 1.25 V. The pin itself still switches between 0 and 5 V.
The stock Uno R3 uses six PWM pins
The stock Uno R3 uses six PWM pins
Use digital pins 3, 5, 6, 9, 10 and 11. Default PWM is approximately 490 Hz on 3, 9, 10 and 11, and 980 Hz on 5 and 6. These correspond to periods of about 2.04 ms and 1.02 ms.
analogWrite(pin, value) requests duty using values from 0 (always off) to 255 (always on). A useful nominal mapping is value = round(255 × D): 25% gives 64. Hardware timer modes introduce small differences in the exact duty, particularly near the ends of the range.
Supporting detail: Addendum 355 — Official frequency table and timer limitations.
Change duty and frequency, then compare an ADC reading; Interactive
Change duty and frequency, then compare an ADC reading
Print / static comparison: 25% duty at 500 Hz gives a 2 ms period, 0.5 ms HIGH time and a 1.25 V complete-cycle time mean for an ideal 0–5 V waveform. A point sample is one instant, not that average.
The same PWM waveform sampled at different phases
Finite sample set
Each raw sample
Selected-sample mean
ADC code / lower edge
500 samples/s, phase 10%
5 V
5 V
1023 / 4.995117 V
500 samples/s, phase 60%
0 V
0 V
0 / 0 V
2000 samples/s, phases 1%, 26%, 51%, 76%
5, 0, 0, 0 V
1.25 V
Mean lower edge 1.248779 V
An unloaded 10 kΩ / 1 µF RC filter has a 10 ms time constant. In the settled repeating response its 25%, 500 Hz ripple runs from about 1.1579 V to 1.3453 V while its cycle mean remains 1.25 V. Changing a control recomputes that settled response; this model does not show startup.
With a separate 5.000 V ADC input, 3.000 V gives code 614; code 800 has lower edge 3.90625 V.
The explorer is a model, not a board connection. Its frequency and sampling controls do not configure an Uno or claim a board throughput. A raw sample uses normalized phase with HIGH on [0, D) and LOW on [D, 1); the stated finite sample count defines the reported sample mean. ADC controls use the ideal bin convention on Analog-to-Digital Conversion; 5.000 V is assumed exact.
Supporting detail: Addendum 356 — Why more samples can still give the wrong mean.
An RC filter smooths PWM but leaves ripple
An RC filter smooths PWM but leaves ripple
Put a resistor in series with the PWM signal and a capacitor from the output node to ground; measure the voltage across the capacitor. This RC low-pass filter slows voltage changes. The capacitor charges while PWM is HIGH and discharges while it is LOW.
The time constant is τ = R × C. A longer time constant relative to the PWM period reduces ripple but makes the output respond more slowly when duty changes. The explorer shows the settled waveform with τ = 10 ms, assuming an ideal source and no load. A load changes the result; the filter is not a motor power supply.
Microchip's AVR131 PWM filtering note explains the tradeoff: the low-pass filter must reject PWM base-frequency ripple without removing the slower signal of interest, and a low-impedance load can discharge the capacitor unless buffered. This explorer deliberately assumes no load.
Supporting detail: Addendum 357 — What the smoothed trace calculates.
PWM changes LED brightness and motor drive; Practice
PWM changes LED brightness and motor drive
Rapid switching changes an LED's average light output while a resistor or driver limits its on-state current. Perceived brightness is not perfectly proportional to duty. For a DC motor, PWM commands a suitable power driver; the board pin does not supply the motor current. The driver must handle the motor and its inductive current.
Increasing duty usually increases the available drive, but motor speed also depends on load. Use DC Motor Torque, Speed, and Power to connect speed, torque and current. See Electrical Safety before wiring.
How turbines and generators turn other forms of energy into electricity, how photovoltaics differ, and how to compare a generation mix.
A generator converts motion into electrical energy
A generator converts motion into electrical energy
A generator does not create energy. It takes mechanical work at a shaft and delivers electrical energy to a circuit, with some energy becoming heat along the way.
A turbine is a rotating machine driven by a moving fluid. Steam, flowing water, wind, or hot combustion gases can turn its blades. The turbine turns the generator; the generator supplies electricity. An engine can also drive a generator without a turbine.
Supporting detail: Addendum 358 — How rotation produces electricity.
Different heat sources can feed the same steam cycle
Different heat sources can feed the same steam cycle
Burning fossil fuels or biomass can heat water to make steam. Nuclear fission supplies heat without combustion. Geothermal systems use heat from the Earth, and concentrated solar systems use mirrors to collect sunlight as heat. The equipment differs, but a steam-based plant follows the same basic chain: heat, moving steam, shaft rotation, electricity.
Not every turbine uses steam. A hydroelectric turbine takes energy from water flowing downhill. A wind turbine takes energy from moving air. A combustion turbine uses hot gases directly; a combined-cycle plant also recovers exhaust heat for a steam cycle.
Photovoltaic cells skip the turbine
Photovoltaic cells skip the turbine
A photovoltaic (PV) cell converts light directly into electrical energy through the photovoltaic effect in a semiconductor. A connected load receives DC electricity. An inverter can convert that DC to AC.
Solar PV and concentrated solar thermal are different routes. PV produces electricity in the cell; solar thermal first collects heat. That distinction matters when considering thermal storage.
A generation mix is more than a list of percentages
A generation mix is more than a list of percentages
A generation mix describes how much electricity comes from each source over a stated place and time. Installed capacity describes how much power equipment is rated to supply. Those are different measures: a large rated capacity does not mean a source supplied the same share of annual energy.
Predict: which generator produces more energy?
Compare two hypothetical generators over the same 365-day, 8760-hour period. Generator A is rated at 1 MW with a given 25% capacity factor. Generator B is rated at 0.5 MW with a given 60% capacity factor. Which produces more energy over the year? Decide before opening the check.
Check the rated-power and period-energy comparison
Period energy = rated power × period hours × capacity factor Capacity factor = period energy ÷ (rated power × period hours)
Fixed stated ratings and given illustrative factors over 8760 hours
Generator
Rated power
Capacity factor
Average power
Period energy
A
1 MW
25% = 0.25
0.25 MW
1 × 8760 × 0.25 = 2190 MWh
B
0.5 MW
60% = 0.60
0.30 MW
0.5 × 8760 × 0.60 = 2628 MWh
Generator B has the smaller rating but produces more energy in this given example. MW measures power; MWh measures energy over time. Do not treat 1 MW as 1 MWh for the year, and write 25% as 0.25 in the multiplication, not 25.
Capacity factor is not conversion efficiency, the percentage of hours switched on, dispatchability, reliability, or a source's share of an energy mix. Partial-load operation contributes too; the factor does not require a generator to alternate only between off and full power.
These ratings and factors are fixed hypothetical inputs for the stated period, not real-plant data. EIA's published factors use time-adjusted capacity methods; this example does not reproduce that method. The EIA capacity and generation FAQ distinguishes rated power from energy produced over a period and defines the capacity-factor comparison.
Compare cost, emissions, variability, and dispatchability — the ability to adjust output when requested. Wind and sunlight vary with weather and time. Fuelled generation and reservoir hydro can often be scheduled, but fuel, water, maintenance and operating limits still matter. Storage shifts energy in time; it is not an extra primary energy source.
No current percentage mix is supplied here. For dated U.S. generation data, consult the U.S. EIA's Electricity explained: electricity in the United States, and record the reporting year and whether the figures describe generation or capacity.
Engineering Fundamentals/Electrical Systems
Energy Storage Methods
Pumped water, stored heat and rechargeable batteries hold energy for later use in different ways.
Pumped hydro stores energy by lifting water
Pumped hydro stores energy by lifting water
Use electricity to pump water uphill, then let it flow downhill through a turbine and generator when electricity is needed. The stored energy is gravitational potential energy.
The cycle returns less electrical energy than it consumed because pumping, flow and generation all have losses. It needs suitable elevations, reservoirs and water management; it cannot be placed wherever a battery can.
Thermal storage holds energy in a hot material, such as a fluid or solid. A concentrated solar plant can collect heat while sunlight is available, store it, and later use it to produce steam and electricity. Stored heat can also serve heating loads directly.
Insulation slows heat loss; it does not eliminate it. Returning heat to electricity adds conversion losses. Choose the storage route for the energy form the load needs.
Rechargeable batteries store energy chemically
Rechargeable batteries store energy chemically
A battery supplies DC through electrochemical reactions. A primary battery is intended for a single discharge life and replacement. A secondary battery is designed to be recharged with a suitable charger, restoring chemical energy for another discharge.
Primary cells are useful portable energy supplies, but they are not reusable storage for electricity from a generator. Do not try to recharge a primary cell. Rechargeable does not mean unlimited life: cycling and aging reduce usable capacity.
Choose storage for the load and the site; Practice
Choose storage for the load and the site
A small portable instrument needs a compact energy supply, so a battery is a practical fit. A site with suitable upper and lower reservoirs can consider pumped hydro for large stationary storage. A solar thermal plant needing heat after sunset can store heat without first converting it to electricity.
Compare the required power, the energy needed over time, the storage duration, available space and terrain, losses, and service life. These examples identify a good fit; they do not establish that one technology is always cheapest.
Compare primary alkaline, rechargeable nickel, lead-acid and lithium-ion batteries, and the short history behind them.
Capacity, self-discharge and aging are different
Capacity, self-discharge and aging are different
A cell is one electrochemical unit. A battery may contain one cell or several. Its chemistry helps determine voltage, mass, charging needs and how well it holds charge.
Self-discharge is loss of stored charge while no load is connected. Aging is loss of the ability to hold or deliver charge, even after recharging. Both depend on the cell design, temperature and storage conditions, so a chemistry name is not a shelf-life specification.
A capacity rating also depends on discharge current, temperature and the voltage at which the test stops. Use the particular cell's data, not a single capacity assigned to every AA or D cell.
Common primary alkaline cells serve devices such as clocks, remote controls and flashlights. They are widely available and retain charge relatively well in storage. Their useful capacity and terminal voltage fall more under heavy loads and cold conditions.
They are not intended to be recharged. Leakage can damage equipment, especially when cells are exhausted or left in storage. Rechargeable-battery memory effect is not a useful concern for a primary cell.
NiCd and NiMH are rechargeable nickel batteries
NiCd and NiMH are rechargeable nickel batteries
Nickel-cadmium (NiCd) and nickel-metal hydride (NiMH) use alkaline electrolytes, but they should not be confused with primary alkaline cells.
Two rechargeable nickel families.
Family
Uses and strengths
Limits
NiCd
Legacy cordless tools and industrial backup equipment; capable of substantial discharge currents in suitable designs.
Cadmium is toxic and requires appropriate battery recycling. Repeated partial cycling can cause memory-related voltage depression. Self-discharge matters during storage.
NiMH
Rechargeable consumer cells and hybrid-vehicle packs; generally more capacity than comparable NiCd cells and no cadmium.
Conventional cells can self-discharge noticeably; low-self-discharge versions improve charge retention. Voltage depression can occur, but memory concerns are generally less pronounced than with NiCd.
Use a charger designed for the chemistry and cell. Fast charging is appropriate only when the cell and charger support it. Do not deliberately drive a pack to zero volts to prevent memory effect: a weaker cell can be forced into reverse polarity by the others.
Supporting detail: Addendum 359 — Why a remote-control recommendation needs more than a chemistry name.
Lead-acid trades low mass efficiency for useful power and cost
Lead-acid trades low mass efficiency for useful power and cost
Lead-acid batteries appear in engine starting and stationary backup supplies. They can deliver high starting currents and are relatively inexpensive, but they are heavy for the energy stored.
They self-discharge during storage. Prolonged storage while discharged promotes sulfation, which can reduce capacity; this is not the NiCd memory effect. Starting and deep-cycle designs serve different loads. Use the specified charging method: the electrolyte is acidic, lead is toxic, and charging can release gas. Flooded, absorbed-glass-mat and gel designs all exist; modern lead-acid does not always mean gel.
Lithium-ion needs protection; LiPo is not automatically better
Lithium-ion needs protection; LiPo is not automatically better
Lithium-ion batteries power portable electronics, tools and electric vehicles. Their energy per unit mass is generally considerably higher than NiMH, with relatively slow self-discharge and no routine need for full discharge to prevent memory effect. They still lose capacity through calendar aging and cycling.
Protection and charge control must keep voltage, current and temperature within the cell's limits. A bare cell may not contain its own protection circuit. The pack design must provide the required protection; a protection circuit is not a substitute for a compatible charger.
Lithium-ion polymer, often called LiPo, commonly appears as a light pouch cell in portable devices and model aircraft. The packaging allows thin shapes; some designs support high discharge rates. It does not guarantee higher energy density, lower cost or better resistance to physical damage. Pouches need protection against puncture and crushing. Self-discharge and memory behaviour are broadly those of lithium-ion.
Nominal voltage and charging limits depend on the particular chemistry and cell. Do not use a single voltage for every lithium-ion battery, and do not confuse rechargeable lithium-ion with primary lithium-metal cells.
Battery history moves from a pile to portable rechargeable cells
Battery history moves from a pile to portable rechargeable cells
The important sequence is the change in what batteries made possible.
Volta, around 1800: the voltaic pile made a sustained electrochemical source practical to demonstrate.
Gaston Planté, 1850s: lead-acid introduced a rechargeable battery.
Carl Gassner, 1880s: dry-cell development made the electrolyte easier to contain for portable use. “Dry” means immobilized electrolyte, not absence of moisture.
Waldemar Jungner, 1890s: nickel-cadmium added another rechargeable chemistry.
Lewis Urry, 1950s: work on the modern alkaline cell improved portable primary batteries.
Lithium-ion, 1990s: commercialization enabled rechargeable products with high energy per unit mass, building on earlier work by several researchers.
Supporting detail: Addendum 360 — Scope of this short chronology.
Engineering Fundamentals/Electrical Systems
Battery Capacity and Packs
Convert Ah to Wh, use C-rate and current to estimate performance, and predict the effect of series and parallel cells.
Ampere-hours measure charge; watt-hours measure energy; Practice
Ampere-hours measure charge; watt-hours measure energy
A 2 Ah cell and a 2 Ah battery can store very different amounts of energy if their voltages differ. Ah tells you charge. To estimate energy, you also need voltage.
Energy (Wh) ≈ capacity (Ah) × nominal voltage (V) Energy (J) = energy (Wh) × 3600
For an ideal 2.4 Ah, 3.6 V cell: 2.4 × 3.6 = 8.64 Wh, or 8.64 × 3600 = 31,104 J. Convert mAh to Ah by dividing by 1000 before multiplying by voltage.
Supporting detail: Addendum 361 — Why the battery estimate uses an approximate sign.
C-rate sets a current scale; load current sets ideal runtime; Practice
C-rate sets a current scale; load current sets ideal runtime
A discharge rate of 1C means a current numerically equal to the capacity in Ah divided by one hour. The rate has units of h−1. Here C is a rate notation, not the coulomb symbol.
Rated maximum current (A) ≈ maximum discharge C-rate (h⁻¹) × capacity (Ah) Ideal runtime (h) = capacity (Ah) ÷ load current (A)
A 2.4 Ah cell rated for continuous 3C discharge has a rated current estimate of 3 × 2.4 = 7.2 A. At a constant 1.2 A load, ideal runtime is 2.4 ÷ 1.2 = 2 h. At 3C, the ideal duration is one-third of an hour, or 20 minutes.
A C-rate may describe a test rate, a charge rate, a continuous limit or a short pulse limit. Only a specified maximum discharge rating belongs in the maximum-current equation. Actual pack limits may be lower because of wiring, temperature or protection hardware. A constant-power load also changes current as voltage changes.
Series adds voltage; parallel adds charge capacity
Series adds voltage; parallel adds charge capacity
For matched cells, connect cells in series to increase voltage. Put identical series strings in parallel to increase Ah at the same voltage. 3s2p means three cells per series string and two strings in parallel: six cells altogether.
Pack V = series count × cell V Pack Ah = parallel count × cell Ah Pack Wh ≈ pack V × pack Ah
With 3.6 V, 2.4 Ah cells, a 3s2p pack is 10.8 V, 4.8 Ah and 51.84 Wh. At 3C it has an ideal rated-current estimate of 14.4 A. A 1.2 A pack load gives 4 h ideal runtime.
This is an electrical model, not a pack assembly procedure. It assumes matched cells, balanced series operation and equal current sharing between parallel strings. Real packs need appropriate cell matching, interconnections and protection. See Series and Parallel Circuits.
Explore a pack by changing one input at a time; Interactive; Practice
Explore a pack by changing one input at a time
First double the series count: voltage and energy double, but Ah and runtime at the same pack current do not. Reset it, then double the parallel count: Ah, energy, rated current and ideal runtime double. The load current below is measured at the pack terminals.
Predict first: same current or same ideal power?
Before checking the results, predict whether ideal runtime will stay the same or double in each comparison, and explain what must happen to current. Start with 3.6 V, 2.4 Ah cells in a 3s2p pack at 1.2 A, then try two different meanings of “the same load”:
Same pack current: change only the series count from 3 to 6 and leave the load-current input at 1.2 A.
Same ideal nominal pack power: keep 6s2p, calculate I = P ÷ V = 12.96 W ÷ 21.6 V = 0.6 A, then enter 0.6 A in the existing load-current input.
Paper example: 3.6 V, 2.4 Ah cells; 3s2p; continuous discharge rating 3C; load 1.2 A.
With no JavaScript, use these equations to explore other packs. This example remains in the print view.
Check the fixed-current and fixed-power comparison
Same cells and parallel count, with two different load bases
Case
Nominal voltage
Capacity
Nominal energy
Pack current
Nominal load power
Ideal runtime
3s2p starting case
10.8 V
4.8 Ah
51.84 Wh
1.2 A
12.96 W
4 h
6s2p, same current
21.6 V
4.8 Ah
103.68 Wh
1.2 A
25.92 W
4 h
6s2p, same ideal power
21.6 V
4.8 Ah
103.68 Wh
0.6 A
12.96 W
8 h
Check: at the same current, both packs still have 4.8 Ah, so t = Ah ÷ I stays at 4 h while the 6s2p pack supplies twice the nominal power. At the same ideal power, twice the nominal voltage needs half the current, so the ideal runtime becomes 8 h.
The 6s2p case uses twelve cells instead of six and stores twice the nominal energy. The longer fixed-power runtime is not a free benefit.
This comparison assumes matched cells, constant nominal voltage, the stated Ah is available and the entered load is ideal. It does not predict changing discharge voltage, load or converter losses, reserve capacity, aging, cutoff or protection behavior. The model reports when the requested current exceeds the entered rating; a result below that rating is not a safety certification.
Choose solder, flux, and a tip that transfers heat, then prepare a stable bench and a tinned iron.
Solder melts; the parts being joined do not
Solder melts; the parts being joined do not
Soldering joins metal parts with a filler metal that melts below the parts' melting temperatures. It is closer to brazing than welding: the base metals do not melt. Electrical soldering connects wires, printed circuit boards (PCBs), and electronic components.
A good connection must be mechanically secure and conduct electricity. The molten solder must wet both surfaces: spread onto and bond with them, rather than sit on top as a ball. Clean surfaces, flux, and heat at both parts make that possible.
A temperature-controlled station regulates the iron's tip temperature. A basic iron may have no temperature control; a cordless iron changes how it is powered, not how a joint is made. Check the tool's instructions and choose settings suitable for the solder and components.
Tip shape and size matter. A fine point reaches small spaces, but a chisel's broad face often transfers heat more effectively. Use the largest tinned contact face that fits the joint without touching neighboring connections. Interchangeable tips let one iron handle different work; change them according to the tool's instructions.
Supporting detail: Addendum 362 — What the iron's “sweet spot” means.
Match the solder and flux to electrical work; Practice
Match the solder and flux to electrical work
Leaded solder: common tin-lead alloys melt at lower temperatures than common tin-copper or tin-silver-copper lead-free alloys. Leaded solder is still sold, but lead is restricted in many products. Follow the specified alloy for the work.
Lead-free solder: common electrical alloys use tin with copper and/or silver. They may need a different heating process and can solidify with a duller finish. “Lead-free” does not mean “no fumes.”
Diameter: fine solder wire makes it easier to meter a small amount into a small joint. Thick solder feeds more metal for the same length; it is easy to overfill a small pad.
Flux: helps remove surface oxides during heating so solder can wet the metal. Rosin-core solder carries flux inside the wire; additional compatible electronics flux may help. Do not substitute plumbing acid flux.
Read the alloy and flux label, including any residue-cleaning instructions. See Chemicals and Safety Data Sheets for handling information.
Helping hands or a PCB vise hold the parts still while your hands hold the iron and solder. Keep a proper stand or cradle within reach. Use a damp soldering sponge or brass wool for tip cleaning, and have solder wick (copper braid) or a desoldering pump available for removing excess solder.
It gets hot. Really hot. Park the iron in its stand, and allow the work to cool before touching it. Use ventilation or fume extraction that keeps the plume away from your face and other people; most visible fume comes from flux. Wash your hands after handling leaded solder, and do not eat or drink at the bench.
Supporting detail: Addendum 364 — Further reading on flux fume.
Clean, tin, and keep the working face coated
Clean, tin, and keep the working face coated
With the iron at working temperature, briefly clean the tip on brass wool or a damp soldering sponge. Apply fresh solder to coat its working face, then remove the excess on the cleaner. Leave a thin coating; do not wipe it bare and let it sit hot. Re-tin as needed and before storage as directed by the tool manufacturer.
Heat both parts, feed solder into the joint, let it cool without movement, and inspect the bond rather than its shine alone.
Heat both parts, then feed solder into the joint
Heat both parts, then feed solder into the joint
Prepare the iron and bench using Soldering Equipment and Setup. The iron heats the parts; the heated parts melt the solder. Touch the tinned working face to both wires, or to both the pad and the component lead. Feed solder into the joint, away from the iron's contact point when access allows.
Supporting detail: Addendum 366 — A one-second count is a rhythm, not a temperature test.
Work through the joint in this order; Checklist; Practice
Work through the joint in this order
1. Strip and clean. Expose only the conductor needed for the connection without nicking it. Clean the surfaces to be joined.
2. Support the parts. Form the connection and secure it so it cannot move during soldering.
3. Flux if needed. Use flux compatible with the solder and electrical work.
4. Heat BOTH parts. Put the tinned working face of the iron against both parts at the joint.
5. Feed solder into the heated joint. Let it wet both surfaces. Do not melt a blob on the iron and wipe it onto cold parts.
6. Remove the solder, then the iron. Stop feeding once the connection has enough solder and both surfaces are wetted.
7. Hold still while it cools. Let the solder solidify without moving the connection.
8. Inspect. Check wetting, coverage, clearance from adjacent connections, and damage before powering the circuit.
Look for wetting and shape; shine alone is not a verdict; Practice
Look for wetting and shape; shine alone is not a verdict
A good joint flows onto both surfaces. On a typical through-hole pad, look for a smooth transition from pad to lead, often a concave fillet (an inward-curving slope). Tin-lead joints are often shiny. A sound lead-free joint may be dull; dullness alone does not diagnose a cold joint.
Solder balls up or fails to bond to one surface, often because the parts were not heated adequately. A rough or dull appearance can be a clue, but inspect the contact and shape too.
Disturbed
The connection moved while solidifying, leaving a cracked or disrupted joint. Secure it before reworking.
Too much solder
A large mound hides the connection and makes bridges easier to miss. Remove excess so the joint can be inspected.
Too little solder
The intended connection lacks coverage or a continuous bond. Reheat both surfaces and add only what is needed.
Bridge
Solder joins connections that should be electrically separate. Remove it before applying power.
Keep the circuit disconnected. Secure loose parts, clean and re-tin the tip, and use compatible flux if needed. Reheat both surfaces to remake a poorly wetted or disturbed joint. Use wick or a pump to remove excess solder or a bridge; do not pry at a pad while the solder is solid.
Repeated heating can damage components or lift copper pads from the board. If a joint still will not wet, let it cool and get help finding the cause. Inspect again after repair. A continuity check can help find an open connection or an unintended short, but it does not prove mechanical strength.
Form a supported wire splice, insulate it with heat-shrink, or heat a circuit-board pad and lead together for a through-hole connection.
Make the splice mechanically sound before soldering; Practice
Make the splice mechanically sound before soldering
Solder should not be the only thing holding loose wires in position. Form a stable splice, support it during soldering, and provide strain relief so pulling or bending the cable does not load the soldered joint. Follow the wire and assembly requirements; these sketches show splice shapes, not a qualification standard.
Lay-over or lap: stripped ends overlap alongside one another. Support and strain relief are especially important because the overlap does not lock itself together.
Twist or pigtail: stripped ends twist together and leave the connection on the same side. Cover the joined end completely when insulating it.
Western Union: an inline connection with each free end wrapped around the opposite wire. It is a commonly used, strong splice when properly formed; it is not automatically the best choice for every wire or assembly.
Slide suitable heat-shrink tubing onto a wire before joining it, and keep it away from the soldering heat. After soldering, allow the joint to cool and inspect it. Move the tubing over all exposed conductor, overlapping intact insulation at both ends of an inline splice, then shrink it with the appropriate heat source according to its instructions.
Choose tubing whose unshrunk size passes over the splice and whose recovered size fits the wire. Avoid sharp wire ends that could puncture it. Ordinary heat-shrink provides insulation; do not assume it makes a waterproof connection or replaces strain relief.
Supporting detail: Addendum 368 — When pre-tinning helps.
On a PCB, heat the copper pad and component lead together; Practice
On a PCB, heat the copper pad and component lead together
A pad is the exposed copper connection area on a printed circuit board. A component's lead is its metal leg. In through-hole assembly, the lead passes through a hole in the board. Insert the correct component in the correct orientation and support the board and component before heating.
Place the tinned working face against both the pad and lead. Feed solder into the heated connection and let it flow onto both, then remove solder and iron in that order. Hold still while it cools. Inspect the joint and the gaps to neighboring pads.
Where the component's assembly instructions call for trimming, cut the excess lead above the cooled joint without cutting into the solder fillet. Wear the required eye protection and control the clipped end so it does not fly away or remain on the board. Do not shorten connector pins that must still mate with another connector.
Addendum 1. “It’s not the voltage that gets you, it’s the current”
The saying is true. What usually gets taken from it — that the voltage does not matter
— is not. Current is electricity actually moving through you, and it takes very little of
it to do real harm. Volts sitting on a wire nobody is touching do nothing at all.
Two things together decide how much current you get: how hard the electricity is being pushed,
which is what voltage measures, and how hard your body holds it back, which is called resistance.
Harder push, more current. More resistance, less.
Your resistance is not a fixed number — wet skin holds current back far less than dry
skin does, so the same push moves much more current through you. That half of it cannot be relied
on, which is why the line is drawn on the half that can be: the push.
Addendum 2. The international standards are not one number
On datasheets you will meet a different set of figures, and there the AC and DC limits
are not the same:
50 V AC / 120 V DC
Extra-Low Voltage under
IEC 61140 and IEC 60364-4-41 — 50 V AC rms, or 120 V
ripple-free DC. “Ripple-free” is a real condition, not a figure of speech:
past roughly 10 % rms ripple the supply is treated as AC and the lower number applies.
30 V AC / 60 V DC
Class ES1 in IEC 62368-1, the
standard behind most benchtop and consumer equipment. ES1 is the class that needs no safeguard
at all; ES2 runs up to 50 V AC / 120 V DC and requires one.
Addendum 3. All sixteen sections, and the four OSHA does not enforce
This is OSHA's own list, from Appendix D to 29 CFR 1910.1200. The numbers
and headings are fixed; a manufacturer cannot renumber them or reorder them.
Section 1
Identification — product identifier, recommended use and
restrictions on use, who made it, emergency phone number.
Section 2
Hazard(s) identification — classification, signal word,
hazard statement(s), symbol(s) and precautionary statement(s).
Section 3
Composition / information on ingredients — chemical name,
CAS number, and for a mixture, the ingredients classified as health hazards and how much of
each.
Section 4
First-aid measures — by route of exposure, plus the symptoms
that matter and when to get medical attention.
Section 5
Fire-fighting measures — suitable and unsuitable
extinguishing media, and what the chemical gives off when it burns.
Section 6
Accidental release measures — the spill response.
Section 7
Handling and storage — "conditions for safe storage,
including any incompatibilities".
Section 8
Exposure controls / personal protection — the OSHA
permissible exposure limit, the ACGIH threshold limit value, engineering controls, PPE.
Section 9
Physical and chemical properties — physical state, odor,
flash point, auto-ignition temperature, density, pH and the rest.
Section 10
Stability and reactivity — reactivity, conditions to avoid,
"incompatible materials", hazardous decomposition products.
Section 11
Toxicological information — the health effects and the data
behind them, including any carcinogen listings.
Section 12
Ecological information
Section 13
Disposal considerations
Section 14
Transport information
Section 15
Regulatory information
Section 16
Other information — "the date of preparation of the SDS
or the last change to it".
Twelve through fifteen are the odd ones out.
The headings have to be there: a note to the standard says an SDS "must also include the
headings" for those four, "in order", to stay consistent with the international
system the format comes from. What goes under them is a different question. Appendix D
says "Sections 12-15 may be included in the SDS, but are not mandatory", and a second
note to the same paragraph says "OSHA will not be enforcing information requirements in
sections 12 through 15, as these areas are not under its jurisdiction."
Those four cover the environment, waste, shipping and other agencies' regulations —
EPA and DOT ground, not OSHA's. So Section 13 tells you what the manufacturer suggests doing
with the leftovers. It does not tell you what happens to them here. Ask.
Two more things about the shape of the document. The section order is fixed
but the order within a section is not — preparers "are not required to
present the information in any particular order within each section", so two sheets can
look different inside the same numbered box. And a heading with nothing under it is not an
oversight: where there is no relevant information, "the SDS shall clearly indicate that no
applicable information is available." Read that as nobody has the data — not as
nothing to worry about.
Addendum 4. Signal words, pictograms and H-numbers — how Section 2 is written
There are exactly two signal words, and OSHA defines them in
1910.1200(c): a signal word indicates "the relative level of severity of
hazard", and "'Danger' is used for the more severe hazards, while 'warning' is used
for the less severe."
Severity is relative to the same kind of hazard, and that is the part that catches
people. Flammable liquids in OSHA's Appendix C are the clean example — all three
categories carry the same Flame pictogram, and the signal word is the only
thing separating them:
Category 1
Danger — "Extremely flammable liquid and vapor"
Category 2
Danger — "Highly flammable liquid and vapor"
Category 3
Warning — "Flammable liquid and vapor"
So “warning” does not mean mild. A Category 3
flammable liquid still catches fire. The signal word ranks a hazard against others of its own
kind; it is not a statement that the chemical is safe.
The pictograms are a fixed set of eight — a black symbol in a
red-bordered diamond standing on a point. OSHA names them: Flame, Flame Over Circle,
Exclamation Mark, Exploding Bomb, Corrosion, Gas Cylinder, Health Hazard, and Skull and
Crossbones.
The eight OSHA Hazard Communication pictograms
Flame
Flame Over Circle
Exclamation Mark
Exploding Bomb
Corrosion
Gas Cylinder
Health Hazard
Skull and Crossbones
The H-numbers are an index, not the warning. Real sheets often print a code
such as H225 beside a hazard statement. Those codes come from the international GHS
scheme this format is built on, which treats them as reference labels rather than as a
substitute for the statement itself. OSHA's Appendix C does not use them at all — it
specifies the sentence. Read the sentence.
Addendum 5. Telling a current sheet from an old one
Section 16 carries "the date of preparation of the SDS or the last
change to it." That is the only date on the document, and it is how you tell a live sheet
from one that has sat in a binder for a decade.
Keeping it current is the manufacturer's job, not yours. Under
1910.1200(g)(5), when a manufacturer or importer "becomes newly aware of
any significant information regarding the hazards of a chemical, or ways to protect against the
hazards, this new information shall be added to the safety data sheet within three
months."
Addendum 6. What makes a flammables cabinet “approved”, and how to spot one
OSHA calls it a storage cabinet and defines it by a fire test rather than by
how solid it looks. 29 CFR 1910.106(d)(3) requires cabinets to "limit the
internal temperature to not more than 325 °F. when subjected to a 10-minute fire test",
with all joints and seams staying tight and the door staying closed throughout.
The same paragraph requires the marking, which is the fastest way to recognise one:
"Cabinets shall be labeled in conspicuous lettering, 'Flammable - Keep Fire Away.'"
Addendum 7. The word for this, and where it comes from
“Nip point” is not shop slang. It is the term the machine-guarding standard uses.
29 CFR 1910.212(a)(1) requires guarding against “hazards such as
those created by point of operation, ingoing nip points, rotating parts, flying chips and
sparks.”
OSHA’s Machine Guarding eTool puts it plainly: “In-running nip point
hazards are caused by the rotating parts on machinery.” Its longer treatment,
Concepts and Techniques of Machine Safeguarding (OSHA 3067), gives three kinds:
“Parts can rotate in opposite directions while their axes are parallel to each other.
These parts may be in contact (producing a nip point) or in close proximity.” —
meshing gears.
“Nip points are also created between rotating and tangentially moving parts. Some
examples would be: the point of contact between a power transmission belt and its pulley, a
chain and a sprocket, and a rack and pinion.”
“Nip points can occur between rotating and fixed parts which create a shearing,
crushing, or abrading action.”
So belts, chains, sprockets and gears are rotating hazards by name. What makes them
dangerous is that they draw material in — not that two parts close on each other.
OSHA is just as direct about the plain shaft: “Rotating motion can be dangerous; even
smooth, slowly rotating shafts can grip hair and clothing, and through minor contact force the
hand and arm into a dangerous position.”
These parts are meant to be behind covers, and the standard is specific about it —
29 CFR 1910.219(f)(3): “All sprocket wheels and chains shall be
enclosed unless they are more than seven (7) feet above the floor or platform.”
Addendum 8. What the investigations actually describe
Oregon’s state fatality-investigation program, summarizing the record for this class of
machine: “The most common causes of death and injury from metal lathes include
entanglement of clothing in moving parts, being hit by loose objects on the lathe (e.g.,
chuck keys, tools, metal shavings) and being struck by a part that has not been adequately
secured.” (OR-FACE 2012-18-1, Experienced Journeyman Machinist Killed While
Operating an Engine Lathe, 2014.)
Four investigated deaths, all the same event — something attached to a person touched
something turning, and the machine did the rest:
Smoothing a part while it turned. A 69-year-old machinist with over 30
years’ experience “reached over the work piece to smooth out a radiused transition
with emery cloth and a file in hand” and “his loose clothing (left arm sleeve)
became entangled around the rotating work piece”. A co-worker 30 feet away heard “a
strange ‘winding-up’ sound”. Of that same part, the shop foreman had said that
“the rough surface could grab clothing or gloves”. (OR-FACE 2012-18-1.)
Stock sticking out the back of the spindle. A 52-year-old machinist was
set up on a 103-inch steel bar: “Due to the length of the material, 24 inches were
sticking out the back of the lathe, unguarded, and held in place with a clamping device that
rotates as the lathe rotates.” He reached across the running machine and “the sleeve
of his shirt became entangled”. (Kentucky FACE 21KY002, 2021.)
A burr on the end of the bar. A lathe operator in his twenties had a
1 7/8-inch stub of 1-inch bar standing past the tailstock. “The right pocket of his
shirt was caught by the rotating tailstock burr. His shirt wrapped around the stock and
tightened at the decedent’s neck and chest.” The listed contributing factor is
“walking to and/or reaching over unguarded rotating bar stock”. OSHA makes the same
point in general: the danger “increases when projections such as set screws, bolts, nicks,
abrasions, and projecting keys… are exposed on rotating parts.”
(Michigan FACE 14MI034, 2014; OSHA Machine Guarding eTool.)
A drill press. “As Employee #1 reached into the unguarded point
of operation, his shirt sleeve or gloves became entangled in the drill bit. Employee #1 was
pulled toward the machine, entangling Employee #1’s long hair. The drill press
continued to spin, completely pulling Employee #1 into the operating area.” She died
of her injuries. The same report records that the spindle “had speeds that ranged from 45
to 1115 rotations per minute”. (OSHA accident 114097.015, 20 February 2019.)
Why abrasive cloth keeps appearing. The UK Health and Safety Executive
publishes a sheet on this one task: “Every year there are serious accidents involving the
use of emery cloth on metalworking lathes. These accidents result in serious injuries such as
broken bones, dislocations, lacerations, amputations and occasionally death.” The mechanism
it names is the one above: “Accidents occur when hand-held emery cloth is entangled in the
rotating parts of the machine or where the emery cloth is snagged on the rotating component
dragging the operator into the danger zone.” Its own rules are that emery
cloth “should NEVER be applied directly by hand on manual metalworking lathes”, and
that gloves “increase the risk of entanglement and” are “never acceptable near
rotating parts of machinery”. (HSE Engineering Information Sheet No 2, rev 1,
2015 — that is HSE’s guidance; ask what the procedure is in the shop you are
standing in.)
And the drill press is not the exception it looks like. OSHA’s own
drill-press training script lists, among the ways accidents happen, “getting dangling
jewelry, loose clothing, or hair caught in the drill chuck (rotational hazard)”, and states:
“The primary hazards of drill presses are contact at the point of operation and
rotational hazards. An operator can risk serious hand injury when working too
close to the drilling area, wearing gloves, loose clothing, loose hair, or jewelry.”
Addendum 9. Why belts and chains count as rotating, not pinching
OSHA sorts machine hazards by the motion that causes them, and “pinch point” is
the vocabulary it attaches to parts that travel, not to parts that turn. From
Concepts and Techniques of Machine Safeguarding (OSHA 3067):
Reciprocating motion — “Reciprocating motions may be hazardous
because, during the back-and-forth or up-and-down motion, a worker may be struck by or caught
between a moving and a stationary part.”
Transverse motion, which means movement in a straight continuous line
— “Transverse motion (movement in a straight, continuous line) creates a hazard
because a worker may be struck or caught in a pinch or shear point by the
moving part.”
A belt on a pulley is a rotating hazard that draws material in; a table running up against a
column is a moving hazard that closes on it. Both can take a hand, and the vocabulary is worth
keeping straight because the two do not have the same tell. You avoid the first
by giving it nothing to grip. You avoid the second by knowing where the gap is going.
Guarding is not a local preference. 29 CFR 1910.212(a)(1) —
quoted already in Rotating machinery above for its definition of a nip point — is
a guarding requirement first: one or more methods of machine guarding shall be provided to
protect the operator and other employees from hazards including those created by point of
operation, ingoing nip points, rotating parts, flying chips and sparks.
The reason a rule like this is written without exceptions is that the exceptions are exactly
where people get hurt. A guard comes off for a legitimate setup, the setup takes longer than
expected, somebody else walks up to a machine that looks normal and is not. The standard's own
answer to “but this task genuinely needs the guard off” is not a more
careful operator — it is Lockout/Tagout, the next card on this page, which is
a procedure rather than a permission.
29 CFR 1910.147(a)(1)(i): “This standard covers the servicing
and maintenance of machines and equipment in which the unexpected energization or start
up of the machines or equipment, or release of stored energy could cause injury
to employees.”
Two things are worth reading twice. Unexpected is the whole point — the
hazard is not that the machine runs, it is that it runs while someone has a hand inside it. And
stored energy is named alongside energization, because a machine that has been
switched off and unplugged can still contain everything it needs to move once.
“Servicing and maintenance” is much broader than it sounds. The standard defines it
as “constructing, installing, setting up, adjusting, inspecting, modifying, and
maintaining and/or servicing machines or equipment”, and adds: “These
activities include lubrication, cleaning or unjamming of machines or equipment
and making adjustments or tool changes, where the employee may be exposed to the
unexpected energization or startup of the equipment or release of hazardous energy.” Setting
up, clearing a jam and changing a tool are all on that list.
Stored energy gets its own requirement — 1910.147(d)(5)(i):
“Following the application of lockout or tagout devices to energy isolating devices, all
potentially hazardous stored or residual energy shall be relieved, disconnected, restrained, and
otherwise rendered safe.” The lock comes first, and then the energy already in the machine
is dealt with. Both, in that order.
Addendum 12. Why the chuck key rule is worded as a grip and not as a reminder
A key left in a chuck is launched the instant the machine starts. Written as
“remember to remove the key” the rule depends on you remembering at the one
moment you are busy with something else; written as the key never leaves your hand there
is nothing to remember, because a key that is still in the chuck is still in your hand and you
cannot start the machine.
Do not let a spring be the thing that saves you. Some chuck keys are
spring-loaded and eject themselves when you let go — ours are, on the lathe. Not all keys
are, and our Jacobs chuck keys are not. So the habit has to be the same on every
machine, or it is a habit that works until you walk up to a different chuck.
A drill-press chuck key is lighter than a lathe chuck key and carries far less energy. It is
still dangerous: it is in the list of things that become projectiles in Rotating
machinery above, and “less mass” is not the same as “will not hurt you”
when it leaves a spinning chuck at the distance you are standing.
Addendum 13. Why dry sand is on the list, and why it is probably not on yours
Sand does work. The Aluminum Association’s Guidelines for Handling Aluminum
Fines (F-1) lists fine dry sand, “preferably finer than 20 mesh,” next to
approved dry powders as effective for isolating an aluminum fines fire. It also says
what has to be true first.
Dry. F-1 says dry sand. Damp sand is water, and water
“will react with the aluminum fines to form flammable hydrogen gas.”
Already in the room. “A plentiful supply should be easily available
in the operating area and stored in covered bins or drums.” Sand fetched after the fire
starts is not that.
With the right tool waiting beside it. “Long handled shovels should
be available at each bin or drum, and should be constructed of non-sparking metal.”
Laid, not thrown. The shovels “lay the sand or powder around the
edge or perimeter of the fire.” You are walling it in. Anything thrown at the pile
raises the dust cloud that is the actual explosion.
Decided before it started, by someone senior. “Qualified
supervisory personnel should decide in advance whether it is better to attempt to fight the
fire or to withdraw to a safe location and allow it to burn itself out.”
Those are preconditions, not tips. If you cannot point at the covered sand bin and
the non-sparking shovel beside it right now, you do not have this option — and
the call to fight it was never yours to make on the spot. Alarm, evacuate, report.
Addendum 14. Why context matters more than one dash
Short center marks may look different from long axes, and reduced drawings can make small
gaps hard to see. Use a circle, an axis in another view, a section label, or an attached note
to confirm the reading. If the supplied drawing is illegible, obtain a readable copy.
Addendum 15. Why one view can hide an entire change in shape
Looking from the front collapses depth. A shallow block and a deep block can have identical
front outlines. Looking down on them separates those possibilities. Even three matching
outside outlines do not prove that internal holes or recesses are identical; hidden lines,
sections, dimensions, and notes still matter.
Addendum 16. Why more pictures do not automatically mean more information
Repeated information takes space and creates more places for a revision to disagree.
A useful additional view makes something clearer: shape, depth, location, or access to a
dimension. A pictorial can help orientation, but it does not automatically replace the
views and callouts needed to define the part.
The historical NASA GSFC manual (1994), §3.1
explicitly permits one or two views when they completely define an object. Its §3.5 describes
sections, auxiliary views, and details. This is a useful design principle, not a claim that
that manual governs every drawing.
Addendum 17. Use the glass box to explain the swap
In third-angle projection, the viewing plane is between the observer and the object.
In first-angle projection, the object is between the observer and the viewing plane.
Unfolding those planes places the named views on different sides of the front view.
The angle names refer to projection quadrants. They do not mean rotating the part by
one degree or three degrees, and they do not specify the number of views.
Addendum 18. A documented U.S. example, with its scope
The NASA Goddard Engineering Drawing Standards Manual (1994), §3.1, printed p. 25
states: Third-angle orthographic projection shall be used for mechanical engineering drawings.
That is a requirement in that manual, not proof that every U.S. drawing uses third-angle.
Autodesk's Fusion documentation gives a current software example: its ASME drawing setting
uses third-angle projection. Bricsys's projection-type reference
likewise identifies third-angle with U.S. practice.
Addendum 19. Isometric drawing and isometric projection use different scales
An ordinary isometric drawing lays out axis-parallel lengths at the chosen drawing scale. A geometrically projected isometric view foreshortens all three axes equally. Do not mix an isometric projection scale with ordinary drawing lengths in one sketch. The angle of a drawn edge on the paper is not generally its angle on the part.
Addendum 20. One drawn line can represent several boundaries
The edge view of a surface can coincide with the outline of another surface. A line is therefore not a unique surface label. Match its endpoints and the surfaces meeting there using another view. The colored areas and heavy highlighted segments here are teaching aids, not extra physical edges.
Engineering Graphics and CAD/Reading Drawings/Section Views
Addendum 21. How the explorer decides what is hatched, and its sources
Each part is built from boxes and round features with vertical axes. The explorer cuts that solid exactly along the plane: the cut face shown on the 3D part and the hatching in SECTION A–A come from the same computed region, and holes inside it remain gaps. The view then shows the first surface you meet looking in the arrow direction. A line is drawn where that surface changes, and where the cut face meets a surface beyond the plane. In an offset section, the cut faces at the two legs are drawn as one face, with no line at the jog. A half section shows the outside on one side of the center line and the section on the other.
Engineering Graphics and CAD/Reading Drawings/Section Views
Addendum 22. Drawing standards and scope
These are introductory conventions, not clause quotations. The current edition of ASME Y14.3 and related drawing standards governs formal work, subject to the edition invoked by the drawing or contract. Consult that edition for exceptions and exact line requirements. Do not identify a material solely from generic diagonal hatching.
Addendum 24. When one auxiliary view is not enough
An oblique face is inclined to all three principal projection planes. It is not seen on edge in any of them. An initial auxiliary view can establish an edge view, followed by a secondary auxiliary view showing true shape. That two-stage construction is different from the primary construction below.
For formal conventions, consult the current ASME Y14.3 and related standards, using the edition invoked by the drawing or contract. These introductory explanations do not quote clauses. Continue through the Engineering Graphics and CAD collection for dimensioning topics.
Addendum 26. Which parts are standards, and which are layout guides?
ASME Y14.5 governs dimensioning conventions; its spacing guidance allows for legibility and reproduction. The current edition governs new ASME work unless the drawing or contract specifies another edition. ASME currently lists Y14.5-2018 (R2024). These pages explain conventions in plain words rather than reproducing the standard. For an existing drawing, read its stated standard and revision.
Addendum 27. Why older drawings may look different
Aligned text rotates with the dimension line. You may meet it on older drawings and in other drafting systems. “Old” and “new” alone are not enough to identify the applicable rule. These examples use the ordinary ASME orthographic convention; specialized coordinate dimensioning has additional presentation rules.
At the nominal values a closed chain may add up perfectly. Real parts vary within permitted limits, so the extra requirement can conflict with otherwise acceptable sizes. Changing one value also risks leaving its duplicate unchanged. The theory belongs in Tolerances and Fits.
Legacy notes may say .30 DIA, .55 DP, C'BORE, C'SINK or SP FACE. Modern symbol notation moves that meaning into the symbols shown above. A through hole may be clear from the drawing without THRU, but an isolated diameter value does not prove a through condition. Read the views and notes together.
Use the standard and edition named on the drawing. The current ASME edition governs new ASME work unless another edition is specified; the ASME catalog lists Y14.5-2018 (R2024). A reference sheet headed “current 2009” is historical, not evidence of today’s edition. Surface finish requirements are a separate language: see Surface Texture and Finish.
A model can reveal a space conflict that was hard to see in a sketch. A prototype can reveal a behavior that the model did not predict. These findings can send the team back to the geometry or even to the original concept. Sketches remain useful during refinement; drawings can be drafted before the design is final.
Addendum 31. Does every design require a separate drawing?
Some workflows communicate requirements through an annotated model and associated data. Others use drawings as the controlling documents. Follow the agreed deliverables and identify which information governs. A plain shaded model does not automatically communicate material, tolerances, or approval status.
Addendum 32. Find the commands in your CAD version
Start with the vendor's Onshape drawing help or SOLIDWORKS Help, selecting your installed release where applicable. Consult its drawing creation, projected view, dimension, and update topics. Command sequences are intentionally kept generic here.
A component may live outside the folder you copied. SOLIDWORKS File Utilities describes Pack and Go and tools that update references when files move or change names.
Addendum 36. Why this lab does not imitate a folder copy
A plain folder copy can omit a component stored elsewhere, but real reference resolution is more complicated than matching visible filenames. This local in-memory lesson predicts a declared graph only. It does not claim that copying these names would repair a real design, and it does not model Onshape documents, cloud permissions, or PDM-managed identities.
Addendum 37. Viewing direction is separate from drawing layout
A standard view tells you where you look from. First-angle or third-angle projection tells you where that view belongs on a drawing sheet. Explore the geometry in Orthographic Projection and the Glass Box. An angled model view is useful for recognizing shape but is not a substitute for dimensions.
Onshape camera and render options links to navigation and display controls. Current browser controls can separate shading choices from hidden-edge choices; older outlines may list them as combined styles.
Addendum 41. Rollback follows the regeneration sequence
SOLIDWORKS Rollback Bar help explains moving through the feature sequence. A file can be saved with its bar rolled back, so inspect the bar's position when reopening a model.
Addendum 42. Viewing history, restoring, and branching serve different purposes
Viewing an earlier state is inspection. Restoring changes a workspace back to an earlier state. Branching gives you a separate place to continue editing. Check the active workspace before any restore or merge. See Onshape Versions and History and Document Management.
Onshape creates sketches in a Part Studio and lets you choose a plane, a planar part face, or a mate connector that supplies a coordinate system. This page uses ordinary planes and faces. See Onshape: Sketch Basics.
Addendum 44. Find the tools by their software names
Onshape names include Line, Corner rectangle, Center point rectangle, Center point circle, 3 point circle, Tangent arc, 3 point arc, Spline, Point, and Construction. Its Slot tool builds around selected sketch curves. See Sketch Tools and Slot. These names describe ways to create geometry, not different rules for constraining it.
Addendum 47. Why horizontal plus vertical can already supply a right angle
A horizontal line and a vertical line already have perpendicular directions. Adding a 90-degree driving dimension can duplicate the existing control. Check the stored rules first. See Onshape: Working with Constraints.
Addendum 48. Check the circular relation definitions
See Onshape's Concentric and Equal. The SOLIDWORKS 2025 relation table correctly places the coradial definition; the 2026 table misplaces its center-and-radius sentence under Perpendicular.
Addendum 51. Why subtracting one per relation gives wrong answers
Coinciding a free point with a fixed point supplies two coordinate conditions. Putting a free point on a fixed line supplies only one. A repeated rule may supply no new independent condition. These counts assume ordinary, nondegenerate geometry: nonzero line lengths and positive radii. At special configurations, independent equations and usable motion require more care; do not assign a universal DOF reduction to each icon.
Addendum 52. Software treatment of redundant dimensions
SOLIDWORKS can make a redundant dimension driven; its geometry-status help describes the driven dimension as gray. Onshape's Dimension tool distinguishes driving from driven dimensions and documents the automatic conversion. See Sketch Geometry Status and Onshape: Dimension.
Addendum 54. Redundancy is not the same as contradiction
A repeated condition may agree mathematically yet be rejected as a second driving control. Some redundant geometric relations are tolerated: SOLIDWORKS documents a redundant perpendicular relation that leaves a sketch fully defined. Do not assume that every extra icon causes an error. See SOLIDWORKS: FAQ Sketch Relations and Onshape: Working with Constraints.
Addendum 55. Why a small edit can break a later feature
A face or edge can disappear when the shape changes. A sketch attached to that face, or a fillet attached to that edge, then has a missing reference. Repair the first failed feature before chasing errors farther down the tree. Reordering is constrained by dependencies: a feature cannot use geometry that has not yet been created.
Addendum 57. Fewest features is not always the best model
A single complicated sketch can hide many unrelated decisions. Several named features may be easier to edit. Count features only after stating which operations are allowed and what the model must do when changed. A feature tree is also not a manufacturing operation sheet: a CAD cut does not specify tooling or setups.
Addendum 59. Closed profiles, thin features, and surfaces
Closed regions are the simplest starting point for solids. Open sketches can be used with thin-feature or surface options, but those are different constructions: a surface has no solid volume, while a thin feature adds a wall thickness. Check the result type before accepting the preview. See Onshape: Extrude.
Addendum 61. Check overlap and axis selection before adding complexity
A section that crosses the axis, overlaps itself during rotation, or creates zero-thickness contact can fail. Simplify the section, verify its closure and axis, and inspect a small-angle preview. For the command entry points see SOLIDWORKS: Sketching with Extruded or Revolved Bosses/Bases. A turned part may suggest a revolve, but CAD history does not specify a lathe process; see Lathe Operations.
Addendum 62. More profiles do not automatically make a better surface
Extra sections and guides can introduce unwanted waves or conflicting conditions. Start with the fewest that describe the intended shape, then add a control for a specific problem. Profile and guide rules vary with solid, surface, and thin options. See Onshape: Loft and SOLIDWORKS: Description of Sketch Relations.
Addendum 63. Copied geometry and recalculated end conditions can differ
Onshape feature patterns have a Reapply features option for regenerating the seed's dependencies and end conditions at each instance. A seed that ends at a sloping face may need different geometry at each copy. Do not assume every pattern automatically recalculates that boundary. See Linear Pattern and Circular Pattern.
Addendum 65. Definitions, instances, and design changes
Changing a shared part definition can update several instances. Moving one instance in an assembly changes its placement, not the shape of every copy. A configuration can select a particular variant of a component; record the intended variant when sharing or drawing it.
SOLIDWORKS: Renaming Components distinguishes display names from file names and explains updating references in closed documents. Saving an open assembly alone does not automatically repair every closed drawing. Availability differs for platform-connected installations.
SOLIDWORKS: Pack and Go Overview describes collecting related files into a folder or ZIP. Use your installed edition's help for the exact controls.
Addendum 68. Why subtracting one DOF per mate gives the wrong answer
For one free rigid part relative to a grounded part, a planar-face coincident mate leaves three DOF. A cylindrical-axis concentric mate leaves two. Adding a shoulder-face coincident mate perpendicular to that axis removes axial sliding and leaves one rotation. A redundant mate may remove no new freedom. Count the independent motions that survive each step.
See SOLIDWORKS: Types of Mates for supported selections. These geometric names are not a one-to-one map to Onshape commands.
SOLIDWORKS: Top-Down Design explains how layout or other-component geometry controls a feature and creates external references. Merely editing a part while an assembly is visible does not by itself establish that dependency.
Addendum 71. Library hardware still needs checking
Onshape: Standard Content explains insertion and sizing. SOLIDWORKS Toolbox is an add-in described in its machine-design overview. Check the resulting model and BOM properties rather than modeling every thread from scratch.
Addendum 73. A joint preview is not always a full-assembly test
Onshape: Mates distinguishes the mate-dialog preview, which can ignore other mates, from assembly animation. Use a whole-assembly check to assess the connected mechanism.
Onshape: Exploded Views describes saved explode steps and selecting the result in a drawing. An exploded presentation does not demonstrate that the parts can physically be installed in that order; check access separately.
Onshape: BOM Table describes inserting the assembly's BOM and using balloons to pull its identifiers. Keep the drawing, table, and view tied to the same intended design state.
Addendum 76. Subassembly display changes what the table means
Onshape: Bill of Materials documents structured and flattened views and subassembly BOM behavior. A hidden or excluded row can change what the reader sees, so review the table's scope instead of trusting a row count alone.
Addendum 77. Why matching mass does not prove the shape is right
Different shapes can have the same volume and density, and therefore the same mass. A missing cut and extra material removed elsewhere can cancel numerically. Treat mass as one independent check alongside dimensions, feature locations, and drawing views.
Addendum 78. Vocabulary, brand attribution and source scope
ISO/ASTM 52900:2021 is the current fundamentals-and-vocabulary standard and describes additive shaping as successive addition of material. Its public abstract does not reproduce the full family list. The family structure and readable mechanisms here are checked against the NIST AM technology overview and the seven-family discussion in ORNL's Additive Manufacturing Design Guidelines. Stratasys's legal terms identify FDM as a registered trademark and PolyJet as a trademark; its PolyJet technology page documents the bounded photopolymer-droplet, UV-cure and support example used here. This page paraphrases sources and uses original graphics rather than copied standard or vendor art.
Addendum 80. Why the support statement is qualified
Ohio State's laser-PBF research summary explains support structures used to anchor overhangs and address thermally induced distortion in that context. A current Colibrium EB-PBF example documents process strategies that reduce or eliminate traditional supports for some applications. The exception is why this page states a case rather than an absolute.
Addendum 81. STL and 3MF carry different information
STL represents the surface with triangles and does not record a unit of length. A 3MF file can carry units and multiple objects; a slicer's 3MF project can also carry settings. Support for those extra settings varies between applications. Neither filename alone proves a job is ready for your printer. Prusa documents saving projects as 3MF and its supported file formats.
Addendum 82. Why more infill does not solve every strength problem
Material near the outside can be especially useful when resisting bending. Infill also supports top surfaces and can help resist compression. The useful balance depends on the load and shape. Prusa's infill guidance discusses these different roles.
Addendum 83. Where the threshold and the load rule come from
PrusaSlicer's overhang threshold is measured the same way as here: Prusa's support material guide calls it "the most horizontal slope (measured from the horizontal plane) that you can print without support material." Prusa's modeling guide says printers can cleanly print overhangs at "an angle between 45 and 60 degrees, depending on your nozzle diameter and settings," and warns that a fillet facing the bed creates a steep overhang. That is why 45° is only a starting value here.
Ahn and colleagues measured FDM ABS specimens and found that strength depends on the direction of the deposited roads; their first build rule is to "build parts such that tensile loads will be carried axially along the fibers" (S.-H. Ahn et al., Anisotropic material properties of fused deposition modeling ABS, Rapid Prototyping Journal 8(4), 2002). The tool shows only the direction; it gives no strength values.
The build-direction convention follows ISO/ASTM 52900: for planar layer-by-layer processes, the positive z-direction runs normal to the layers, from the first layer to later ones.
Addendum 84. Why a hairline is a workflow setting, not a cutting guarantee
The teaching deck uses hairline strokes for vector cuts and strokes of at least 0.5 pt for raster content. Preserve those values only when the specified driver procedure calls for them. Stroke width alone does not establish cut depth, material suitability, or a safe setting.
Addendum 85. Manufacturer guidance for selecting a starting setup
Epilog's material settings guidance treats its recommendations as starting points. A settings table cannot identify an unknown sheet or replace approval for a material.
Epilog's Fire Warning (Fusion Ascent manual, p. 1) states the unattended-operation prohibition and warns that PVC produces toxic and corrosive gases. These are process-specific limits, not a claim about this shop's inventory.
Addendum 87. Why there is no universal minimum wall or perfect press-fit allowance
Printer paths depend on nozzle and profile; laser edges depend on the sheet and setup. Material batches and finishing change dimensions too. A small test of the critical feature supplies evidence that a generic dimension cannot. Use Tolerances and Fits to distinguish the intended size from acceptable variation.
Addendum 88. Why one feed rate does not fit every cut
Thickness, wood, blade and available power change how readily material cuts. Pushing harder does not fix binding or a poorly chosen setup; it can make control worse.
Addendum 89. Why thickness matters as well as material
A thin section needs enough teeth engaged to avoid snagging; a thick section also needs room between teeth to carry chips away. Select the blade for both conditions rather than assuming all metal needs the same high TPI.
Addendum 90. Why larger drills usually need fewer revolutions per minute
At the same spindle speed, a larger bit's outer edge travels faster. Diameter, work material and bit material all affect the speed choice. “Larger or harder means slower” is a starting trend, not a speed setting.
Different industries draw the primary/secondary boundary differently. Here, use the raw-resource-to-stock and stock-to-part distinction. Extraction supplies the raw resource; mining alone does not turn ore into an ingot. A supplier's finished product can also be the next manufacturer's starting material.
Addendum 92. A laser cut does not have to vaporize all the removed material
Material may melt and be expelled from the cut; vaporization can also contribute. The classification depends on removal, not on which thermal mechanism dominates. TWI explains melt removal in laser cutting.
Addendum 93. Why another book may show a different family list
Other books may give composites a separate family, split glass from ceramics, or organize materials by bonding and structure. This collection keeps the instructor's four-family model. Engineered composites belong within Wood & Composites, including composites with no wood in them.
Some materials fit more than one description. In the course's examples, plain concrete sits with Ceramics & Glass; steel-reinforced concrete illustrates Wood & Composites when the combined material system is the subject. Concrete itself also has a composite structure. State what is being classified rather than treating these labels as mutually exclusive scientific definitions.
Addendum 94. A supplier value that checks the floating claim
Plaskolite's OPTIX acrylic data lists a relative density of 1.19, with water as the comparison. This supports the conclusion that a solid piece is denser than water. Family descriptions are screening guides; use the actual grade's data for a design.
Addendum 95. Hard to machine does not mean impossible to machine
Corning's MACOR glass-ceramic is specifically designed for machining with conventional metalworking tools. That is a useful counterexample to a blanket claim that ceramics cannot be worked after forming.
Addendum 96. Stress, strain and modulus give the comparison units
For a simple axial test, engineering stress is force divided by original cross-sectional area. Engineering strain is change in length divided by original length. Stress has units such as MPa; strain is a ratio with no unit.
In a linear elastic region, the slope of stress against strain is Young's modulus, a measure of material stiffness. Yield strength concerns permanent deformation; ultimate tensile strength is the highest engineering tensile stress reached in the test. A nonlinear curve does not, by itself, prove that a material has no yield behavior.
Addendum 97. Why a single “toughness number” needs its test method
The area under a tensile stress–strain curve through fracture measures energy absorbed per original volume in that test. Impact tests and fracture-toughness tests describe related but different behavior. Temperature, loading rate and flaws can change the result, so compare like tests.
Addendum 98. Not every material has one useful melting-point number
Pure crystalline substances can have a sharp melting point; many alloys melt over a range. Glass and amorphous thermoplastics soften over a range rather than showing a sharp crystalline melting transition. Thermosets and wood decompose rather than melting into a reusable processing liquid. Use material-specific processing and service data.
Addendum 99. Softening, melting and heat resistance are different questions
Some thermoplastics soften over a range rather than having one sharp melting temperature. A part can lose stiffness and fail under load well before it flows. Thermosets also have service-temperature limits: being unable to remelt does not make them heatproof. Use the grade's data sheet for the actual load and temperature.
Addendum 100. Why a short strength test does not settle a long service life
Temperature, time, moisture and chemicals can change both dimensions and load-carrying ability. A part that survives a brief pull may still creep over months. Curbell's dimensional-stability guide connects these effects to material selection.
Addendum 102. Where the resin comparison comes from
The American Composites Manufacturers Association guide, Appendix D, compares composite resin systems. The resin holds and transfers load between the reinforcing fibers; the fibers and their orientation strongly affect the resulting composite.
The number-to-material matches are published in the City of Sioux Falls RIC guide. The PET Resin Association consumer guide supplies the familiar label terminology. Checked October 27, 2026. This is an identification reference, not a specification for manufacturing compliant labels.
A shallow depression opposite a heavy rib suggests sink.
Scraping during release suggests inadequate draft or another ejection problem.
A sudden thick-to-thin step suggests uneven cooling and difficult filling.
Protolabs' defect guide illustrates these relationships. Wall and draft requirements depend on resin, texture, depth and tooling; no single angle or thickness fits every part.
Addendum 113. Find the quantity where the two estimates are equal
Set total costs equal: 900 + 14N = 18000 + 2N. Then 12N = 17100, so N = 1,425 parts. Below that quantity A costs less; above it B costs less under these assumptions.
This model leaves out financing, mold replacement, setup changes, inspection, shipping and rejects. A flexible mold that must be replaced during a run adds another tooling cost. Recalculate when the assumptions change.
Addendum 115. Why a slower cut can produce more heat
A tooth that advances too little spends more time sliding against the work. The next tooth may also recut trapped chips. Useful chips carry some heat away, so reducing chip thickness without reducing rubbing is not a reliable cooling strategy. ACRYLITE's drilling guidance identifies low feed or excessive RPM as causes of melted chips; its routing guidance treats feed, cutting edges and RPM together.
Addendum 117. Why a clean-looking bond can peel off
The bond is only as good as the material it touches. Mold-release residue, oil or an unsuitable coating can become the weak layer. Peel loads concentrate force at an edge; an overlapping joint can distribute load more effectively, although its dimensions still need validation. 3M explains low surface energy, and its bonding guidance shows why PE and PP are difficult, rather than impossible, to bond.
Addendum 118. Why heat alone does not guarantee a strong or sealed weld
Temperature, force, time and joint fit work together. Too little heating leaves an unfused interface; excessive heating can degrade the polymer. Ultrasonic joints often use a small molded ridge, an energy director, to concentrate heating. A continuous-looking bead does not prove a leak-tight seam. Leister's extrusion-welding guidance identifies matching filler and joint geometry; Dukane's Guide to Ultrasonic Plastics Assembly explains energy directors for ultrasonic welding.
Addendum 119. Insert dimensions come from the chosen insert system
SPIROL's hole-design guidance explains how oversized holes reduce performance and undersized holes can introduce stress or cracks. Its insert design guide distinguishes heat-installed thermoplastic inserts from other installation methods.
Materials and Manufacturing Processes/Plastics/FDM 3D Printing
Addendum 120. Where additive manufacturing fits the five course categories
This course uses purpose to choose a primary category. Additive shape-building is Forming because creating the shape is the intended result; bonding between deposited roads is a secondary fabricating effect rather than joining previously separate parts. Other technical taxonomies organize these processes differently. The standard AM family name here is material extrusion. Subsequent support removal is Separating; annealing is Conditioning; sanding or painting is Finishing.
Materials and Manufacturing Processes/Plastics/FDM 3D Printing
Addendum 121. Material guidance is grade-specific
Filament names describe families, not identical recipes. Pigments, fillers and blends change behavior. Prusa's material guide separates common filament families and their printing requirements. It does not establish what any particular shop printer can process.
Addendum 122. Stress relief and crystallinity are different changes
Residual stress is locked-in stress remaining after manufacturing. Heating can allow molecular motion that relaxes it. Some polymers, including PLA, can also develop more ordered regions during suitable heat treatment. Acrylic stress relief and PLA crystallization therefore do not share a universal temperature recipe. ACRYLITE's annealing guidance describes stress relief for its sheet. Prusa's annealing experiments show why dimensional change must be checked on printed specimens.
Addendum 123. Other ways processors change plastic properties
Industrial radiation treatment can crosslink selected polymers, but the result depends on the polymer and dose; some systems also undergo chain breakdown. Additives and reinforcements usually enter during material formulation rather than as a finishing step on a completed part. Fibers can increase stiffness, meaning a higher elastic modulus in the relevant direction, not a lower one. These changes require grade-specific data.
Surface treatment can leave stress or expose existing stress to a solvent. Fine cracks may appear during later cleaning or bonding. ACRYLITE's edge-finishing guidance discusses polishing and compatibility; Prusa's ABS guidance identifies acetone smoothing for ABS. Choose a verified material/process pair, then check both appearance and fit.
Addendum 125. Powder coating needs a complete substrate and cure system
Interpon's heat-sensitive-substrate overview distinguishes powder-coating systems for heat-sensitive substrates, including thermal and UV curing approaches. A conventional metal-part powder cure is not a default recipe for a plastic part.
Addendum 126. What makes the cell walls work together?
Cellulose reinforces the cell wall, while lignin and hemicelluloses help form its surrounding structure. This is a useful natural-composite analogy, but a tree is more complex than fibers suspended in glue. Cell arrangement, moisture, knots, and grain direction all affect a real board.
Most commercial hardwoods have vessels, visible as pores in end grain, along with supporting fibers. Softwoods rely mainly on long cells called tracheids for support and water transport. These differences influence appearance and processing, but do not make every member of either group behave alike.
Addendum 130. Why the mixed-unit formula divides by 12
Convert the length in feet to inches by multiplying by 12. Dividing the resulting cubic inches by 144 gives 12/144 = 1/12. The formula counts 144-cubic-inch units; it is not a linear-foot conversion.
Addendum 133. Why tooth geometry changes the surface
Across the grain, fibers can break beyond the intended cut if they are pushed away before being severed. Beveled teeth help slice those fibers. Along the grain, chip removal is a major concern. A blade's tooth shape, spacing, sharpness and feed all affect the result; tooth count alone does not identify its job.
Ridge Carbide Tool's saw-blade design glossary defines gullet, kerf and hook angle; its top-grind guide compares tooth shapes. Choose a blade specified for the machine and cutting application.
Addendum 135. Why “router bit” is more useful than “end mill” here
CNC routing can use end-mill-like spiral cutters, but routing also includes bearing-guided and shaped profile bits. “End mill” alone does not describe the tooling a beginning woodworker will encounter. Whiteside's template-bit range illustrates tooling for following patterns; its catalog also includes straight bits, flush-trim spiral bits and roundover profiles.
Addendum 136. Why a planer alone can preserve a bow
Feed rollers can press a bowed board flatter during the cut. When the pressure is released, the board can spring back. Uniform thickness and flatness are different requirements. Specialized fixtures can provide a reference for other methods, but the sequence here assumes an ordinary jointer and thickness planer.
Moisture lowers the temperature at which the wood's matrix softens. This is why moist heat can make wood bendable without melting it. The USDA Forest Products Laboratory's Wood Handbook chapter on specialty treatments discusses plasticizing wood. Its Bending Solid Wood to Form compares species and bending conditions.
Addendum 138. Why the indoor moisture target depends on the building
The handbook's interior recommendations were developed from well-ventilated buildings without unusual moisture sources or air conditioning. Air conditioning and other building conditions can change the appropriate target. These are installation guidelines, not a universal kiln-drying specification; see Recommended Moisture Content, page 13–3.
Addendum 139. Why dividing by the initial mass answers a different question
30 / 230 × 100 = 13.0% gives the water fraction of the initial sample, not wood moisture content on the oven-dry basis. Wood MC can exceed 100% when water mass exceeds dry wood mass. The calculation does not set a suitable target for furniture. An actual oven-dry determination requires an appropriate laboratory method and equipment; these exercises provide the dry mass.
Addendum 140. What “stronger than the wood” actually demonstrates
In a well-made joint tested under a particular load, failure may occur in the surrounding wood rather than at the bond line. That shows the bond outlasted that wood under those conditions. It does not show that every adhesive joint exceeds every strength of wood, or that an end-grain butt joint is as strong as an uncut member. Grain direction, stress type, moisture, temperature and time under load can change the result.
Addendum 142. Further product-specific preparation guidance
General Finishes' wood preparation guide is a starting point for that manufacturer's systems. Use the exact product's current instructions to choose the final grit and recoat schedule.
Addendum 143. Why two pieces of the same alloy can behave differently
Permanent deformation involves movement of crystal defects called dislocations. Grain boundaries, dissolved alloying atoms and small particles can obstruct that movement. Cold working and heat treatment change these obstacles. Composition alone therefore cannot tell you the strength of a finished piece.
Addendum 144. Why connecting two different metals can change corrosion
When dissimilar metals are electrically connected in a conducting liquid, such as salty water, galvanic corrosion can accelerate attack on the more active metal. Material pairing, exposed areas and the environment matter. Isolation and drainage can be as important as the alloy choice.
Materials and Manufacturing Processes/Metals/Types of Steel
Addendum 145. Sources and quoted designation meanings
The Metals Service Center Institute identifies the first digit as “family of steel,” the second as “additional elements,” and the third and fourth as “nominal carbon content”; its example is 1018 at 0.18% carbon. Total Materia's SAE-AISI introduction gives the final two digits as “the carbon content in hundredths of a percent” and lists 41XX as “Chromium-molybdenum steels.”
The Aluminum Association's aluminum-alloy overview identifies these series and their principal additions. It describes 1xxx as “aluminum 99 percent or higher purity.” The series names do not list every element in an individual alloy; for example, the Association also identifies magnesium and possible copper and chromium additions in 7xxx alloys.
The Aluminum Association identifies 6061 use in truck and marine frames and 7075 use in aircraft. Metal Supermarkets' 6061/7075 comparison supports the T6 tensile-strength comparison, tank and tooling uses, machinability and welding differences. Its fabrication discussion notes that restoring the weld area's original temper in 6061 may require further heat treatment and aging. Compare the supplier's data for the actual temper and product form.
Addendum 148. Why an attractive surface can still be the wrong purchase
A shiny bar can have the wrong alloy, condition, straightness or size allowance. Conversely, inexpensive hot-rolled stock can be a sound choice when later machining removes the scale and establishes the final dimensions. Compare total processing cost, not appearance alone.
Addendum 149. Steel microstructures are not the four steel families
Ferrite and austenite are different iron-based crystal phases. Cementite is iron carbide, Fe₃C, a hard, brittle phase. Pearlite is a layered arrangement of ferrite and cementite. Martensite can form from austenite during sufficiently rapid cooling in suitable steel. These terms describe structure, not the buying categories carbon, alloy, stainless and tool steel.
Carbon can diffuse during slower transformations. Quenching can suppress those transformations and produce martensite. The outcome is not determined by cooling speed alone: chemistry and section size affect what forms throughout the part.
Addendum 150. Further reading on conditioning processes
Bodycote's heat-treatment overview provides entry points for annealing, hardening, tempering, stress relief and solution-and-age treatments. AEC's alloy and temper guide is a starting point for aluminum terminology. Neither an overview nor a qualitative sketch replaces a material-specific process specification.
Materials and Manufacturing Processes/Metals/Forming Metal
Addendum 152. Why a larger pattern does not replace a riser
Pattern allowance addresses final size. Feeding addresses a different problem: a solidifying region may need more liquid metal to avoid an internal shrinkage void. A riser must remain able to feed that region. The diagram identifies parts of a mold, not a production gating design.
Materials and Manufacturing Processes/Metals/Forming Metal
Addendum 153. Cold forming does not guarantee an unchanged dimension
Cold forming generally requires greater force than comparable hot forming. It avoids a separate hot-working step, but that does not prove every production cycle is faster. Springback, residual stress and later processing can change dimensions. Forging can also be hot, warm or cold; heat is not part of its definition.
Materials and Manufacturing Processes/Metals/Forming Metal
Addendum 156. Porosity can be useful or unwanted
Oil impregnation fills connected pores in a bearing so it can retain lubricant. Porite describes this use of porous sintered metal. That does not mean every powder-metal part is porous by design or that every part needs impregnation.
Materials and Manufacturing Processes/Metals/Joining Metal
Addendum 158. Why MIG is a familiar name but GMAW is the broader term
MIG refers to metal inert gas welding. GMAW also covers processes using active shielding gases or mixtures, often called MAG. Gas and filler selection depend on the alloy and process; the familiar shop name is not a complete welding specification.
A small active area coupled to a large noble area can suffer concentrated attack when both areas contact the electrolyte. That is why coating only the active member is not automatically a cure: a small defect in that coating can leave a small wetted anode coupled to a large cathode. The relevant areas are those participating in the wet corrosion cell, which can change as a joint dries. A compatibility decision must consider the complete joint and environment.
Addendum 164. How to check a center when a caliper touches the hole edge
Measure from the reference edge to the nearest hole edge, then add half the measured hole diameter to obtain that center coordinate. Use the same reference and direction as the drawing. This example does not specify a precision pin fit; a more demanding interface needs a more capable measurement method and a reviewed tolerancing scheme.
The nominal hole spacing is 70 mm, derived from 85 − 15. The separate ±0.5 mm x-coordinate limits can allow spacing from 69 to 71 mm. If an interface needs a tighter spacing, the designer must change the requirements; the inspector must not invent a tighter limit.
Materials and Manufacturing Processes/Manufacturing Documentation/Bills of Materials
Addendum 165. Consumption, purchase cost and batch yield answer different questions
You may need to buy a whole sheet even when one part uses a small fraction. That purchase is a cash requirement; the allocated fraction is the material estimate for the part. For a batch that consumes the entire stock unit, dividing its cost by the number of acceptable parts includes the loss from rejected pieces. Avoid charging the same waste once in the allocated share and again as an added allowance.
Addendum 166. Why there is no universal operation order
A feature may become inaccessible after assembly; a coating may need to be applied first. A larger blank may help holding, but its final cut must preserve the reference used for the holes. Record the reason for a departure from the usual sequence. The five process categories describe kinds of change, not a fixed order.
Addendum 167. Where to find product-specific instructions
Start with the manufacturer's product documentation, such as Smooth-On's technical bulletin and SDS directory. Its printed-pattern compatibility FAQ is a further-reading lead when investigating an uncured surface against a resin print. Check the complete instructions for the particular materials before selecting a treatment.
Addendum 168. Why a shorter cycle does not reduce every cost equally
A 10% reduction in a time-based processing charge reduces that portion by 10%. Material, setup and rent do not automatically fall. Capacity limits, tool replacement, scrap and quantity discounts can change the model outside its assumed range.
Equal variable costs mean the lower fixed cost wins, or both routes tie everywhere if fixed costs also match. A negative crossing lies outside positive production quantities. For a fractional crossing, compare costs at the neighboring whole-part quantities. This is process-cost break-even, not sales-revenue profit break-even.
Addendum 170. Why 20% loss means a 25% increase per useful amount
If 80% of purchased material reaches the product, one useful unit needs 1/0.80 = 1.25 purchased units, not 1.20. State whether a waste percentage is based on purchased material or on the useful amount.
Addendum 172. Why the loosest tolerance is not automatically cheapest
A tolerance that permits poor fit can increase assembly trouble, rework and failure. The goal is a manufacturable design that still meets requirements.
Addendum 173. Process time is not automatically value-added time
Rework takes processing time but corrects a failure. Inspection does not itself create the desired feature. A necessary machine cycle can transform the product even while the operator waits. Name whose time and which activity you are classifying.
Addendum 175. Bounded model reference: scheduling equations and limits
These equations describe the bounded ideal model; they do not report the current live settings.
For job i: A start = (i − 1)tA; A end = i × tA; transfer = min(ceil(i / batch) × batch, N) × tA. B start is the later of transfer and previous B finish; B end = B start + tB. Waiting before A = A start; held for batch = transfer − A end; waiting at B = B start − transfer. The three waits plus tA + tB equal that job’s completion time from order release 0.
Bounds: N 1–20 jobs, transfer 1–N, station times 1–20 whole min/job. This original scheduling example is separate from the map’s fixed 120-minute queue. It does not diagnose a factory or identify a universal optimal batch. Real setup, transport, limited space and variation can change the decision; no demand, quality or capacity forecast is made.
Addendum 176. A queue suggests a question, not a proven cause
A queue may reflect a capacity constraint, batching, missing information or an unreliable next step. Observe demand, timing and variation before calling one operation the bottleneck. A working day and a calendar day are not interchangeable time units.
Addendum 177. What a sweep can and cannot establish
A sweep combines the part's shape with its orientation and support. Runout is not a direct measurement of formal concentricity. A height sweep relative to a plate can reveal variation, but calling it a flatness inspection requires the proper setup and evaluation. Follow the drawing's specified inspection method.
Consult the actual tool's instructions and specifications. The Mitutoyo Quick Guide covers micrometers, calipers, height gages, gauge blocks, and indicators. The Starrett catalog separates graduations from accuracy and illustrates several instrument arrangements. The Mitutoyo ABSOLUTE caliper specifications provide examples of 0.0005 in / 0.01 mm display increments.
Addendum 179. Other 0.001 in verniers can have different spacing
A 50-division vernier can span 49 main-scale spaces of 0.050 in. Each vernier space is 0.049 in, again leaving a 0.001 in difference. Read the actual main scale; do not apply the trainer's 0.025 in spacing to that tool. The Starrett catalog, page 102, illustrates the 50-division arrangement.
For a small angle, the error is approximately the offset multiplied by the tilt in radians. An offset of 2 in and a tilt of 0.0005 rad give about 0.001 in of error. This is distinct from simply looking at the scale from an angle. See the Abbe discussion in the Mitutoyo Quick Guide, page 11.
If the lower edge of a slot is 0.600 in above the reference and the upper edge is 0.900 in above it, the center is (0.600 + 0.900) / 2 = 0.750 in above that reference. Half the difference, 0.150 in, is half the slot height; it still must be added to the lower height.
On the arrangement described in the Starrett catalog, page 306, 12 vernier spaces span 23 main-scale degrees. Each vernier space is 23/12 degrees, or 1°55′: 5 minutes short of two degrees. The line alignment reveals that difference. Page 308 distinguishes a plain universal bevel from the graduated protractor used with it.
Addendum 185. Why the family name does not settle performance
Base fluid, additives, dilution and water quality all affect the result. A neat oil can use mineral, vegetable or other base oils; “straight” describes using it undiluted. A synthetic is not automatically harmless or maintenance-free. See the fluid-family comparison on page 7 of Washington State Department of Ecology's metalworking-fluid guide and HSE's exposure overview.
Addendum 186. Why some milling runs dry while other milling needs fluid
A milling tooth repeatedly enters and leaves the material. Coolant can increase its temperature swing and promote thermal cracking in susceptible edges. Other operations need lubrication to limit adhesion, cooling to control distortion, or flow to clear chips. Sandvik Coromant's dry and wet milling guidance explains these competing demands.
Cimcool's refractometer FAQ covers zeroing, the boundary and factor conversion. Master Fluids' concentration guide discusses product factors and contamination. A refractometer is a concentration estimate, not a bacteria test or proof that the fluid is fit for reuse.
The aim is small oil droplets dispersed throughout the water, rather than water trapped inside an oil-rich mixture. Cimcool's mixing explanation describes the emulsifier's role. Mixing order is separate from the arithmetic: the right measured amounts still need the right preparation method.
Addendum 189. Derive the balance, or solve for an unknown addition volume
Concentrate already in the tank plus concentrate added equals concentrate in the final tank: VC/100 + AP/100 = FT/100. Multiply through by 100 and solve for P. This tracks concentrate, not the Brix number.
If a premix concentration P is already chosen, solve for its addition volume: A = V(T − C) ÷ (P − T). Check that A is positive and that V + A fits within the allowed fill level. If P = T and C differs from T, no finite addition reaches T exactly. If C = T already, adding premix at T preserves it.
Addendum 190. Why inspection and measurement belong together
Concentration alone does not describe contamination or biological condition. HSE's metalworking-fluid guidance calls for maintaining fluid quality and checking bacterial contamination. A supplier-directed fluid-management program may include pH and microbial checks as well as concentration; use its methods and action limits. Master Fluid Solutions' FAQ explains odor, residue and concentration-related skin irritation.
Addendum 191. Supplier instructions determine the cleaning treatment
HSE's sump-cleaning guidance emphasizes supplier-selected cleaner and circulation times. An extensively contaminated system may need treatment before draining and additional cleaning cycles; the general checklist is not a microbial decontamination recipe.
Addendum 192. Why the waste route depends on what is in the tank
Washington State Department of Ecology's metalworking-fluid guide, pages 12–13, illustrates how formulation and contamination change waste management. Its state-specific rules are not a disposal authorization elsewhere. EPA's used-oil guidance also distinguishes qualifying used oil from other wastes and notes that state requirements can be stricter. The product SDS is a starting point; used coolant also contains material picked up during machining.
Addendum 193. Why finer teeth do not fix every bad cut
More teeth share the load, but smaller gullets have less room for chips. Too much feed can overload the teeth; too little can make them rub. A wandering cut also calls for checking the blade condition, tension, guides, and workholding against the manuals. Changing speed alone cannot correct loose work or a worn guide.
Addendum 194. Why the answer can be a fraction of a tooth
The product counts tooth spacings across the contact length. Actual engaged tooth tips are discrete, and the number changes as the blade moves. Entry, exit, variable pitch, and curved sections also change contact. This estimate explains the selection principle; it does not guarantee a fixed count throughout a real cut.
Addendum 195. Manufacturer resources for the next selection step
Consult the chart supplied with the blade. Public starting points include Starrett's carbon blade range and DoALL's blade FAQ. Product-specific recommendations govern; the estimates here are teaching calculations.
Addendum 196. Why relief cuts help with some outlines
A relief cut runs in from a scrap edge toward the outline, allowing waste to separate in smaller pieces. Plan relief cuts on the waste side and preserve the finishing allowance. They can provide room to approach a contour from another direction; they do not make the blade itself capable of a smaller turning radius.
Addendum 197. Why joining includes more than making a weld
Alignment keeps the band running straight. The prescribed annealing or tempering cycle restores suitable flexibility at the joint, and finishing removes raised weld material. A sound-looking joint alone is not proof that the loop is ready to run. DoALL's blade welder range is a starting point for equipment-specific documentation.
Addendum 199. Why facing can reveal a tram problem
A tilted spindle puts opposite sides of a face cutter at different heights. Adjacent passes may leave steps even with the vise correctly aligned. Surface finish alone does not identify the cause: check the geometry before changing cutting data.
Addendum 200. Read the whole sweep, not just two endpoints
The simplified direction diagram is another view of the linear preset. Jaw tilt is exaggerated; the traverse arrow follows the contact point and does not name physical table travel.
A smooth change suggests angular misalignment. A sudden jump at one spot suggests a chip, burr, damaged jaw or unstable contact. Tightening can move the vise, which is why the final sweep matters. Equal endpoint readings alone cannot reveal a bowed or damaged face between them.
Addendum 201. Why the force divides this way—and what the model cannot tell you
Take moments about the heel: Fpart(a + b) = Pb. Vertical balance gives Fpart + Fheel = P. These are upward reactions on the strap; the strap pushes downward on the part and heel with equal magnitudes.
This neglects strap weight, friction, deformation and additional contacts. It does not calculate stud force from wrench torque, allowable loads, sliding resistance or the number of clamps needed. Those depend on the hardware, workpiece and cutting forces. See Carr Lane's strap-clamp guide for the underlying geometry and hardware guidance.
Mitutoyo: Dial Test Indicators and the Cosine Effect shows the stylus geometry and correction. Its What is Cosine Error? video demonstrates the difference using a test indicator against a plunger indicator. Do not apply a plunger-indicator correction rule to a lever indicator without checking its instructions.
Addendum 203. Check both repeatability and the offset sign
Repeat the touch from the same direction. On manual feed screws, account for backlash when reversing; a handwheel reading can change while the table has not yet moved. Do not use a rough saw edge as though it were a finished datum. The radius correction is geometry, independent of the control's button sequence.
Addendum 206. A real trade-off within one product family
BIG DAISHOWA's mechanical-chuck guidance describes two clamping configurations for its slim HMC(S): the roughing configuration increases clamping force at the expense of greater runout. That is a qualified product example, not permission to tighten another chuck farther or a ranking of all milling chucks.
The eccentric ring retains and extracts the collet as the nut is loosened. Missing that engagement can prevent correct seating. Use REGO-FIX's ER assembly instructions for the mechanism and Haas: ER Collet Essentials for a public demonstration.
Addendum 208. Why adding the tool can change the answer
HAIMER's balancing guide (PDF) discusses assembly unbalance. Albrecht's APC catalog (PDF), Handling APC and Ultra, states that the marked balance condition excludes collet and tool and that shank slots affect the assembled result. A small runout reading is not a substitute for that separate balance and speed check.
Addendum 209. Check your selection reasoning without a video
A defensible answer identifies the limiting feature or load, names a candidate mechanism, and states what its manufacturer must confirm. Different products can satisfy the same job. If the only justification is a brand name or a universal star rating, the selection is incomplete.
Addendum 211. Why the two-for-aluminum, four-for-steel rule is only a starting point
Tool designers trade chip space against the core and cutting-edge arrangement. Purpose-built tools and controlled engagement can make other flute counts appropriate. See Harvey Performance: Why Flute Count Matters.
Addendum 212. Check the coating's material recommendation
Harvey Tool's coating guide distinguishes ferrous applications from aluminum applications. Its AlTiN and TiB2 entries illustrate why a coating name must be matched to the work material.
Addendum 213. Several faults can look or sound like chatter
Runout or one damaged edge can make one flute carry more load and leave uneven tooth marks or non-uniform edge wear.
Rubbing or built-up edge can smear material, generate heat and produce a poor finish without a regenerative vibration.
Chip re-cutting can scratch the finish and damage edges when chips remain in the cutting zone.
A forced vibration follows a repeating input from the cutter, interrupted cut, drive or surrounding system. Chatter is the self-reinforcing case; both still require finding the flexible path and the excitation.
After the approved safe stop, inspect the pattern, cutter and setup together. Sound is useful for noticing a change, not for identifying the failed component. Seco Tools’ vibration guidance connects insufficient stiffness and damping to self-excited chatter and identifies surface-finish and cutting-edge-wear consequences.
Addendum 214. How the inspection decides, and what its numbers are
The part is kept as a list of every cut: the space each tool swept through. The top of the metal
at any point is the raw top lowered by every cut that reaches that point. The inspection measures
walls, floors, holes and chamfers at sampled locations on that surface, with numbers rounded
to a hundredth of a millimetre. A display grid plus probes derived from each cut and drawing
boundary look for excess metal and gouges. Passing means the modeled checks pass; it does not
certify every point of a real surface. Removed volume is an estimate from the 0.25 mm grid;
very small cuts can change the analytic surface without a resolved grid volume.
Walls and holes pass within ±0.10 mm, the bore within ±0.05 mm, and floors and
faces within ±0.05 mm.
Tapped holes are accepted when their drilled diameter falls inside the minor-diameter limits for
a 6H internal thread: 4.917 to 5.153 mm for M6×1, and 6.647 to 6.912 mm for
M8×1.25. These are finished minor-diameter limits, used here as a teaching proxy for pilot
quality; they are not universal tap-drill recommendations or a complete 6H inspection.
Addendum 215. How the simulator reads and runs a program
Each line is read in the order a control carries out the parts of a line: feed rate, spindle
speed and tool first, then the tool change, the spindle, coolant, the modes, the move, and last the
program end. So S2500 M3 G1 X20 F100 starts the spindle before it moves. Two codes
from one group on a line, such as G0 G1, are an error.
The interpreter first reads the whole program, and a second machine runs it at once to find its
path, its time and the first place it would stop; that is the path drawn before you press Play.
Pressing Play runs the program again on the block, move by move. The metal, the vise and the tools
are those of the simulator in Milling Operations: every cut is kept as the space the tool swept,
and a move that would break a tool rule or hit the vise stops where it would happen.
An arc’s end point has to be on its circle to within 0.005 mm or 0.1 % of the
radius, whichever is larger. A rapid, or a feed with the spindle stopped, stops a hair short of the
first metal it would touch. The volume removed is an estimate from a 0.25 mm grid.
Addendum 216. When a rough or hard exterior can change the choice
Conventional milling can be useful in a qualified first pass on a rough surface because its
gradual entry can reduce the impact on a brittle cutting edge. Tooling guidance also documents
specialized exceptions such as machining through titanium alpha case before returning to climb
milling. That is not a rule to choose conventional whenever stock has rust or scale: the layer’s
hardness and abrasiveness, the work material, tool grade and geometry, engagement, fixturing and
the approved process all matter. Use the tooling manufacturer’s data and the method approved for
the machine.
Addendum 217. Why some machines climb mill without trouble
A feed drive can be designed to reduce backlash, for example with a preloaded ball nut.
The important question is whether the machine controls that movement, not simply whether it is called CNC.
The chip is the same shape either way; what changes is whether the machine can hold the table
against the pull of the cut.
Modern Machine Shop's column Eliminate Backlash From Machining Centers (Mike Lynch, 2000) defines backlash as “any non-movement that occurs during axis reversals.” This page uses the CourseWiki definition on Screw Threads: clearance that must be taken up after reversing before the load moves. In a real drive, elastic deflection can add lost motion as well; the lab below leaves it out.
Addendum 219. A readout that measures the slide, and when the clearance still matters
The MIT 2.670 milling machine notes (section “Using the Micrometer Dials”) also point out that a digital readout measures the bed position directly, so its reading is not thrown off by backlash. The clearance is still in the drive. A force that pushes the carriage along the screw can move it across the clearance without the handwheel turning; Climb and Conventional Milling explains when a cutting force does that.
Addendum 220. What the model means, and why it is not a prediction for every CNC
The coordinates describe the cutter relative to the workpiece, viewed from above: +X right, +Y up. A moving table travels in the opposite sense. The drive infers position from motor/screw motion, with no compensation or linear-position correction. The first approach seats both axes and calibrates the coordinates at the start, before the plunge. That reference is kept through the cut.
With positive initial seating, each actual coordinate c is updated as c = min(max(c, q), q + B), where q is the motor-inferred coordinate and B the total clearance. Negative seating uses the band [q − B, q]. These are shifted forms of the same play operator as the screw lab above. Each axis holds until a band edge reaches it. If the axes take up clearance at different moments within a command segment, the actual path has an extra bend; the cutter sweep includes it.
Every cut segment removes a disc swept along that actual segment, a capsule with the cutter's 2 mm radius. The area shading compares the actual and zero-backlash histories at the same command step. Span measurements intersect those capsules with the two centre sections. They are not a best-fit diameter, an overall size tolerance or a guarantee of the rest of the contour.
All other effects are idealized away: no runout, deflection, wear, servo lag, cutting-force pull, thermal error or compensation. Friction is assumed to hold a slide inside its clearance. The shapes, clearance settings and viewing speed are illustrative. Restart begins a fresh workpiece; changing a setting recomputes the experiment.
HEIDENHAIN describes direct linear-axis measurement as working “without intervening mechanical elements”. Such feedback changes what the controller can observe; this lab deliberately does not model that correction. Haas's ballbar interpretation guide distinguishes lost motion at reversal from controller-related reversal spikes. Only rigid lost motion is included here.
Addendum 221. Feed per tooth is not always the thickness of the chip
Feed per tooth is how far the work moves between teeth. The chip a tooth actually cuts is only
that thick when the cutter is at least half buried across its diameter. In a narrower cut, each
tooth meets the work at a slant and the chip comes out thinner. Climb and Conventional Milling
shows this: at a width of cut of 10% of the diameter, the thickest part of the chip is 60% of the
feed per tooth.
Some cutting data raises the feed per tooth for narrow cuts to make up for this. Read what your
data assumes before using its numbers, and ask if it does not say. Thinner chips also take more
energy per cubic inch, which is one reason a power estimate is a band.
Sandvik’s specific cutting-force explanation
shows why chip thickness and cutting-edge geometry affect the energy estimate.
Haas’s spindle power curves
illustrate why available power depends on RPM; read the machine’s own curve and duty
rating rather than treating its headline horsepower as available everywhere.
The solid round section has area moment of inertia I = πd⁴/64. With x measured from the clamp, displacement magnitude is y(x) = Fx²(3L − x)/(6EI). At the tip, x = L, so δ = FL³/(3EI). Both displacement and slope are zero at x = 0.
Use N for force, mm for length and diameter, and N/mm² for E. The controls show E in GPa: multiply by 1,000 to get N/mm². The answer is in mm; multiply by 1,000 for µm.
For F = 100 N, L = 40 mm, d = 10 mm and E = 600 GPa, I = 490.874 mm⁴ and δ = 0.007243 mm = 7.243 µm. Halfway along that tool, y(L/2) is 5/16 of the tip value, or 2.264 µm. These are calculated examples, not measured cutter data.
The steady-rest instructions show a rest fixed to the bed, while the follower-rest instructions show the rest attached to the saddle so it travels with the cutter. The drawings here explain those generic roles; they are not setup instructions or copies of manufacturer artwork.
Addendum 225. Rake and chipbreakers depend on the whole cutting setup
Rake describes the slope of the surface the chip flows over. Clearance keeps the tool below the edge from rubbing. Material matters, but hardness alone does not dictate positive, neutral or negative rake: tool material, edge strength, holder geometry and rigidity also matter. Use the tool maker's cutting geometry and range for the application.
A chipbreaker guides a chip into a tighter curl so it can break. It may be molded into an insert or ground into a tool. It works within a range of feeds and depths; a very thin chip can curl without breaking. A chipbreaker is not a guarantee of short chips at every setting.
Addendum 226. How a manual lathe keeps every pass on one helix
The carriage is coupled to the leadscrew by closing the half-nut. On a lathe
with an inch leadscrew cutting an inch thread, the thread dial shows when to close
it so that each pass drops into the same groove. Many machinists also feed the tool in with the
compound travel set near 30° from the radial cross-feed direction, so that most of the cut is taken by one flank of the tool.
The simulator simplifies all of this. It keeps every pass on one helix for you, feeds the tool
straight in, and checks a simplified 60° thread by its crest and root diameters. A real thread is
checked against a thread table with thread gauges or measuring wires.
Engineering Fundamentals/Motion and Rotation/Gear Ratios
Addendum 227. Why tooth counts work, and what the dashed circles mean
The gears here share one tooth size, called module, and a 20° pressure angle. Their pitch diameters are proportional to tooth count. The dashed pitch circles roll together at equal tangential speed, so nA × NA = −nB × NB when clockwise is positive on both shafts. Here n is signed rotational speed and N is tooth count.
Tooth flanks are involute curves. Actual tooth surfaces can slide during contact even though the pitch circles roll. The drawing samples those curves, simplifies the tooth roots and adds a small visual clearance. It is a motion model, not a manufacturing drawing.
The lab assumes rigid external spur gears, fixed shaft centers, matched tooth size and steady transmitted load. It starts lossless; its efficiency control applies the same specified loss to every actual mesh, including both meshes around an idler. Acceleration, elasticity, backlash dynamics, detailed friction, noise and tooth strength are omitted. Changing tooth counts moves the centers to maintain the correct mesh; it does not represent swapping a gear into a fixed gearbox housing.
Engineering Fundamentals/Motion and Rotation/Gear Ratios
Addendum 229. Why adding losses is only an approximation
For a 1000 W input and three 96% stages, the losses are 40 W, 38.4 W and 36.864 W. Each 4% applies to a smaller incoming power. Adding 4% + 4% + 4% incorrectly takes every loss from the original 1000 W.
Engineering Fundamentals/Motion and Rotation/Gear Ratios
Addendum 230. Follow both stages of one loaded train
A 24-tooth driver at 1440 rpm and 4 lbf·ft drives 48 teeth. That shaft also carries a 15-tooth driver for a 45-tooth output. Both stages are 96% efficient, with no other losses. After stage 1: 720 rpm and 4 × 2 × 0.96 = 7.68 lbf·ft. The shared shaft carries that same 720 rpm into stage 2. Final output: 1440/(2 × 3) = 240 rpm and 7.68 × 3 × 0.96 = 22.1184 lbf·ft, versus 24 lbf·ft ideally. Overall efficiency is 0.9216.
Engineering Fundamentals/Motion and Rotation/Gear Ratios
Addendum 231. Worked design: a winch with a speed ceiling and torque floor
A motor supplies 1680 rpm and 24 lbf·ft. The output must be at most 40 rpm and at least 950 lbf·ft. Available gears have 10–60 teeth, with unlimited copies; each reduction stage is at most 6:1 and 97% efficient. There are no idlers or other losses.
Speed requires i ≥ 1680/40 = 42. Two stages give at most 6² = 36, so try three.
Three stages give ηtotal = 0.97³ = 0.912673. Torque requires i ≥ 950/(24 × 0.912673) ≈ 43.3708. Torque controls.
Choose 12 → 48, 15 → 45, and 16 → 60 teeth: i = 4 × 3 × 3.75 = 45. Every tooth count and stage ratio meets its limit.
ωout = 1680/45 ≈ 37.33 rpm ≤ 40 rpm. τout = 24 × 45 × 0.912673 = 985.68684 lbf·ft ≥ 950 lbf·ft. Both pass. Three external meshes make the output opposite to the input.
This is one feasible train, not a claim of an optimum or a complete winch specification. For load force at a drum, continue to Torque; for travel speed, use Rotation and Linear Speed.
Addendum 233. Why cutter selection includes more than width
Reach, neck clearance and tooth arrangement affect access and cutting behavior. See Harvey Performance's keyseat cutter considerations. A nominal tool width does not certify the width of the finished slot.
Machining/Production and Nontraditional Processes/Broaching
Addendum 234. Why the finishing teeth need not keep getting taller
Once the intended profile is reached, further rise would make the feature larger. Repeated finishing teeth can maintain the final size as earlier teeth wear. See Nidec's precision cutting tools reference for broach terminology.
Machining/Production and Nontraditional Processes/Broaching
Addendum 235. Production advantages depend on the job
Tool cost, material, cut length, machine capacity and required finish determine the economics. Broaching is not automatically the cheapest process. Pilot Precision's broach overview includes both short-run sets and one-pass production tools. Cutting Fluids and Application Methods explains lubrication choices.
Addendum 238. Why a damaged or uneven point makes a poor hole
Unequal lip lengths or unequal angles make the two lips remove different amounts of material. The drill can cut oversize or wander. A rounded edge can rub instead of producing a chip. Inspect the point and replace or correctly sharpen a damaged drill before trying to compensate with more force.
Addendum 239. Why “always center drill first” is too broad
The starting recess determines which part of the next drill touches first. An unsuitable angle or an oversized pilot can load the drill's outer corners before its center is supported. Accurate starting also depends on tool rigidity, alignment and the surface being entered. A center-drilling step alone does not guarantee location.
Changes in chip shape, sound, thrust or finish can indicate rubbing, chip packing, a damaged point or unsuitable cutting data. Continuing to force the tool does not diagnose the cause.
Addendum 241. A nominal tool size is not a finished-hole guarantee
Tool condition, alignment, runout, temperature and workholding affect the result. A reamer stamped with the desired diameter still needs an appropriate prepared hole and cutting conditions. Inspect the actual bore rather than accepting it from the tool marking.
Addendum 242. Check the entire joint before substituting a fastener
Diameter, pitch, length and head clearance are only part of the selection. The nut or tapped material, coating, bearing surfaces, installation conditions and intended load also matter. A bolt that can be screwed into the hole has passed an assembly check, not a strength calculation.
Addendum 243. Chart basis and the approximation's limits
The three comparisons were checked against page 1, cutting-tap column, of North American Tool's Tap Drill Sizes — Inch & Metric with Drill Size Formulas, using the supplied four-page copy. Only these selected rows are used here; the chart is not reproduced. The estimate and a selected stock drill need not be identical. The chart's metric percentage formula gives about 77% when the entire pitch is subtracted, which is why “about 75%” must remain approximate.
Addendum 244. Keep percentage and fraction separate
For a metric cutting-tap estimate, the supplied chart gives hole diameter = major diameter − (percentage × pitch / 76.98), entering 75 for 75%. Equivalently, multiplying a reference thread depth by 75% requires the fraction 0.75. Mixing those conventions introduces a factor-of-100 error. This formula estimates geometry, not allowable joint load.
Addendum 245. Why the local setup decides what is permitted
Recognizing a production process does not authorize it on a particular machine. Spindle speed, tapping attachment and power-tapping procedure depend on the particular machine and setup.
A taper goes from 1.100 to 0.950 in over 3.000 in. Its diameter changes 0.150 in, so the rate is 0.050 in/in, or 0.600 in/ft. At half the length, the diameter has changed half as much: 0.075 in. These are teaching dimensions, not a standard machine taper.
Addendum 247. Why the factor of two belongs in the angle formula
Cut the cone through its axis. One side forms a right triangle whose rise is (D − d)/2 and whose run is l. Tangent is rise divided by run. Using the whole diameter change as the rise gives the wrong tool path.
Addendum 248. Why this is an estimate rather than an exact setting
The taper gives tan(α) = TPI/2. If L is the actual distance along the tilted work between support points, the ideal geometric offset is L sin(α). At shallow angles sin(α) and tan(α) are nearly equal. The usual formula substitutes L tan(α); real center contact and setup error add further differences. It is not a method for steep cones.
Addendum 249. Radial depth and compound travel are different quantities
If compound travel is c at angle β from radial, its radial component is h = c cos(β); therefore c = h / cos(β). The corresponding diameter reduction is 2h. Check whether a dial reads actual slide travel or diameter change before using it.
Addendum 250. Why only certain threading-dial positions return to the groove
The threading dial is geared to the leadscrew and carried with the carriage. Its rotation tracks their relative position. For a selected thread, certain dial positions repeat the relationship that lets the tool enter the same helical groove when the half-nuts close. Other positions can put the tool between previous passes, cutting a second groove.
Addendum 251. Verify the formula without a thread-depth table
Split the symmetric 60° tooth down the middle. The right triangle has axial width P/2 and radial height H. Its 30° angle gives tan(30°) = (P/2)/H. Rearranging gives the formula above. If a defined profile removes radial heights a at the crest and b at the root from this triangle, its height is H − a − b. Neither a nor b can be guessed from pitch alone.
For a hypothetical sharp-V, 20-per-inch thread, P = 0.050 in and H = 0.04330 in. At 29° from radial, ideal compound travel would be H/cos(29°) = 0.04951 in. These calculations isolate geometry; they are not settings for cutting a real 20-per-inch fastener.
Addendum 253. A manufacturer's explanation of the marking
Norton: Grinding Wheel Basics explains the five fields and manufacturer-specific variations. A wheel specification and its separately marked maximum operating speed answer different questions.
Addendum 255. Why a wheel can glaze, and where ring testing applies
Glazing depends on the wheel grade and operating conditions as well as the work material. Hard material alone does not diagnose it. Norton's ring-test guidance explains the method's application and limitations; follow the full manufacturer procedure before mounting.
Addendum 256. Carbide needs consistent temperature control
General Carbide: The Designer's Guide to Tungsten Carbide, page 50, explains thermal shock and the effects of interrupted coolant during grinding. Follow the tool manufacturer's cooling guidance for HSS as well; permission to cool a warm bit is not permission to quench an overheated one.
Addendum 258. Why a real grinding plan needs more than the quotient
The calculation assumes a flat starting face and no wheel wear or elastic error. A real plan may reserve material for lighter finish cuts, include dressing and spark-out, and stop to measure. Stock removal from two faces must be assigned to each face; do not silently count it twice.
A motor encoder measures the motor, while a linear scale can measure the slide directly. Screw error, backlash and elastic deflection between the sensor and the cutting point may remain. Homing establishes a reference; repeating homing is not a general cure for lost motion. See Oriental Motor's closed-loop stepper overview for an example of feedback used with steppers.
Addendum 260. Why positive compensation can use a negative offset
Positive compensation describes addition, not the sign of the stored number: adding a negative value shifts the compensated Z position in the negative direction. The Haas mill programming workbook's tool-length compensation section explains G43's addition of the selected offset to commanded positions.
Addendum 261. Check the conversion in both directions
Subtract endpoints: (26−6,4−4) = (20,0); (26−26,19−4) = (0,15); (11−26,19−19) = (−15,0). Add those changes to A: (6+20+0−15,4+0+15+0) = (11,19). The net move is (5,15), not the final absolute position.
A short program can be written directly in a text editor. Conversational programming asks for feature dimensions at the control. Manual data input (MDI) lets the operator enter commands at the control, often for immediate execution. These routes still require correct modes, geometry and setup data; they do not bypass prove-out. Tormach's post-processor guidelines identify control-specific requirements.
Addendum 263. Why an extra axis changes the work a turning center can do
Ordinary turning produces surfaces around the spindle axis. A powered tool plus controlled work angle can reach features at selected angular positions. See the Haas options programming reference for one manufacturer's C-axis implementation.
Addendum 264. Control example: separate geometry and wear fields
The Haas lathe manual, Operation, describes separate X/Z geometry wear, radius and tip-direction fields. Its button sequences and offset conventions must not be assumed on another control.
Addendum 265. Calculate where a speed ceiling starts to matter
With 90 m/min and a ceiling of 1800 RPM, the crossover diameter is 90 × 1000 / (π × 1800) = 15.92 mm. At 10 mm, unrestricted CSS would request 2865 RPM, so the simplified steady-state result is 1800 RPM. Acceleration and other machine limits can reduce actual speed further. See Haas's spindle-speed commands workbook for its G50/G96/G97 implementation.
Addendum 266. Reference for the code convention used here
The G96–G99 entries in the Haas lathe manual describe S in CSS versus RPM and F per minute versus per revolution. Consult the manual for your own control before transferring these meanings.
Addendum 267. Why a good diameter measurement does not prove a taper is correct
The two axis touch-offs locate tangent lines, not every possible contact point on the nose. The normal to an angled surface points in another direction, so its tangency requires another offset. Haas's tool nose compensation discussion describes the resulting undercut or overcut on tapered and curved profiles.
The Haas G41/G42 entry connects the compensation side to the selected tool offsets. The Haas SL-10 Programming Workbook (hosted by the University of Florida), printed pages 59–61, explains the imaginary tool tip, tip direction and approach/depart moves. Use the current manual for the installed control when programming.
Addendum 269. Why no universal cycle template is shown
The Haas G71 reference distinguishes path types and radial cut depth from diametral finish allowance. The Hurco ISNC G71 reference supplies its own two-block definition. A familiar cycle number does not establish compatible parameter meanings.
Addendum 270. Check roughing depth and remaining material
The first pass changes diameter from 24 to 22 mm, a 1 mm radial cut. The second changes 22 to 20.6 mm, a 0.7 mm radial cut. Finishing from 20.6 to 20 removes 0.3 mm radially. Extending the OD cuts beyond Z−25 leaves room for the cutoff blade and places the finishing departure on material that will not belong to the finished part.
Addendum 271. Why the gauge itself needs limits and wear checks
Gauges cannot be manufactured to an infinitely exact size. Their own tolerances and wear allowances are selected under the applicable gauging specification. Repeated use can shrink a plug or enlarge a ring and change its decision.
Addendum 272. Why a small sample range is not the full process spread
The range uses only the two extremes observed in this sample. More readings, different tools, temperature changes and later production may reveal variation not present in these five parts. Standard deviation is another measure of spread that uses every reading's distance from the mean; no standard-deviation calculation is needed for this example.
Indices such as Cp and Cpk compare estimated process variation and its position with specification limits. Their interpretation depends on the data, stability, distribution and application requirements. A single threshold is not a universal acceptance rule, and a five-reading classroom example is not a capability study.
Addendum 274. Cell, system and integration describe different scopes
A flexible manufacturing system may coordinate multiple machines or cells with material handling and scheduling. Computer-integrated manufacturing is the broader idea of connecting manufacturing information and activities. These terms overlap in use, but are not interchangeable names for one machine configuration.
The dielectric fluid normally insulates the gap. A voltage pulse breaks down that insulation locally and permits a discharge. Between pulses, the fluid helps cool the region and flush debris. Debris removal and gap control help keep discharges stable. Sinker EDM commonly uses dielectric oil; wire EDM commonly uses controlled deionized water, though oil-based wire machines also exist.
Addendum 276. Why one offset does not describe every pass
Discharge energy, flushing and finishing passes change the working gap and surface. Actual compensation comes from the machine's process data and inspection. CHMER's EDM FAQ defines the offset as the wire radius plus the discharge gap, and notes that the gap changes with discharge energy.
Addendum 278. Why hardness alone does not set ECM performance
The reaction removes metal without requiring a harder cutting edge. Metal chemistry and current conditions still affect dissolution, so “all metals machine at the same rate” is not a valid selection rule. Tooling and electrolyte control can make ECM attractive for repeated parts, while adding development effort for a one-off feature.
Addendum 279. Why the material and laser must be matched
Different materials absorb different wavelengths differently. Power and beam delivery also limit the usable thickness and quality. See TRUMPF's laser-cutting overview.
Addendum 282. Why a shaped tool does not give an exact-size copy
Abrasive particles occupy space around the tool and also wear it. The finished cavity therefore depends on the tool, abrasive action and process control, not simply on copying the tool's nominal dimensions. Bullen describes loose-abrasive ultrasonic machining.
Addendum 284. How the axial stiffness is calculated
Let m = cos θ and n = sin θ. For this plane-stress orthotropic layer, the compliance in the load direction is S̄11 = m⁴/E1 + n⁴/E2 + m²n²(1/G12 − 2ν12/E1). Then Ex = 1/S̄11 and εx = σx/Ex. The full stress and strain transformation supplies transverse and shear strain.
Addendum 285. Primary mechanics source and model boundary
NASA Reference Publication 1351, Basic Mechanics of Laminated Composite Plates, sections I and II, defines isotropic and orthotropic behavior, develops plane-stress compliance and off-axis transformation, and identifies extension–shear coupling. Its stated scope separates elastic response from strength. The constants and examples on this page are original illustrative teaching inputs, not values from that report.
Addendum 286. How the laminate stiffness and the free-panel response are calculated
Each ply's reduced stiffness Q (MPa) comes from E1, E2, G12 and ν12, and is rotated to the ply angle to give Q̄, using engineering shear strain γxy. With z measured up from the midplane and each ply running from zbottom to ztop (mm):
A = Σ Q̄ (ztop − zbottom) in N/mm; B = Σ Q̄ (ztop² − zbottom²)/2 in N; D = Σ Q̄ (ztop³ − zbottom³)/3 in N·mm.
The force resultants N (N/mm) and moment resultants M (N·mm per mm) relate to midplane strain ε⁰ and curvature κ (1/mm) by N = A ε⁰ + B κ and M = B ε⁰ + D κ. The interactive applies N with M = 0 and solves all six equations together. The drawn surface is w = −(κxx² + κyy² + κxyxy)/2, exaggerated by the stated factor.
For the rose, a pull Nθ along direction θ has components (cos²θ, sin²θ, sinθ cosθ) Nθ. Flat-held: Ex(θ) = 1/(h · vᵀA⁻¹v) with v = (cos²θ, sin²θ, sinθ cosθ) and laminate thickness h. Free: the same, with the in-plane block of the inverted six-by-six A-B-D matrix in place of A⁻¹.
Reversing the ply order (the bottom ply listed first) leaves A and D unchanged and reverses the sign of every B term, so the same pull makes the opposite curl. A single ply is symmetric about its own midplane, so it reproduces the one-ply result above: 40 GPa along the fibers and 10 GPa across.
Addendum 287. Primary mechanics source and model boundary
NASA Reference Publication 1351, Basic Mechanics of Laminated Composite Plates (A. T. Nettles, 1994) defines balanced and symmetric laminates, derives the A, B and D matrices and the laminate constitutive equations, shows that a symmetric laminate has B = 0, and works an unsymmetric laminate example in which a tensile load alone bends the plate. It also notes that unsymmetric laminates can warp from processing temperature changes, which this lesson excludes. The ply constants, ply thickness, loads and panel size here are original illustrative teaching inputs, not values from that report and not design data.
Addendum 288. Why technical writing cares about the space
Leave a space between a numerical value and its unit symbol: 8 m,
15.0 kg, and 0.50 s. SI also uses a space before
°C and %. Consistent notation is a
low-cost way to keep a drawing, a spreadsheet, and a controller reading the same thing.
The BIPM SI prefix
table is the primary list used here, including the 2022 ronna, quetta, ronto, and quecto
additions. The NIST SI Units
reference explains SI base and derived units and their technical-writing role.
Addendum 290. Dimensional analysis is also a design check
If a mass density is in kg/m3 and a CAD model volume is in
m3, the cubic meters cancel and the result is kilograms. That is why
CAD mass-property settings, material cards, and drawing units must be read together rather
than as separate menus.
Addendum 291. Two more conversion cases from the unit
Machine run time: an automated machine has operated for 15 years and
150 days. With the stated classroom assumption of 365 days per year,
(15 × 365 + 150) d × (24 h / 1 d) = 135,000 h. Real maintenance
records should use actual calendar dates and include leap days.
Supply-chain fuel: a truck rated 15 mpg has
15 mi/U.S. gal × (1.609344 km / 1 mi) ×
(1 U.S. gal / 3.785411784 L) = 6.37716 km/L. A 150 km one-way route is a 300 km
round trip, requiring 300 km / 6.37716 km/L = 47.0429 L, or
47.0 L, assuming the quoted fuel economy holds for the trip.
The NIST SI Units reference
documents SI base and derived units. The NIST conversion conventions define the inch as exactly
0.0254 m; this page derives square and cubic factors from that exact value. U.S. liquid gallon
values are explicitly labeled whenever they are used.
Addendum 293. The calculus idea, after the practical one
Over a smaller and smaller time interval, average velocity approaches instantaneous
velocity. In calculus notation, velocity is the derivative of position with respect to time:
v = dx/dt. For this course, begin by naming the interval, position change, and
direction correctly; the derivative notation is a compact extension of the same idea.
The NIST SI Units reference
lists velocity as a derived unit example. Direction is an added physical requirement: two
motions may have the same speed but different velocities because their directions differ.
NASA’s
Newton’s second-law resource connects force, mass, and acceleration for grades 9–12.
The calculation here uses the average velocity-change form first; a real machine profile may
have changing instantaneous acceleration within the same interval.
Addendum 296. Check the CAD assumptions before trusting mass properties
Confirm the assigned material, density, document unit, bodies included, and whether the
model represents solid material or an internal void. A precise calculation based on the wrong
material card is still wrong.
NASA Glenn’s
weight-and-mass explanation distinguishes F = ma from
W = mg. The NIST SI
Units reference lists kilograms as an SI base unit and newtons as a derived unit. Those
conventions are used here with g0 = 9.80665 m/s2 for the
standard-gravity examples.
The density conversion is from
NIST
SP 811, Appendix B, which lists slug per cubic foot to kilogram per cubic meter as
5.153 788 E+02; 0.00194032 is its reciprocal.
Engineering Fundamentals/Motion and Rotation/Angular Motion
Addendum 298. Why a radian is barely a unit at all
A radian is an arc length divided by a radius — a length over a length. The two cancel,
so NIST gives the base-unit expression for the radian as m/m and its value as
simply 1: the radian and steradian are “special names for the number one that
may be used to convey information about the quantity concerned.”
That is not trivia. It is why a torque in N·m multiplied by an angle in
rad comes out as energy in joules with no conversion factor anywhere, and why a
formula that mixes rotation with straight-line motion works only when the angle is in radians.
Degrees and revolutions are counts somebody picked; the radian is the ratio the geometry
already contains.
Engineering Fundamentals/Motion and Rotation/Angular Motion
Addendum 299. Where 0.1047198 comes from
One revolution is 2π radians and one minute is 60 seconds, so one revolution
per minute is 2π/60 = 0.104719755… radians per second. It is not a
measured constant; it falls straight out of the two definitions. Turning it over gives
60/(2π) = 9.5492966… revolutions per minute in one radian per second.
Engineering Fundamentals/Motion and Rotation/Angular Motion
Addendum 300. Where these values were checked
NIST
SP 811, Appendix B gives revolution per minute to radian per second as
1.047 198 E−01, revolution to radian as 6.283 185 E+00, and
degree to radian as 1.745 329 E−02. The 9.549297 r/min in one rad/s is the
reciprocal of the first of those.
NIST
SP 811, Chapter 4, Table 3, lists the radian with symbol rad, value
1, and base-unit expression m/m. The rule that every unit symbol takes
a space except the degree, minute, and second of plane angle is
NIST
SP 811, section 7.2.
Addendum 301. Why the radian is the only angle unit that works
A radian is defined as arc length divided by radius. Multiply an angle in radians by a radius
and you get the arc length back — which is exactly the distance the rim travelled. Do the
same thing per second and you have the rim speed. Degrees and revolutions carry an extra
arbitrary count inside them, so they need a conversion factor first. The radian does not,
because it was built out of the same geometry the formula describes.
Conversion factors from
NIST
SP 811, Appendix B: revolution per minute to radian per second 1.047 198
E−01, inch to meter 2.54 E−02 (exact), and mile per hour to
meter per second 4.4704 E−01 (exact).
The grinding-wheel requirement is quoted from
29 CFR
1910.215(d)(1): “The spindle speed of the machine shall be checked before mounting of
the wheel to be certain that it does not exceed the maximum operating speed marked on the
wheel.”
NIST
SP 811, Appendix B lists pound-force foot (lbf·ft) to newton
meter as 1.355 818 E+00, and separately lists foot pound-force
(ft·lbf) to joule as the same 1.355 818 E+00 — the two
entries that establish the word-order convention used above. The reciprocal, 0.7375621, gives
newton metres to pound-force feet.
That M is the prefix symbol for 106 and m the symbol for
the metre is from the prefix and base-unit tables in
NIST
SP 811, Chapter 4.
Addendum 304. Turning a torque into work, and where the radian goes
A constant torque about a fixed axis that turns through an angle does work: W = τθ, with the angle
in radians. Because the radian is a ratio of two lengths, NIST gives its base-unit expression as
m/m and its value as 1. Nothing is added to the units, so:
1 J = 1 N·m (torque) × 1 rad ·
1 ft·lbf = 1 lbf·ft (torque) × 1 rad
This is the practical payoff of the radian being dimensionless: a motor rated in
N·m turning through an angle in rad gives you joules directly,
with no factor to look up. Use degrees or revolutions instead and the relationship breaks,
because both of those carry a chosen count inside them.
All conversions from
NIST
SP 811, Appendix B: foot pound-force to joule 1.355 818 E+00; watt hour to
joule 3.6 E+03 (exact); kilowatt hour to joule 3.6 E+06 (exact);
British thermal unitIT to joule 1.055 056 E+03, with
Btuth1.054 350 E+03, Btu (mean) 1.055 87 E+03,
Btu (39 °F) 1.059 67 E+03, Btu (59 °F) 1.054 80
E+03 and Btu (60 °F) 1.054 68 E+03 listed separately;
calorieIT to joule 4.1868 E+00 (exact).
The horsepower hour figure is derived rather than quoted: one horsepower is
7.456 999 E+02 watts in the same table, and an hour is 3,600 s, so
745.6999 W × 3,600 s = 2,684,520 J to six figures.
NIST
SP 811, Chapter 4, Table 3, gives the joule as J, expressed as
N·m and in base units as m2·kg·s−2,
and the radian as rad, value 1, base-unit expression
m/m.
One horsepower is 550 ft·lbf/s, which is 550 × 12 = 6,600
lbf·in per second. One revolution per minute is 2π/60 rad/s. Putting a
torque τ in lbf·in and a speed N in rpm into
P = τω gives τN(2π/60) lbf·in per second, and
dividing by 6,600 converts that to horsepower:
Every constant in the shortcut is a unit conversion. Nothing about the physics is buried in
it, which is why the same relationship in coherent SI units needs no constant at all.
NIST
SP 811, Appendix B lists horsepower (550 ft·lbf/s) to watt as
7.456 999 E+02 and horsepower (electric) to watt as 7.46 E+02
— two separately defined units, which is why 745.6999 and 746 both appear above. The
0.001341022 hp in one watt is the reciprocal of the first. Foot pound-force to joule is
1.355 818 E+00 in the same table.
NIST
SP 811, Chapter 4, Table 3, gives the watt as W, expressed as J/s
and in base units as
m2·kg·s−3.
Power factor is defined by
Fluke as
“the ratio of working power, measured in kilowatts (kW), to apparent power, measured in
kilovolt amperes (kVA).” The 63,025 constant is derived above from the horsepower
definition and the rpm-to-rad/s conversion, not quoted.
Addendum 308. What the explorer assumes, and where to check a selection
The explorer compares ordinary drives on parallel shafts. “Separated” means a belt or chain span is practical but a single compact gear pair cannot reach. Speed labels are relative to the chosen component's rating, with no universal rpm cutoff. It excludes load sizing, life prediction, efficiency percentages and automatic cost rankings. “Candidate” means worth sizing, not approved for use.
Addendum 309. Manufacturer references for belt geometry and faults
Gates, Preventive Maintenance Manual, “Belt identification,” “Installation,” and “Belt drive problem diagnosis,” supplies the length/profile distinctions and troubleshooting checks. Gates' industrial synchronous-belt guide explains toothed engagement and dry belt contact. Use the exact belt's data for a real selection.
Addendum 310. Derive the inverse and check speed and wrap
Multiply the length approximation by 4C: 4CL = 8C² + 2π(D + d)C + (D − d)². Set B = 4L − 2π(D + d), giving 8C² − BC + (D − d)² = 0. The quadratic formula gives C = [B + √(B² − 32(D − d)²)]/16. Use this larger root and require C > (D + d)/2 so the pitch circles are separated. An impossible length produces no valid layout.
Assuming no slip, n_small / n_large = D/d and v = πd n_small. With d in mm, divide v by 1000 to get m/min; with d in inches, multiply by 0.0254. Speed n is in r/min; N remains the symbol for teeth.
The tangent-span angle is α = asin((D − d)/(2C)); small-pulley wrap is θ = 180° − 2α, with α expressed in degrees. Less wrap means less grip. The drawing uses circular arcs and tangent spans; the length equation approximates that geometry. Its error grows as (D − d)/(2C) grows, so very unequal, closely spaced pulleys need a more exact calculation for final selection.
The checked ASME public listing names B29.1 as Precision Power Transmission Roller Chains, Attachments, and Sprockets, edition 2011 (R2022). See ASME B29.1. The examples above come from public manufacturer tables, not an unread clause of the paid standard.
Addendum 312. ISO scope and the source of the millimeter dimensions
The ISO 606:2015 public abstract describes short-pitch precision roller and bush chains with associated sprockets. Its scope includes dimensional and strength characteristics; a chain number alone is not a load rating. The dimension examples are from Renold Roller Chain tables, “European (BS) Standard — Simplex.” Renold's Chain Standards guide explains series and strand suffixes.
Addendum 314. Where the formulas come from, and what this model leaves out
Geometry. The pin centres sit on a circle of radius R = p / (2 sin(180°/N)). The leaving pin turns at ω, so its horizontal speed is ωR cos θ and its height above the sprocket centre is R cos θ. The pin hands over to the next one when θ reaches ±180°/N, so v runs from ωR cos(180°/N) to ωR. One pitch leaves per tooth, so the average chain speed is N·p·n. Shigley's text derives the same maximum and minimum exit speeds: Budynas and Nisbett, Shigley's Mechanical Engineering Design, 8th ed., section 17-5, Eqs. 17-30 and 17-31.
Two ways to state the same spread. Tsubaki's Complete Guide to Chain, section 2.2.1 (printed page 15), divides by the fastest speed: (Vmax − Vmin) / Vmax = 1 − cos (180°/N). Shigley's Eq. 17-31 divides the same spread by the average speed. For 9 teeth that gives 6.03 % and 6.15 %. The table shows both columns, and the prediction bands accept either.
Design guidance. Shigley's text adds: For smooth operation at moderate and high speeds it is considered good practice to use a driving sprocket with at least 17 teeth. Follow the chain maker's selection procedure for a real drive.
Left out on purpose. This model has one sprocket with rigid links, pins seated exactly on the pitch polygon, and a taut span kept level. In a real drive the span's far end rides on a second sprocket, so the span also tilts. Tsubaki notes that the centre distance relative to the chain pitch, plus manufacturing and alignment errors, changes how much chordal action you get. The model does not include chain stretch, joint clearance, wear, lubrication, vibration or resonance. The tooth form is drawn schematically, not to a standard tooth profile. Pitch follows the pin-to-pin definition in the first card; the governing standard for these chains is ASME B29.1, linked there.
Addendum 315. Check the size definitions with one gear
A spur gear with 30 teeth and 60 mm reference diameter has m = 60/30 = 2 mm. The diameter is 60/25.4 in, so its equivalent diametral pitch is 30/(60/25.4) = 12.7 teeth/in. In general, m = 25.4/Pd. Two gears can have different diameters and tooth counts while sharing the same tooth size.
Addendum 316. Normal and transverse measurements use different planes
The normal plane cuts across a tooth at right angles to its slant; the transverse plane cuts across the gear at right angles to its shaft. Module (tooth size) and pressure angle can be specified in either plane, so compare values measured in the same plane. For this helical pair, match normal module, normal pressure angle and helix-angle magnitude, with opposite helix hands.
Addendum 317. Primary references for the geometry and helical mesh
KHK, Calculation of Gear Dimensions, sections 4.1 and 4.3, distinguishes reference geometry, profile shifts, and normal/transverse helical dimensions. KHK, ABCs of Gearing, B, develops tooth terminology and spur/helical calculations. KHK's helical-gear catalog gives mating-series and bearing-thrust cautions. Use the mating table for the exact product.
Addendum 318. Why the efficiency and strength comparisons need conditions
The IIT Kharagpur lesson Power Screw Drives and Their Efficiency (sections 6.1.1–6.1.2, hosted by IDC) explains square-thread machining cost, trapezoidal sturdiness, and added friction from inclined flanks. Its force model supports a conditional comparison: hold lead angle, contact friction and other losses comparable. It does not establish a universal ranking against V-thread fasteners.
The buttress working flank makes efficient thrust transmission possible in its intended direction; that is a geometry-based explanation, not a promise of the same measured efficiency as square. Reverse travel is possible, but heavy loading on the opposite flank does not retain the same advantages. Compare actual screw-and-nut ratings, not shape alone.
Addendum 319. Where wear and operating limits enter the selection
Thomson: Lead Screws Q&A — Application Considerations describes sliding-contact heat and wear and the relationship between load and speed. Its discussion also distinguishes the generic lead screw from the ACME form. The absence of radial wedging does not remove contact pressure on the working flank.
Addendum 320. The exact standard entries used here
NBS Circular 479, Unified Screw Thread Standards, tables 4 and 6, prints the designation entries 1/4, 20, UNC-1A and 1/4, 28, UNF-1A. The examples above omit the class suffix to teach size and pitch. This historical public standard verifies those combinations; it is not a source of current production acceptance limits. The current Unified inch thread standard is ASME B1.1-2024.
NAAMS Metric Fastener Standards, archived sheet F–2.1, dated 05/29/15, lists M6 x1.0 under screw size and M6 x 1.0 under nominal thread diameter and pitch. Only that designation is used here. ISO 261 identifies the general-purpose metric M-thread family; its catalog entry is not being used as a dimension table.
IIT Kharagpur: Friction in Screws, opening page, defines right-handed advance using clockwise rotation away from the person turning the screw. This observer convention avoids ambiguous arrows.
Addendum 322. Check the definition, not just the label on a catalog
Thomson: Screw Pitch and Lead defines lead as nut travel per screw revolution and states the pitch-times-starts relationship. A supplier may list lead directly. Do not multiply a value already labelled lead by the number of starts a second time.
Addendum 323. Derive the 2π from equal power, or one revolution of work
Ideally, power in equals power out: Tω = Fv. With n in rpm, ω = 2πn/60 rad/s and v = nL/60. Cancel n/60 at nonzero steady speed to get F = 2πT/L. Equivalently, one revolution puts in work 2πT and moves the load through L, doing work FL.
With losses, Fv = ηTω. The motion ratio stays fixed, so the reduction appears in force. See Power and Efficiency. At zero speed both powers are zero; this derivation does not predict breakaway torque or static holding capacity. Lowering a load that drives the screw requires a different friction analysis.
Addendum 326. Why two locating supports can create unwanted load
A warming shaft wants to lengthen. If a housing prevents that length change, elastic deformation creates axial reactions. These can consume clearance, increase friction and cause heating. Actual force depends on shaft, bearing and housing stiffness, temperatures and initial clearance. A floating seat also has friction; “radial only” describes its intended support duty, not literally zero incidental axial force.
Addendum 327. Position preload versus spring preload
Position preload sets the bearing rings at a fixed relative distance, for example with shims. Compared with that arrangement, a spring allows more axial movement under an added load. The spring can maintain preload as dimensions change, but the shaft position changes more under load.
No manufacturer restriction confining brass shims to a nonrotating ring was verified. Material and mounting instructions must come from the actual assembly documentation.
Addendum 330. Why voltage and resistance are called derived units
Of the four units above, only the ampere is a base unit — one of the seven that the
rest of SI is built from. The others are derived: their definitions are ratios of units
already defined. NIST expresses the volt as W/A and the ohm as V/A,
and traces both back to base units as
m2·kg·s−3·A−1
and
m2·kg·s−3·A−2.
That is why unit cancellation works on electrical problems exactly as it does on mechanical
ones — the electrical units are made of metres, kilograms, seconds, and amperes underneath.
The technique on Dimensional Analysis does not need a separate electrical version.
Addendum 331. The dropped voltage does not disappear
The power lost in the cord is P = I2R = (10 A)2 × 0.1588
Ω = 15.9 W. That power becomes heat in the conductor, spread along its whole
length.
Notice the squared current. Doubling the load to 20 A does not double the loss, it
quadruples it, to about 64 W. This is why the drop that is harmless on a light load becomes a
real problem on a heavy one, and why the length and gauge of a cord matter more the more current
the tool draws. The condition and routing of the cord itself are covered on
Electrical Safety.
NIST
SP 811, Chapter 4, Table 3, gives: volt V, expressed as W/A, base
units m2·kg·s−3·A−1;
ohm Ω, expressed as V/A, base units
m2·kg·s−3·A−2;
coulomb C, base units s·A; watt W, expressed as
J/s; pascal Pa, expressed as N/m2; and farad
F, expressed as C/V.
The ampere is listed as one of the seven SI base units, with symbol A, by both
BIPM and
NIST. The rule that a unit symbol
takes a capital first letter when the unit is named after a person is
NIST
SP 811, Chapter 6.
Engineering Fundamentals/Electrical Systems/AC and DC
Addendum 333. Why use RMS instead of the average voltage?
A symmetrical sine wave averages to zero over a whole cycle, yet it still heats a resistor. RMS is the DC voltage that would produce the same average heating in that resistance. Square the instantaneous voltage, average those squares over a cycle, then take the square root. The square-root-of-two conversion applies to a sine wave; do not apply it to an arbitrary inverter waveform.
Engineering Fundamentals/Electrical Systems/AC and DC
Addendum 334. Why RMS answers the heating question
Analog Devices' RMS explanation
shows why ordinary signed or absolute averages do not predict heating for arbitrary waveforms. Its
power note
distinguishes average power from the RMS value of a power waveform: RMS voltage or current can calculate
meaningful average power in the stated load. This classroom explorer uses a purely resistive fixed load; it
does not model impedance, power factor, temperature, a meter's coupling mode, or an actual circuit.
Engineering Fundamentals/Electrical Systems/AC and DC
Addendum 335. A comparison with the same power and the same line
In an ideal DC or unity-power-factor comparison, transmitting 8,000 W at 400 V requires 20 A. At 4,000 V it requires 2 A. If the complete line resistance is 0.5 Ω, the losses are 200 W and 2 W. Ten times the voltage gives one hundredth the resistive loss. This simplified comparison omits converter losses and voltage regulation; it is not a design for a real transmission line. For AC loads with a phase shift, see Power and Efficiency.
The historical advantage belongs to the equipment available at the time. Modern converters also make high-voltage DC transmission practical.
Addendum 336. Why a long wire can matter even below its current limit
A wire can stay within its temperature limit yet drop too much voltage for its load. Length increases resistance, and both voltage drop and heating follow from that resistance. The worked cord example in Current, Voltage, and Resistance shows the calculation.
Addendum 337. Definitions used to calculate every result
For AWG number n, diameter d = 0.127 × 92(36 − n)/39 mm. Convert d to meters, then A = πd²/4 in m². Using annealed-copper resistivity ρ = 1.724 × 10−8 Ω·m at 20 °C, R = ρL/A. One foot is exactly 0.3048 m.
With one-way run ℓ, L = 2ℓ and Rloop = ρ(2ℓ)/A. Vdrop = IRloop; percent drop = 100Vdrop/Vsource; Vload = Vsource − Vdrop; wire loss P = I²Rloop. A two-wire single-phase resistive approximation uses the same return path, but this model does not include AC effects.
Addendum 338. Why the parallel formula uses reciprocals
Each branch draws the supply voltage divided by its resistance. Add those branch currents, then divide by the common voltage. The result is a sum of 1/R terms. This reciprocal of resistance is called conductance: parallel branches add ways for current to flow.
Addendum 339. Real meters change the circuit a little
An ideal voltmeter draws no current. A real one has high but finite input resistance. An ideal ammeter drops no voltage. A real one has some resistance and a voltage drop, sometimes called burden voltage. The practice problems use ideal meters unless stated otherwise.
Addendum 340. Check the node count terminal by terminal
The four separate conductor groups are B1+ to S1; the other side of S1 to R1; the other side of R1 to D1 anode; and D1 cathode to B1−. Closing an ideal S1 merges the first two groups into one, leaving three nodes. None of the component bodies is an extra node.
Addendum 341. Where the alignment picture needs care
This is a first picture, not a description of every motor's internal timing. A synchronous motor can rotate at the same speed as the stator field while keeping an angular offset that produces torque. An induction rotor runs slower than the field during normal motoring; that relative motion induces rotor current. A stepper can deliberately stop and hold a commanded position.
Addendum 342. Sources for the torque formula and the commutator
OpenStax, University Physics Volume 2, section 11.5, Force and Torque on a Current Loop, derives the torque on a rectangular loop in a uniform field (equations 11.19 to 11.22). It defines the magnetic moment of an N-turn loop as N·I·A along the loop's normal and describes brushes and a commutator reversing the current. HyperPhysics (Georgia State University), Commutator and Brushes on DC Motor, describes a split-ring device called a commutator that reverses the current as the coil passes the plane perpendicular to the field. Its Torque on a Current Loop page gives the same torque in terms of the magnetic moment.
Addendum 343. Why alternating current alone is not the full explanation
A single winding supplied by single-phase AC makes a field that pulses back and forth; that alone does not establish a starting direction. Single-phase induction motors use an additional starting arrangement. The rotating field, rotor current, and relative speed explain rotation more clearly than saying the rotor field simply opposes the stator field.
Addendum 344. Manufacturer basis for the straight line
maxon's Motor Data and Operating Ranges, p. 10, states: Enhancing the load torque leads to a linear reduction of the speed. It identifies no-load speed and stall torque as the endpoints and specifies fixed applied voltage.
Addendum 345. Derive the halfway result from the straight line
Put x = n/n0. Then T = Ts(1 − x), so P = Tsω0x(1 − x). Since x(1 − x) = 1/4 − (x − 1/2)2, the largest value is 1/4 at x = 1/2. Thus peak power = Tsω0/4, at half no-load speed and half stall torque. The two endpoint maxima cannot occur at the same time.
Portescap's Brush DC Motor Basics, p. 1, point 4, places maximum mechanical power at half the stall torque. On the linear curve, this also means half no-load speed, as derived above.
Addendum 347. Manufacturer basis for the efficiency comparison
Portescap's Brush DC Motor Basics, p. 1, point 3, states: The maximum efficiency is obtained at high speed. Its accompanying torque plot places the efficiency peak below the torque of peak power; the descending speed line therefore puts it at higher speed.
The running conversion follows maxon's gear conversion note: motor speed equals reduction multiplied by load speed, while motor torque equals load torque divided by reduction and gear efficiency. The note also requires checking actual gear torque and speed limits. A separate maxon standstill note explains that power efficiency is undefined when both input and output power are zero. This lesson therefore treats stall as a boundary; it does not calculate blocked-state efficiency or a permissible output torque.
The Uno's internal pull-up is approximately 20–50 kΩ, not a fixed 10 kΩ. Arduino's Uno R3 documentation specifies “20-50k ohm.” At nominal 5 V, a closed switch carries about 0.10–0.25 mA through that resistor, using I = V/R. See Current, Voltage, and Resistance.
Addendum 350. Phototransistor circuits can measure light or switch at a threshold
Vishay's Ambient Light Sensors — Circuit and Window Design shows both light-meter circuits and light-switch circuits. The phototransistor current changes with illumination; the surrounding circuit determines whether the output preserves a range or switches between logic states.
Addendum 351. Why an ultrasonic measurement can be digital
The HC-SR04 manufacturer datasheet, hosted by SparkFun describes an Echo pulse whose width represents the range. Digital describes the two voltage states; the information can be carried by their timing. A single digitalRead tells you the current state, not the pulse duration.
Addendum 352. Arduino's resolution and timing figures
The official analogRead reference source gives “5 volts / 1024 units” and “about 100 microseconds (0.0001 s)”. That is roughly 10,000 reads per second on ATmega-based boards using the usual API, not an absolute ADC hardware limit or a guaranteed loop rate. Computation, communication and delays take additional time. The published analogRead reference is the learner's API lookup.
Addendum 353. Why dividing by 1023 answers a different question
There are 1024 codes but only 1023 intervals between code labels 0 and 1023. Multiplying by 5/1023 stretches those endpoints to exactly 0 and 5 V; that is endpoint scaling, not the nominal ADC step. The explorer and practice consistently use 1024. Real converters have transition offsets, noise and reference error; their exact thresholds are not predicted by this classroom bin model. A code cannot recover the original voltage exactly.
ADC conversion floors each individual ideal sample into a bin. Averaging the reconstructed lower edges therefore need not equal converting the analog sample mean. For a 25% raw 0–5 V sequence with one HIGH and three LOW samples, the analog sample mean is 1.25 V; the lower-edge reconstructions average 4.9951171875/4 = 1.248779296875 V. Neither operation recovers information between sample instants.
Addendum 355. Official frequency table and timer limitations
The Uno R3 row of Arduino's analogWrite reference source states “490 Hz (pins 5 and 6: 980 Hz)”. See also the published analogWrite reference. A frequency near 31 kHz requires changing timer configuration; it is not the stock setting. analogWrite sets duty, not frequency. Arduino's Secrets of Arduino PWM explains prescalers and timer modes. Changing timers can also affect other functions and libraries.
Addendum 356. Why more samples can still give the wrong mean
If the sample clock repeatedly lands at the same PWM phase, every point can read HIGH or every point can read LOW even though the full-cycle time mean is 1.25 V. A sample-and-hold output keeps the most recent point value between samples; holding is not averaging. A carefully spaced finite set can match the cycle mean, but a higher rate or larger count alone does not guarantee an unbiased result. This bounded comparison does not claim reconstruction of an unbandlimited switching edge from a Nyquist test.
During each constant input interval, V(t) = Vtarget + (Vstart − Vtarget)e−t/τ. The model solves for a repeating steady state, then draws the charging and discharging curves. It omits startup, output resistance, component tolerances and loading. At 0% or 100%, the settled output is simply 0 V or 5 V.
Relative motion between a magnetic field and conductors induces a voltage. With a closed circuit, current flows and the shaft must supply work against the electrical load. Motor action and generator action reverse the direction of energy conversion; see Electric Motor Principles. Actual machines and controls determine how they can operate in either direction.
Addendum 359. Why a remote-control recommendation needs more than a chemistry name
A low average load makes charge retention important, but it does not by itself select NiCd over NiMH. Compare the actual cells' self-discharge, usable capacity, voltage and charging requirements. A low-self-discharge NiMH cell behaves differently from an older conventional NiMH cell.
This overview uses the historical sequence in the course generation-and-storage notes, with dates rounded to eras. Invention, patent and market introduction are different milestones; the dates are not intended as a priority claim. The development of lithium-ion was a multi-researcher effort, not solely the work of the company that first sold it.
Addendum 361. Why the battery estimate uses an approximate sign
Wh = Ah × V is exact for constant voltage. A real cell's voltage changes during discharge, so nominal voltage gives an energy estimate. Usable charge also changes with load, temperature, age and the cutoff voltage. These calculations assume the stated capacity is available.
Use the broad, clean, solder-coated working face of the tip against both parts. Do not interpret “side of the iron” as the barrel or an uncoated surface. The useful contact area, not the sharpest point or the highest temperature setting, delivers heat into the joint. A tiny point can be hot and still transfer heat poorly.
Heat applied to a cell can damage its seals and internal parts. Lithium cells in particular can fail dangerously if damaged. Use the intended battery holder or connector instead of applying a soldering iron to a battery.
The UK Health and Safety Executive's guidance for solderers describes rosin-based flux fume and recommends extraction and keeping your head out of the plume.
A hot tip oxidizes. Oxide interferes with wetting, while a solder coating protects the working face and helps make thermal contact with the joint. Tinning the tip is the time to feed solder onto the tip. Making a joint is different: feed solder into the heated joint.
See HAKKO's tip-life guidance for the construction of plated tips and the effects of oxidation.
Addendum 366. A one-second count is a rhythm, not a temperature test
“Apply iron, one-second count, apply solder” reminds you to heat before feeding. The actual time depends on the joint, tip, alloy, and component limits. Look for solder flowing onto both surfaces. If it will not flow, stop and check cleanliness, flux, contact, and tool settings rather than holding the iron there indefinitely.
Addendum 367. Why lead-free solder may look different
Kester's soldering FAQ, under lead-free joint appearance, explains that tin-silver-copper joints can have a dull surface without being poor joints. Judge the connection, not shine alone.
Some wires and terminals are pre-tinned: a small amount of solder wets the surface before final assembly. This can help the final joint flow, but too much solder makes a wire end stiff and bulky. Follow the connection's assembly method and still heat both parts when making the final bond.
