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Screw Threads and Lead Screws

Thread forms and callouts, and lead screws for converting rotation into linear force and motion.

  1. Screw Threads
  2. Lead Screws
  3. Backlash and Lost Motion
Engineering Fundamentals/Power Transmission

Screw Threads

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

Four schematic axial profiles: square has parallel sides; V has steeply inclined sides; ACME and metric trapezoidal have flat crests and sloping sides; buttress has an asymmetric load flank and supporting flank.
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 useWhat it offersWhat it costs
Square: power screws and jacksHigh efficiency relative to angled flanks under otherwise comparable conditions.Difficult, expensive machining; wear adjustment is difficult.
V / machine-screw thread: bolts and fastening screwsWidely 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 actuatorsEasier 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 pressA 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 1 — 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 2 — 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.
CalloutRead it asPitch
1/4-20 UNCNominal diameter 1/4 in; 20 threads per inch; Unified coarse series1/20 = 0.050 in
1/4-28 UNFNominal diameter 1/4 in; 28 threads per inch; Unified fine series1/28 ≈ 0.03571 in
M6 × 1.0Metric thread; nominal diameter 6 mm; pitch 1.0 mm1.0 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 3 — The exact standard entries used here.

Practice reading an inch callout

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.

With the nut fixed, clockwise rotation viewed from the driving end moves the right-hand screw away from the viewer and the left-hand screw toward the viewer.
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 4 — Direction reference.

Next, distinguish pitch from lead in Lead Screws.

Engineering Fundamentals/Power Transmission

Lead Screws

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.

Unwrapped screw surfaces compare a single-start screw with pitch 2 mm and lead 2 mm to a triple-start screw with the same pitch 2 mm and lead 6 mm. A, B and C label the separate ridges.
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 5 — 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.
TorqueLead for force calculationForce
N·mmetres per revolution (mm ÷ 1,000)N
lbf·in (often written lb-in)inches per revolutionlbf

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 6 — 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.
StartsLeadSpeedIdeal forceActual force
12 mm/rev10 mm/s3,770 N1,508 N
36 mm/rev30 mm/s1,257 N503 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.

  1. L = 0.20 × 1 = 0.20 in/rev.
  2. v = 900 × 0.20 = 180 in/min = 3 in/s.
  3. Ftheoretical = 2π × 12 / 0.20 = 376.99 lbf.
  4. 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.

Practice actuator force

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.

  1. 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.
  2. L = 4 mm/rev = 0.004 m/rev.
  3. Factual = 0.30 × 2π × 21.6 / 0.004 ≈ 10,179 N = 10.18 kN.

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.

Practice handle torque and clamp force Practice a triple-start CNC screw

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 7 — 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 ÷ L   dial 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.

Handwheel dial reading 0.80 mm: 0 turns and 16 divisions of 0.05 mm.01020304050607080900.80mmIndicator on the carriage reads 1.00 mm.01020304050607080901.00mm
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.
Hysteresis loop: carriage position against dial reading. The band between the forward-approach line and the reverse-approach line is 0.20 mm wide along the dial axis. Current dial 1.00 mm, carriage 1.00 mm.−0.30.00.30.50.81.01.3−0.30.00.30.50.81.01.3B = 0.20 mmDial reading from screw rotation (mm)Carriage from indicator (mm)forward approach: carriage = dialreverse approach: carriage = dial + B
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.
Axial section through the thread, drawn riding on the carriage. Screw flank pushing the nut toward +X. To scale: lead 5 mm, clearance 1.00 mm (illustrative 30-degree thread form).+X →Screw flank pushing the nut toward +Xbronze nut, moves with the carriagesteel screw, turns but never slidesDriving forward · To scale: lead 5 mm, clearance 1.00 mmAxial section through the thread, drawn riding on the carriage. Nut held in the clearance: no flank touching. To scale: lead 5 mm, clearance 1.00 mm (illustrative 30-degree thread form).+X →Nut held in the clearance: no flank touchingbronze nut, moves with the carriagesteel screw, turns but never slidesReversed part way · To scale: lead 5 mm, clearance 1.00 mmAxial section through the thread, drawn riding on the carriage. Screw flank pushing the nut toward −X. To scale: lead 5 mm, clearance 1.00 mm (illustrative 30-degree thread form).+X →Screw flank pushing the nut toward −Xbronze nut, moves with the carriagesteel screw, turns but never slidesDriving back · To scale: lead 5 mm, clearance 1.00 mm
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.
MethodDial movesDialCarriageError
Reverse straight to the number25.60 → 25.00 mm25.00 mm25.20 mm+0.20 mm
Back past it, approach forward again25.60 → 24.50 → 25.00 mm25.00 mm25.00 mm0.00 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 LOne divisionClearance BDead band
5 mm/rev0.05 mm0.20 mm4 divisions = 14.4°
2 mm/rev0.02 mm0.20 mm10 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:

  1. Back the handwheel past the target by more than the backlash.
  2. 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 8 — 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
Top view of a contour groove around a circle island. X clearance 0.00 mm, Y clearance 0.00 mm. Complete pass. Shaded cells are swept by the full cutter; the middle is retained material.+X+Y−10010 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
Top view of a contour groove around a circle island. X clearance 0.50 mm, Y clearance 0.00 mm. Complete pass. Shaded cells are swept by the full cutter; the middle is retained material.+X+Y−10010 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
Top view of a contour groove around a circle island. X clearance 0.00 mm, Y clearance 0.50 mm. Complete pass. Shaded cells are swept by the full cutter; the middle is retained material.+X+Y−10010 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
Top view of a contour groove around a circle island. X clearance 0.50 mm, Y clearance 0.50 mm. Complete pass. Shaded cells are swept by the full cutter; the middle is retained material.+X+Y−10010 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 9 — What the model means, and why it is not a prediction for every CNC.

Supporting detail

Addendum

Additional evidence, standards context, and background referenced from the main text.

  1. Engineering Fundamentals/Power Transmission/Screw Threads

    Addendum 1. 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.

    Pratt & Whitney's ACME explanation describes the manufacturing and split-nut advantages. IIT Kharagpur's thread manufacturing lesson explains fastener rolling and other production routes. For thread cutting on a machine tool, see Lathe Operations.

    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.

    Back to reference 1

  2. Engineering Fundamentals/Power Transmission/Screw Threads

    Addendum 2. 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.

    Back to reference 2

  3. Engineering Fundamentals/Power Transmission/Screw Threads

    Addendum 3. 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.

    Back to reference 3

  5. Engineering Fundamentals/Power Transmission/Lead Screws

    Addendum 5. 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.

    Back to reference 5

  6. Engineering Fundamentals/Power Transmission/Lead Screws

    Addendum 6. 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.

    IIT Kharagpur: Power Screw Drives and Their Efficiency, section 6.1.2, relates output work, input work and friction. The calculator uses a given efficiency, not a friction coefficient or a thread-strength model.

    Back to reference 6

  7. Engineering Fundamentals/Power Transmission/Backlash and Lost Motion

    Addendum 7. Where the definition comes from

    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.

    Back to reference 7

  8. Engineering Fundamentals/Power Transmission/Backlash and Lost Motion

    Addendum 8. 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.

    Back to reference 8

  9. Engineering Fundamentals/Power Transmission/Backlash and Lost Motion

    Addendum 9. 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.

    Back to reference 9