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.
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.
“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.
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.
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.
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.
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.
