BIZOMAT MAKEOS · Power Transmission
Silent (Inverted-Tooth) Chain Sprocket Diameters
What pitch, outside, guide-groove and over-pin diameters does this silent chain sprocket have?
Sprocket diameters for ANSI silent (inverted-tooth) chain of 3/8 in. pitch and larger by the handbook formulas: pitch diameter, outside diameter for round teeth, maximum guide groove diameter, gauge pin diameter and the measurement over pins for even or odd tooth numbers.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Chain pitch | mm | Chain pitch (3/8 in. = 9.525 mm and larger). |
| Number of teeth | Number of sprocket teeth. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Chain pitch
- What it is
- The pitch of the silent chain: the centre-to-centre distance between neighbouring link pins, from the chain maker’s data.
- Units and format
- Enter a number in mm: millimetres. The form accepts 9.5 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12.7 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Every sprocket diameter scales in direct proportion to the pitch.
- Get it right
- These formulas are for chain of 3/8 in. (9.525 mm) pitch and larger; smaller chain uses different constants.
What this means: Number of teeth
- What it is
- The number of teeth on the sprocket, which with the pitch sets all its diameters.
- Units and format
- Enter a plain number with no unit. The form accepts 13 to 200. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 21 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Odd and even tooth counts are measured over pins differently; the tool picks the right formula.
Method and formulas
- PD = P ÷ sin(180° ÷ N).
- OD (round teeth) = P cot(180° ÷ N) + 0.08 P; maximum guide groove G = P cot(180° ÷ N) − 1.16 P.
- Gauge pins D_p = 0.625 P; pin-centre diameter = PD − 0.125 P csc(30° − 180° ÷ N).
- Over pins: even N = pin-centre diameter + D_p; odd N = pin-centre diameter × cos(90° ÷ N) + D_p.
- Example: a 21-tooth sprocket for 12.7 mm pitch chain has a 85.211 mm pitch diameter.
Limitations
- Formulas for 3/8 in. and larger pitch; 3/16 in. pitch chain uses different constants.
- Tolerances are in the standard.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Machine or inspect a silent chain sprocket
- Check a worn sprocket against its drawing
- Size the guide groove for a centre-guide chain
Who it is for
- Power transmission engineers
- Machinists
- Maintenance engineers
What you get
- Pitch diameter
- Outside diameter and guide groove
- Over-pin diameter and gauge pin size
Interpreting the result
- Measure over pins to check tooth form and wear; compare with the calculated value and the standard’s tolerance.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3457–3460. Topic reference; no source tables or recommended settings are reproduced.
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Open the Silent (Inverted-Tooth) Chain Sprocket Diameters calculator