KEVOS® MAKEOS · Gears
Spur Gear Measurement over Pins
What should the measurement over two pins read for this external spur gear?
Measurement over two pins (or balls) for an external spur gear with even or odd teeth, from the tooth thickness and pin size, by the involute function.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module. |
| Number of teeth | teeth | Number of teeth. |
| Pressure angle | ° | Pressure angle. |
| Profile shift coefficient | Profile shift coefficient (0 if not shifted). | |
| Tooth thinning for backlash (arc, at pitch circle) | mm | Reduction of arc tooth thickness for backlash, from the gear drawing. |
| Pin diameter (0 = 1.728 × module) | mm | Actual pin or ball diameter; 0 uses 1.728 × module, a common size that contacts near the pitch circle. |
Method and formulas
- Tooth thickness s = m(π/2 + 2x tan α) − thinning; d = m z; d_b = d cos α.
- inv φ = s ÷ d + inv α + d_p ÷ d_b − π ÷ z (solved for φ by Newton’s method).
- Even teeth: M = d_b ÷ cos φ + d_p. Odd teeth: M = (d_b ÷ cos φ) cos(90° ÷ z) + d_p.
- Example: module 2, 25 teeth with 3.456 mm pins measures 54.702 mm over the pins.
Limitations
- External spur gears; helical and internal gears need modified formulas.
- Pins must contact the flanks on the involute; check the contact diameter for small tooth counts.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect spur gear tooth thickness accurately
- Write an inspection dimension on a gear drawing
- Check a gear without a span micrometer
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pin diameter used
- Pressure angle at the pin centre
- Measurement over pins
Interpreting the result
- A larger reading means thicker teeth (less backlash).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2236–2248. Topic reference; no source tables or recommended settings are reproduced.
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