Measurement over pins / balls calculator (spur and helical, ideal pin diameter)
The dimension M measured over pins (balls for helical gears) placed in the tooth spaces. Leave the pin diameter blank to use the ideal pin diameter.
Result
invφ = dp/(z·m·cosα) − (π/(2z) − invα) + 2x·tanα/z
Even teeth: M = z·m·cosα/cosφ + dp Odd teeth: M = (z·m·cosα/cosφ)·cos(90°/z) + dp
Helical gears use αt and mn/cosβ (measured over balls)
Pins (balls for helical gears) are placed in tooth spaces and M is measured across them with flat anvils. With an even number of teeth the spaces are directly opposite; with an odd number they are half a pitch apart, so M = (2 × radius to pin center) × cos(90°/z) + dp. Drawn to scale with the ideal pin diameter.
Printed from Kezuriba (kezuriba.net/en/gears/overpin/)
✎Notes
- In practice, choose the commercially available precision pin (ball) closest to the ideal diameter and enter its size to calculate M.
- On an odd-tooth gear the pins cannot sit in opposite spaces, so the dimension is taken half a pitch apart.
The formulas follow the published technical data listed below and have been checked against the worked examples in those sources. For design or inspection, confirm against your drawing and the standards.