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Gear Measurement Over Pins

Drop two pins (wires) into opposite tooth spaces and measure across them — measurement over pins (MOP) is how you check tooth thickness on an external spur gear without special gauges. This solves the involute geometry for a standard (unshifted) gear; odd tooth counts use a cos(90°/N) factor.

Module m (mm)

Number of teeth N

Pressure angle α (°)

Pin diameter dₚ (mm)

Measurement over pins M

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Pin-contact pressure angle

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Standard (no profile shift) external spur gear. For profile-shifted or helical gears add the shift/helix terms. A helper, not a substitute for engineering judgment.