Gear Over Pins Measurement

Scope: external involute spur gears, with optional profile shift x (0 for a standard gear). Leave the pin blank and the page uses the standard 1.728 ÷ DP pin when it fits this gear, otherwise the best pin.

The pin calculation uses standard involute spur-gear geometry. For the recommended pin, the pin is chosen so its theoretical involute contact point is on the d + 2x·m circle (the reference circle when the profile shift x is 0). Profile shift narrows the tooth space at the base circle by 2x tan α / z. For an entered pin diameter, the tool solves the inverse involute function and applies the separate even- and odd-tooth over-pins relations. The minimum pin is the smallest pin that both touches the working flanks and stands above the tooth tips, so micrometer anvils land on the pins rather than the teeth. The maximum pin places contact at the tooth tip. They are selection limits, not drawing acceptance tolerances. A backlash allowance is made by thinning the teeth at the pitch circle, exactly as on Span & Chord: normal backlash converts to circular with jt = jn ÷ cos α, and each gear is thinned by Δs = jt/2 (shared evenly) or Δs = jt (all on this gear). The thinner tooth widens the space, so the same pin sits deeper: inv φ = D/db − (η + Δs/d). The pin is still the one chosen for the nominal gear. In a range, the minimum backlash gives the largest measurement. This assumes the gears run at the standard centre distance. For diametral-pitch gears the Van Keuren standard pin, 1.728 ÷ DP, is also shown: it is the size used in published over-pins tables and sold as gear measuring wires.

References: Cogwright, FreeCAD Gear Workbench documentation and the BOSL2 gear library.