Gear Identification (Pitch from Teeth and OD)
Identify an unknown spur gear from a counted tooth count and a measured outside diameter - the inverse of the gear-geometry tile, which needs the pitch you are trying to find. Because OD = (N+2)/Pd, the diametral pitch is Pd = (N+2)/OD, the pitch diameter is N/Pd, and the module is 25.4/Pd. Count 40 teeth on a 4.200 in gear -> Pd 10 teeth/in, PD 4.000 in, module 2.54 mm; the measured Pd snaps to the nearest standard so a caliper a hair off still identifies it. 20-degree full-depth involute; confirm against the drawing or a gear gauge.
Formula and source
Pd = (N + 2)/OD; pitch dia = N/Pd; module = 25.4/Pd; snap Pd to the nearest standard value.
Spur gear identification in the diametral-pitch system (20-degree full-depth involute; Machinery's Handbook / AGMA), the inverse of OD = (N+2)/Pd, by name.
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