Spur Gear Tooth Geometry (Diametral Pitch)
From the diametral pitch Pd: pitch dia = N/Pd, OD = (N+2)/Pd, addendum 1/Pd, dedendum 1.25/Pd, whole depth 2.25/Pd, root (N-2.5)/Pd, center distance (N1+N2)/(2Pd). Pd 10, N 40, mate 20 -> PD 4.000, OD 4.200, center 3.000 in; a finer Pd 20 halves every dimension. A shop aid; the gear drawing and AGMA govern.
Formula and source
PD = N/Pd; OD = (N+2)/Pd; addendum = 1/Pd; dedendum = 1.25/Pd; whole depth = 2.25/Pd; root = (N-2.5)/Pd; center = (N1+N2)/(2 Pd).
Spur gear tooth proportions in the diametral-pitch system (20-degree full-depth involute; Machinery's Handbook / AGMA), by name.
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