Gear-Tooth Chordal Thickness (Caliper)
The gear-tooth caliper settings the geometry tile leaves out: chordal tooth thickness tc = (N/Pd) sin(90/N deg) read across the tooth, and chordal addendum ac = 1/Pd + (N/2Pd)(1 - cos(90/N deg)) set as the tongue depth. Pd 10, N 40 -> tc 0.1570 in, ac 0.1015 in (the arc thickness pi/2Pd is 0.15708). Standard 20-degree full-depth involute, no profile shift or backlash allowance. A shop inspection aid; the gear drawing and AGMA govern.
Formula and source
chordal tooth thickness tc = (N/Pd) x sin(90/N deg); chordal addendum ac = 1/Pd + (N/(2Pd)) x (1 - cos(90/N deg)); arc tooth thickness = pi/(2Pd).
Gear-tooth-caliper (vernier) inspection dimensions for a 20-degree full-depth involute spur gear, the standard Machinery's Handbook / AGMA method, by name.
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