Circular tooth thickness from over pins (balls) mesurment for external involute gears or splines.
(Diametral Pitch. AGMA. Inch.)

Input:
Number of teeth:
N
Involute spline over pins dimension drawing.

Diametral pitch:
DP
Helix angle on pitch diameter:
h
Normal pressure angle on pitch diameter:
An
Dimension over pins(balls):
DO
Ball, pin or wire diameter:
D
Output:
Diameter of pin centers:
CC=DD-D (even); CC=(DO-D)/cos(90/N) (odd)
Transverse pressure angle:
Ad=arctan(tan(An)/cos(h))
Helix angle on base diameter:
H=arctan(tan(h)*cos(An))
Transverse pin diameter:
dD=D/cos(H))
Pitch diameter:
PD=N/(DP*cos(H))
Base diameter:
BD=PD*cos(Ad))
Involute function of Ad(rad):
InAd=tan(Ad)-Ad, Ad[rad]
Pressure angle to pin center Bd:
Bd=acos(B_D/C_C)
Involute function of Bd(rad):
InBd=tan(Bd)-Bd, Bd[rad]
Transverse circular tooth thickness on pitch diameter:
td=PD*(InBd-dD/BD-InAd+pi/N)
Normal curcular tooth thickness on pitch diameter:
DO=CC+D (even); DO=cos(90/N)*CC+D (odd)
Pressure angle to point at tangency:
F=arctan(tan(Bd)-D*cos(H)/BD)
Radius to point of tangency:
RF=BD/2/cos(F)


Reverse calculation. Metric (DIN). Internal gear and splines. ZAKGEAR Calculators. Home page.

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