Dimension between pins (balls) for internal involute gears or splines.
(Diametral Pitch. AGMA. Inch.)

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

Diametral pitch:
DP
Helix angle on pitch diameter:
h
Normal pressure angle on pitch diameter:
An
Normal arc tooth thickness on pitch diameter:
Tn
Ball, pin or wire diameter:
D
Output:
Transverse pressure angle:
Ad=arctan(tan(An)/cos(h))
Transverse circular tooth thickness on pitch diameter:
td=tn/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/180*pi
Involute function of pin center Bd(rad):
In_Bd=pi/N-td/PD-dD/BD+InAd
Pressure angle to pin center Bd:
InBd=Tan(Bd)-Bd*pi/180
Diameter of pin centers:
CC=BD/cos(Bd)
Dimension between pins:
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). External gears and splines. ZAKGEAR Calculators.

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