External Spur Gears

TO GET	HAVING	RULE	FORMULA
N	Number of teeth	Given	35
DP	Diametral pitch		10
á	Pressure angle		20
t	Arc tooth thickness		0.155
d	Pin diameter		0.1728
PD	Pitch diameter N/Dp		3.5
BD	Base diameter	PD•COS(á)	3.28892
A		t/PD	0.04429
D		d/BD	0.05254
E		ð/N	0.08976
INVá	Involute function of á	TAN(á)- [á(ð/180)]	0.0149
INVâ	Involute function of â	A+D+INVá-E	0.02197
â	Pressure angle to pin center	see tables (pages G14)	22.65108
CC	Twice the center distance of pin and gear	BD/COS(â)	3.56381
DE	Dimension over pins even # of teeth	CC+d	***********
DO	Dimension over pins odd # of teeth	COS(90/N)•CC+d	3.73302
Ö	Pressure angle to point of tangency	TAN(Ö)=TAN(â)-D	20.04026
RT	adius to point tangency	R BD/[2•COS(Ö)]	1.75045

Determining Dimension over Pins

TO GET	HAVING	RULE	FORMULA
N	Number of teeth	Given	50
DP	Diametral pitch		8
α	Pressure angle		20
d	Pin diameter		0.21144
DE	Dimension over pins even # of teeth		6.53345
DO	Dimension over pins odd # of teeth		***********
PD	Pitch diameter	N/DP	6.25
BD	Base diameter	PD•COS(α)	5.87308
CE	Twice the center distance of pin and gear even # of teeth	DE-d	6.32201
CO	Twice the center distance of pin and gear odd # of teeth	(DO-d)/COS(90/N)	***********
β	Pressure angle to pin center	COS(β)=BD/CE or CO	21.72221
INVβ	Involute function of β	TAN(β)-[β(π/180)]	0.01927
E		π/N	0.06283
D		d/BD	0.036
INVα	Involute function of α	TAN(α)-[α(π/180)]	0.0149
t	Arc tooth thickness	PD(E+INVβ-INVα-D)	0.195

Determining Arc Tooth Thickness Given Dimension over Pins