2
Solution to Homework Set 7.
Problem 7.13.
A 4-tooth/in diametral pitch, 24-tooth pinion is to drive a 36-tooth gear. The
gears are cut on the 20° full-depth involute system. Find and tabulate the addendum, dedendum,
clearance, circular pitch, base pitch, tooth thickness, base circle radii, the length of the paths of
approach and recess, and the contact ratio.
From Table 7.2, see page 336, the addendum is
( )
1
1 4 teeth/in
0.250 in
aP
==
=
Ans.
Also, from Table 7.2, see page 336, the dedendum is
( )
1.25
1.25 4 teeth/in
0.312 5 in
dP
=
Ans.
From the definition on pages 333 and 340, the clearance is
( ) ( )
0.312 5 in
0.250 in
0.062 5 in
cda
=−=
−
=
Ans.
From Equation (7.4), see page 334, the circular pitch is
( )
4 teeth/in
0.785 4 in/tooth
pP
ππ
=
Ans.
From Equation (7.6), see page 340, the base pitch is
()
cos
0.785 4 in/tooth cos20
0.738 0 in/tooth
b
pp
φ
°
=
Ans.
The tooth thickness can be approximated as
( )
2
0.785 4 in/tooth
2
0.392 7 in
tp
=
Ans.
From Equation (7.1), see page 330, the radii of the pitch circles are
2
2
24 teeth
3.000 in
2
2 4 teeth/in
N
R
P
=
and
3
3
36 teeth
4.500 in
22
4
t
e
e
t
h
/
i
n
N
R
P
=
Ans.
Therefore, from Equation (7.15), see page 351, the radii of the base circles are
( )
cos
3.000 in cos20
2.819 in
rR
°
=
and
( )
33
cos
4.500 in cos20
4.229 in
°
=
Ans.