Page 512 - Cam Design Handbook

THB14 9/19/03 7:59 PM Page 500

500 CAM DESIGN HANDBOOK

dq
0 = ¢(). (14.27)
f q
dq i
i
The velocity of point P as a point on either body is equal to radius r multiplied by the
angular velocity dq/dt of the respective body
d q d q
u = p i = r 0 .
p i 0
dt dt
Solving,
dq r
0 = i . (14.28)
dq r
i 0
Solving Eqs. (14.27) and (14.28) simultaneously and knowing that c e = r i + r 0 gives
radii
c c
r = d e q = e in (14.29)
0
f
q
1+ 0 1+ ¢()
i
d q i
d q
c 0
e d q cf ¢()
q
r = d q i = e i in. (14.30)
i
q
i
1 + 0 1 + f ¢()
d q
i
Equations (14.29) and (14.30) are the design equations for the contours of mating cams
in terms of each radius r and angle q.
It is not necessary that the relationship be represented by any mathematical function.
The calculations can be performed by approximations from a table of numerical values.
EXAMPLE Find the profile equations for the following exponential relationship where A
and B are constants:
q
q = Ae i B .
0
Solution We know from Eq. 14.26
q
q = ().
f
0 i
Differentiating the given expression,
A
f ¢() =q e i q B .
i
B
Substituting in Eqs. (14.29) and (14.30) gives the radii
cB
r = e
0
B + q 0
c q
r = e 0 .
i
B + q 0
Thus, with the constant given, tables can be established for the cam dimensions to be cut.