Page 204 - Cam Design Handbook

THB7 8/15/03 1:58 PM Page 192

192 CAM DESIGN HANDBOOK

associated cam profile is the trajectory of the center of the roller follower, which is known
as the pitch curve. Moreover, if the roller-follower cam is machined with a mill having a
radius identical to that of its roller, then the pitch curve is identical to the trajectory of the
cutter center, the curve needed for the programming of the NC machine tool used to
produce the cam disk. Thus, for translating knife-edge and roller followers, the pressure-
angle a can be obtained by:
s ¢ - e
tana = (7.33)
s
where s¢ is the first derivative of the displacement s with respect to the angle y and e as
shown in Fig. 7.8.
On the other hand, for both the knife-edge and the roller-follower, the curvature of the
pitch curve is given by

N
k = (7.34a)
k
D
where (Angeles and Lopez-Cajun, 1991)
N ∫ ( - s¢ - e)(2 s¢ - e) (7.34b)
s s s¢¢)+ (
and
2 32
D ∫[ s + ( s¢ - ] . (7.34c)
e)
2
7.4.2.4 Oscillating Roller Followers. For the oscillating roller follower, the formula
given below can be used to calculate the pressure angle (Angeles and Lopez-Cajun,
1991)
l rq sinf + r(l cosf - ) e
¢()
tana = (7.35a)
rq cosf - ) -e r l sinf
¢()(l
where
¢()
ry
rq (7.35b)
¢() =
¢()
q y
el fy f
¢()sin
ry (7.35c)
¢() =
r
f y
¢() - r
l ef y 2 [1 + ¢()]
¢() =
qy (7.35d)
r 2
and the parameters involved are shown in Fig. 7.9.
Finally, the formula for calculating the curvature of the pitch curve of the oscillating
roller follower is (Angeles and Lopez-Cajun, 1991)
3
(
+
el (1
2
e (1 + f¢) - [ + f¢) +2 f¢)cos f f¢¢sin f]+ l 2
k = (7.36)
k 2 32
[ e (1 + f¢) - 2 el + f¢)cos f l ]
2
+
(1
2
where the argument y of f¢ and f≤ have been omitted for simplicity.