Page 454 - Cam Design Handbook

THB13 9/19/03 7:56 PM Page 442

442 CAM DESIGN HANDBOOK

+0.008 y c 0.8
0.0052 in. Follower end
y acceleration y ≤ 0.6
Acceleration, in./deg. 2 0 Cam acceleration y ≤ 0.4 Displacement, inches
+0.004

c

–0.004 Cam displacement y c 0.2
Follower end
displacement y
0.010 in.ramp
–0.008 0 height
0 15 30 45 60
Cam angle q
FIGURE 13.22. Textile machine polydyne cam example. Follower end displacement of 3-4-5
polynomial.

Assume that the helical spring weighs 0.3lb. The effective weight

4
.
Ê ˆ 2 03
.
w = 55 + + 35 600 lb.
=
.
.
Ë ¯ 3
6
Therefore the dynamic constant from Eq. (13.84) is
w
.
.
C = 0093 N = 22 2.
2
k
f
Substituting in Eq. (13.83) gives the cam profile
+
.
.
.
y = 0 010 1 016 y + 22 2 y¢¢. (13.92)
c
In Fig. 13.22, we plot the resulting displacement and acceleration curves of both the
cam, y c and y c≤, and the follower end, y and y≤, respectively. The velocity curves are not
shown since they are of lesser importance. It should be remembered that all these curves
are compared on the same basis; i.e., the actual cam would be reduced by the lever arm
ratio of 4in/6in or 2/3 scale.
We see that the acceleration curve of the cam y c≤ has smaller values than the acceler-
ation curve of the follower end y≤. This difference is increased as the speed increases. In
other words, at a low speed the two curves are practically identical. In addition, we see
an infinite jerk at the ends of the cam acceleration curve y c≤. This suggests another required
function of the ramp for this 3-4-5 curve, i.e., to provide velocity and acceleration values
dictated by the cam, in addition to taking up the preload (initial displacement) in the
system.
In the displacement curve of the follower, we see the desired 3-4-5 curve shape. The
displacement of the cam indicates a ramp of 0.010in at the beginning of the curve.
However, a serious shortcoming of this design may be observed. At the 15° point, we find
that the cam displacement, y c curve, falls below the follower displacement, y curve, about
0.0052in. If it were possible, the linkage at this point would be in tension. In other words,
the cam would leave the follower. This is alleviated by subjecting the linkage to com-