Page 54 - Cam Design Handbook

THB2 8/15/03 12:48 PM Page 42

42 CAM DESIGN HANDBOOK

Substituting in Eq. (2.50) gives
h Ê pq ˆ
Displacement y = Á1 - cos ˜, (2.52)
2 Ë b ¯
from which we obtain
hp pq
Velocity y ¢ = sin (2.53)
2 b b
hp 2 pq
Acceleration y ¢¢ = cos (2.54)
2 b 2 b
hp 3 pq
Jerk y ¢¢¢ = sin (2.55)
2 b 3 b
Figure 2.9 shows the plotting of these equations. The simple harmonic motion has a smooth
acceleration curve except at the dwell ends, where it has discontinuities (i.e., infinite jerk).
To simplify the cam calculations for displacement, velocity, and acceleration of the
follower, tabulated data for the simple harmonic curve are shown in App. B.

1
EXAMPLE A cam rotates at a constant speed of 30rpm. The follower rises 1/ 2 in. with
simple harmonic motion in 150 degrees of cam rotation. Find the displacement, velocity,
and acceleration of the follower after 30 degrees of cam rotation (a) by use of formulas
and (b) by employing the data in App. B.
Solution (a)
p
.
q
Cam angle = 30 ¥ = 0524 rad
180

Jerk y'" = • Displacement, y Dwell

y, y', y", y'" Velocity, y'

0 Cam Angle q b
Dwell

Acceleration, y"
Jerk y'" = •

FIGURE 2.9. Simple harmonic motion curve—DRD cam.