Page 127 - Cam Design Handbook

THB5 8/15/03 1:52 PM Page 115

CAM MOTION SYNTHESIS USING SPLINE FUNCTIONS 115

1

0

Displacement (cm)
Velocity (cm/rad)
Acceleration (cm/rad/rad)
Constraint
–1
0 45 90 135 180
Cam rotation angle (deg.)
FIGURE 5.4. Cam follower displacement, velocity, and acceleration obtained from cycloidal
motion in Example 2.

TABLE 5.3 Constraints for Example 3

Cam angle Displacement Velocity Acceleration
(degrees) (cm) (cm/rad) (cm/rad/rad)
0.00 0.00 0.00 0.00
36.0 0.01 — —
90.0 0.60 — 0.00
180.0 1.00 0.00 0.00

EXAMPLE 4: A Case with a Large Number of Constraints In this example a total
of 20 constraints has been specified. These constraints are listed in Table 5.4. The results
obtained using a polynomial of degree 19 and sixth-order splines with uniform knot
spacing are shown in Figs. 5.8, 5.9, and 5.10. The better characteristics of the spline func-
tion, particularly of the derivatives near the boundaries of the motion interval, are appar-
ent. No attempt was made at further enhancement of the curves by adjusting the knot
sequence.