Page 138 - Cam Design Handbook

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126 CAM DESIGN HANDBOOK

1

R 1.5 R 6.5

R 2.5
R 4.5 R 5.5

.5
R
3.5

0
0 .5 1
Normalized time
FIGURE 5.13. Rational B-splines (k = 5) constructed with the weight sequence of [1,
1, 1, 1.5, 1, 1] in Example 5.

TABLE 5.6 Weight Sequences and Interior
Knots Used in Example 7

[W] 1 = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
[W] 2 = [1.0, 1.0, 1.0, 1.0, 0.8, 0.8, 1.2, 1.0, 1.0]
[T] 1 = [0.25, 0.50, 0.75]
[T] 2 = [0.30, 0.50, 0.55]

much improved results in which the dip in displacement and the reversals of velocity and
acceleration have all been removed. These improvements have been achieved without
changing the original set of motion constraints, indicating the flexibility of the rational
spline method in synthesizing motion programs for cams.
As illustrated by the foregoing examples, the rational B-spline interpolation approach
to the synthesis of cam-follower motions affords a systematic procedure for cam synthe-
sis that is versatile enough to accomplish many tasks that usually require a variety of tech-
niques. The method is easy to apply, given algorithms to generate the rational spline values