Page 119 - Cam Design Handbook

THB5 8/15/03 1:52 PM Page 107

CHAPTER 5

CAM MOTION SYNTHESIS
USING SPLINE FUNCTIONS

Cecil O. Huey, Jr., PhD
Professor of Mechanical Engineering
Clemson University, Clemson, South Carolina
Dermin Tsay, PhD
Professor, Department of Mechanical Engineering
National Sun Yat Sen University
Kaohsiung, Taiwan

5.1 INTRODUCTION 108 5.5 THE SYNTHESIS OF FOLLOWER
5.2 APPLICATION OF NONRATIONAL MOTIONS OF THREE-
B-SPLINES TO MOTION DIMENSIONAL CAMS USING
SYNTHESIS 109 NONPARAMETRIC B-SPLINES 144
5.3 APPLICATION OF RATIONAL 5.6 SUMMARY 154
B-SPLINES 117
5.4 SPLINE FUNCTIONS APPLIED IN THE
SYNTHESIS OF NONRIGID CAM-
FOLLOWER SYSTEMS 127

SYMBOLS

a = Normal distance between the follower center and the axis of rotation of the cam at
initial position
A j = Constant coefficients ( j = 1,... , n)
C j = Viscous damping coefficient of follower (used in addressing nonrigid follower)
C s = Viscous damping coefficient of the restoring damper
d = Deviation of cam-follower position from static equilibrium position
d¢= First derivative of deviation
d≤= Second derivative of deviation
E i,j(x) = Spline function values at constraint locations (i, j = 1,..., n)
F c = The contact force (used in addressing nonrigid follower)
F j = Kinematic constraint values ( j = 1,... , n)
F p¢ = Preload (used in addressing nonrigid follower)
h = Rise of the follower
k = Order of spline function
K f = Spring constant of follower (used in addressing nonrigid follower)
K s = Spring constant of return spring (used in addressing nonrigid follower)
l = Length of the cam

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