Page 67 - Cam Design Handbook

THB3 8/15/03 12:58 PM Page 55

CHAPTER 3

MODIFIED CAM CURVES

Harold A. Rothbart, D.Eng.

3.1 INTRODUCTION 56 3.7 MODIFIED SINE CURVE 73
3.2 FUNDAMENTALS 57 3.8 MODIFIED CYCLOIDAL CURVE 76
3.3 MODIFIED CONSTANT VELOCITY 3.9 DWELL-RISE-RETURN-DWELL
CURVE 57 MOTION 78
3.4 TRAPEZOIDAL CURVE 61 3.10 COUPLED CURVE SIMPLIFICATION 81
3.5 MODIFIED TRAPEZOIDAL CURVE 61
3.6 SKEWED MODIFIED TRAPEZOIDAL
CURVE 70

SYMBOLS

h = total rise of the follower, in
h¢= maximum rise of follower segment, in
h = maximum follower displacement for full or half curve, in
t = time, sec.
y = follower displacement
dy
y ¢ = = follower velocity, dimensionless
dq
2
dy
y ¢¢ = = follower acceleration, dimensionless
dq 2
3
dy
y ¢¢¢ = = follower jerk, dimensionless
dq 3
dy
2
˙˙ y = = w 2 y¢¢ = follower acceleration
dt 2
dy
˙ y = = w y¢ = follower velocity
dt
dy
3
˙˙˙ y = = w 3 y¢¢¢ = follower jerk
dt 3
A = follower acceleration, in/sec 2
V max = maximum velocity, ips
V 0 = follower initial velocity, in/sec
a = follower acceleration, dimensionless
b = cam angle for rise h, radians
b = angle for maximum follower displacement, radians
b 1, b 2 = periods during positive and negative accelerations respectively, radians
q = cam angle rotation, radians
w = cam speed, rad/sec
v 0 = follower initial velocity, in/radians
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