Page 39 - Cam Design Handbook

THB2 8/15/03 12:48 PM Page 27

CHAPTER 2

BASIC CURVES

Harold A. Rothbart, D.Eng.

2.1 INTRODUCTION 28 2.9 CUBIC NO. 2 CURVE 40
2.2 FOLLOWER CHARACTERISTICS 28 2.10 SIMPLE HARMONIC MOTION
2.3 BASIC CURVE CLASSIFICATION 31 CURVE 40
2.4 CONSTANT VELOCITY CURVE 33 2.11 CYCLOIDAL MOTION CURVE 44
2.5 MODIFIED CONSTANT VELOCITY 2.12 DOUBLE HARMONIC MOTION
CURVE WITH CIRCULAR ARCS 34 CURVE 46
2.6 CONSTANT ACCELERATION CURVE 34 2.13 ELLIPTICAL CURVE` 47
2.7 SKEWED CONSTANT 2.14 COMPARISON OF BASIC CURVES 48
ACCELERATION CURVE 37 2.15 CURVE APPLICATION TO DRRD CAM 49
2.8 CUBIC NO. 1 CURVE 38

SYMBOLS

a = acceleration in/rad 2
A = constant acceleration in/sec 2
a e = semi-major axis of ellipse, in
A = acceleration in/sec 2
b e = semi-minor axis of ellipse, in
C,C 1,C 2 = constants
h = total rise, in
h 1 = displacement at transition point, in
n = any number
a
n = e ratio
e
b
e
V 0 = initial velocity, in/sec
y = follower displacement, in
dy
y ¢ = = follower velocity, dimensionless
dq
dy
2
y ¢¢ = = follower acceleration, dimensionless
dq 2
dy
3
y ¢¢¢ = = follower jerk, dimensionless
dq 3
dy
˙ y = = w y¢ = follower velocity
dt
2
dy
˙˙ y = = w 2 y¢¢ = follower acceleration
dt 2
3
dy
˙˙˙ y = = w 3 y¢¢¢ = follower jerk
dt 3
y 1,y 2 = displacement during acceleration periods 1 and 2, respectively, in
b = cam angle for rise h, rad
b 1 = angle of rotation for rise h 1, rad
f = angle of rotation for cycloidal curve, rad
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