Page 40 - Cam Design Handbook

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28 CAM DESIGN HANDBOOK

n 0 = initial velocity, in/rad
w = cam speed, rad/sec
q = cam angle of rotation

2.1 INTRODUCTION

In Chapter 1, we saw that it is possible to construct a cam by blending crude increments
and observing its appearance. This method is not acceptable in the design of today’s cam
machinery. Now it is necessary to provide accurate mathematical information for the cam
characteristics of displacement velocity, acceleration, and sometimes the jerk. In so doing
one can interpret and control the ultimate design performance. Also, the higher the cam
speed, the more critical is the investigation. This is especially true of the acceleration data
which is the important determining factor of the dynamic loads on cam-follower systems.
This chapter presents mathematically established basic curves which are the first selec-
tion to establish the follower action. They are easy to analyze and manipulate.
Cams can be designed for any acceptable curve or shape. Appendix A lists various
kinds of geometric curves that have been used in the past. They include the ellipse,
parabola, hyperbola, logarithmic spiral, and involute of a circle. Alternative combinations
of these curves combined with the circle and straight line have also been constructed (see
Chapter 15.)

2.2 FOLLOWER CHARACTERISTICS

As previously indicated, a cam can be considered similar to a wedge having a cyclical rise
and fall which establishes the motion of the follower. In all cams, the displacement of the
follower is given by the mathematical relationship
f
y = () q in (2.1)
where q = cam angle rotation in radians. However, since the cam rotates at a constant
angular velocity, the displacement can also be written as

y = () in (2.2)
g t
w
and q = t (2.3)
where t = time for cam to rotate through angle q, sec
w = cam angular velocity, rad/sec
By the use of Eq. (2.1) the follower characteristics can be normalised (dimensionless)
as follows:

The cam profile is usually given as a function of the angle q. Thus
y = follower displacement. (2.4)
The instantaneous angular rate of change of displacement
dy
y ¢ = = follower velocity. (2.5)
dq