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

V ₀ = initial velocity, in/sec

y = follower displacement, in

follower velocity, dimensionless

follower acceleration, dimensionless

follower jerk, dimensionless

follower velocity

follower acceleration

follower jerk

y ₁, y ₂ = displacement during acceleration periods 1 and 2, respectively, in

? = cam angle for rise h, rad

? ₁ = angle of rotation for rise h ₁, rad

= angle of rotation for cycloidal curve, rad

v ₀ = initial velocity, in/rad

? = cam speed, rad/sec

? = 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...