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

follower velocity, dimensionless

follower acceleration, dimensionless

follower jerk, dimensionless

follower acceleration

follower velocity

follower jerk

A = follower acceleration, in/sec ²

V _max = maximum velocity, ips

V ₀ = follower initial velocity, in/sec

a = follower acceleration, dimensionless

? = cam angle for rise h, radians

? = angle for maximum follower displacement, radians

? ₁, ? ₂ = periods during positive and negative accelerations respectively, radians

? = cam angle rotation, radians

? = cam speed, rad/sec

v ₀ = follower initial velocity, in/radians

3.1 INTRODUCTION

In Chap. 2, the characteristics of displacement, velocity, acceleration, and jerk of basic symmetrical curves were presented. These curves were employed because of their simplicity of mathematical analysis and ease of construction. However, for many machine performance requirements, as when the cam requires either special functional motions or must operate at high speeds, the basic symmetrical curves are inadequate and modifications in curve selection are necessary. These modifications can consist of blending, skewing, or combining sectors of the cubic curves, simple harmonic curves, cycloidal curves, constant velocity curves, and constant acceleration curves.

Last, it should be mentioned that cam curve development (not shown) can be accomplished...