Page 45 - Cam Design Handbook

THB2 8/15/03 12:48 PM Page 33

BASIC CURVES 33

2.4 CONSTANT VELOCITY CURVE

The constant velocity or uniform displacement curve is the simplest of all (n = 1). It has
a straight-line displacement at a constant slope (Fig. 2.2) giving the smallest length for a
given rise of all the curves. When the straight-line curve is developed for a radial cam, it
becomes the Archimedes spiral; see App. A.
For a constant velocity curve
y = C + q
C
0 1
at q = 0, y = 0, \ C = 0 (2.13)
o
h
\
at q = b, y = h C =
1
b
h
\displacement y = q (2.14)
b
hw
velocity ˙ y = = a constant (2.15)
b
acceleration ˙˙ y = 0 (2.16)
We see that the displacement is uniform, the velocity is constant, and the acceleration is
zero during the rise. At the ends where the dwell meets the curve, however, we have an
impractical condition. That is, as we go from the dwell (zero velocity) to a finite velocity,
we have an instantaneous change in velocity, giving a theoretically infinite acceleration.
This acceleration transmits high shock throughout the follower linkage, the magnitude of

Accel. = •

··· y, y, y Displacement, y Dwell

·
Velocity, y
h

··
Acceleration, y
Cam angle q b
Dwell
Accel. = •

FIGURE 2.2. Constant velocity curve—DRD cam.