Page 56 - Cam Design Handbook

THB2 8/15/03 12:48 PM Page 44

44 CAM DESIGN HANDBOOK

Velocity
Ê w ˆ
˙ y = C hÁ ˜
v Ë b ¯
1800
= . 09233 1 . ¥5
¥
150
=16 .6194 in sec
Acceleration
Ê w ˆ 2
˙˙ y = C hÁ ˜
a
Ë b ¯
2
Ê 1800 ˆ
¥
= . 3 9924 1 5
. ¥
Ë 150 ¯
= 862 .3584 in sec 2
2.11 CYCLOIDAL MOTION CURVE

The cycloidal motion curve, as the name implies, is generated from a cycloid and has a
sine acceleration curve. A cycloid is the locus of a point on a circle that is rolled on a
straight line. The circumference of the circle is equal to the follower rise h. The cycloid
is the first dwell-rise-dwell curve we discuss that does not have any discontinuities in the
acceleration curve. Therefore, it can be applied to higher speeds than the foregoing curves
even though its maximum acceleration is higher in some cases.
Designate point A (Fig. 2.10) as the center and draw a circle with the radius equal to
h
. Divide this circle into the same number of parts used for the horizontal axis. From
2p
the projection of these points on the ordinate, draw lines that are parallel to the diagonal
AD that intersect the vertical projections of the divisions of this abscissa. These inter-
sections locate the necessary points for the displacement curve.

D

Displacement y a 2p h
h

f
b
S
3 A 1 2 3
b
2 1
Cam angle q
FIGURE 2.10. Cycloidal motion curve construction.