Page 249 - Cam Design Handbook

THB8 9/19/03 7:25 PM Page 237

CAM MECHANISM FORCES 237

SYMBOLS

a = length of the roller-crank, in
d = distance between the roller-crank and cam pivots, in
k = spring constant of the force-closure spring, lb/in
m c = cam moss, lb
n = angular velocity ratio of the cam and the roller-crank in the first half of the cycle
n* = angular velocity ratio of the cam and the roller-crank in the second half of the cycle
r = transmission index
r Fc = moment arm of contact force, in
r s = moment arm of spring force, in
F s = spring force, lb
F c = contact force between roller and cam, lb
I c = moment of inertia of cam, lb-in 2
I r = moment of inertia of roller crank, in-lb-sec 2
2
R c = distance from pivot to com mass center, in
R Fc = moment arm of contact force, in
R s = moment arm of spring force, in
2
R r = distance from pivot to roller crank mass center, in
T = torque in-lb
a = angular acceleration, rad/sec 2
a c = angular acceleration of cam, rad/sec 2
b = angle between the common normal and the line joining the cam and roller-crank
pivots, rad
y = angular position of the force-closure spring location of the cam, deg
f = rotation of the cam, rad
h = angle between the line joining the cam and the roller-crank pivots and the line joining
the cam pivot and the center of the roller, rad
l = pressure angle, deg
m = transmission angle, deg
q = rotation of the roller-crank, rad
w = angular velocity, rad/sec

8.12.1 Kinematic Principles

The physical arrangement of the planar cam-follower system considered here is shown
schematically in Fig. 8.15. The roller-crank and the cam are pivoted about two fixed points,
A 0 and B 0, respectively. A roller mounted at the free end of the roller crank is in contact
with the cam. The rotations of the roller crank and cam are denoted by q and f, respec-
tively. For the purpose of the kinematic analysis that follows, we will use the pitch curve
of the cam. The design objectives are:
• Both cam and roller-crank must rotate through 360° in each cycle.
• They should always be in contact with each other.
• Arbitrary specification of motion relating q and f should be possible including finite
dwells and reversal of motion.
• Transmission criteria should be adequately satisfied to be of practical use.

In mechanism synthesis, it is necessary to have a suitable transmission criterion to be
able to judge the efficiency of transmission of motion and force. The pressure angle is the