Page 108 - Cam Design Handbook

THB4 8/15/03 1:01 PM Page 96

96 CAM DESIGN HANDBOOK

This yields the same results as Eq. (4.5).
Let b = cam angle for maximum rise, h, degrees

h = maximum follower rise, in
Conversion to actual units from normalized equations requires multiplication of each poly-
n
h Ê q ˆ
nomial term by ratio n giving hC Á ˜ . Therefore each term of the 4-5-6-7 polyno-
n
Ë
b b ¯
.
05
mial multiplied by yields, with q in degrees.
60 n
35 Ê q ˆ 4 Ê q ˆ 5 Ê q ˆ 6 Ê q ˆ 7
Displacement, y = - 42 + 35 -10 in
2 Ë 60 ¯ Ë 60 ¯ Ë 60 ¯ Ë 60 ¯
7 Ê q ˆ 3 7 Ê q ˆ 4 35 Ê q ˆ 5 7 Ê q ˆ 6
Velocity, y ¢ = - + - in deg
Ë
Ë
Ë
Ë
660 ¯ 260 ¯ 1060 ¯ 660 ¯
7 Ê q ˆ 2 7 Ê q ˆ 3 7 Ê q ˆ 4 7 Ê q ˆ 5
Acceleration, y ¢¢ = - + - in deg 2
Ë
Ë
Ë
Ë
12060 ¯ 3060 ¯ 24 60 ¯ 6060 ¯
4.6 POLYNOMIAL CURVE MODES OF
CONTROL—DRRD CAM
In the foregoing example we have assigned one or more of the displacement derivatives to
be zero at the boundary. In the dwell-rise-return-dwell cam, other modes of control may be
required to optimize the cam curve. We can impose the following three modes of control:
1. no control
2. interior control
3. assignment of finite quantities to terminal point displacement derivations

The last category, the assignment of finite quantities to terminal point displacement deri-
vations, will not be discussed here. For more see Stoddart (1953) and Chen (1982).
In no control, at the ends of a symmetrical DRRD cam (Fig. 4.5), the displacement,
the velocity, and the acceleration are to be zero. However, at the midstation, displacement,
of course, is 1, velocity is zero, and acceleration is left loose (no control). In addition,
there is zero jerk at the midpoint. Thus the boundary conditions for the rise portion of the
motion are

when q = 0, y = 0, y ¢ = 0; y ¢¢ = 0

y
when q = ( 1 midpoint), y =1, y ¢ = 0, y ¢¢ = no control, and ¢¢¢ = 0.

A polynomial
q
y = C + C + C q 2 + C q 3 + C q 4 + C q 5
0 1 2 3 4 5
is assumed which reduces to
y = C q 3 + C q 4 + C q .
5
3 4 5