Page 107 - Cam Design Handbook

THB4 8/15/03 1:01 PM Page 95

POLYNOMIAL AND FOURIER SERIES CAM CURVES 95

0.020

Cycloidal

0.015
Simple
Displacement, y 0.010 3-4-5 4-5-6-7
harmonic

0.005

0
0 0.02 0.04 0.06 0.08 0.10 0.12 0.14
Cam angle, q
FIGURE 4.4. Comparison of displacement characteristics. (Graph range 2% of lift, 14% of cam rotation.)

C pqr ...
0
C = ps q s r s) ... (4.6)
s
(
( - )( - ) -
EXAMPLE Find the displacement, velocity, and acceleration equations and values for
the 4-5-6-7 follower motion for a DRD cam that has a rise of 0.5in. in 60 degree of cam
rotation.
Solution Using Eq. (4.6)
( )()() 7
56
C = = 35
p ()( )( ) 3
12

( )()() 7
46
C = =-84
q
- )
- )(65
(46 - )(7 5
()( )( ) 7
45
C = = 70
r
- ) - )(7 6
(46 (5 6 - )
()( )( ) 6
45
C = =-20
s
- ) - )(67
(47 (5 7 - )
Thus characteristic curves are
4
6
5
7
y = 35q - 84q + 70q - 20q , dimensionless
6
4
5
3
y¢= 140q - 420q + 420q - 140q , dimensionless
5
3
2
2
y≤= 420q - 1680q + 2100q - 84q , dimensionless.