Page 97 - Cam Design Handbook

THB3 8/15/03 12:58 PM Page 85

MODIFIED CAM CURVES 85

From Fig. 3.16 for cycloidal motion (C1 segment), the characteristic curves are
Ê q 1 pq ˆ
y = h Á - sin ˜
1
Ë b p b 1 ¯
h Ê pq ˆ
y¢ = 1 Á1 - cos ˜
b 1 Ë b 1 ¯
p h pq
y¢¢ = 1 sin
() 2 b 1
b
1
From Fig. 3.15 for harmonic motion (H2 segment) the characteristic curves are
pq
y = h sin
2
2b 2
p h pq
y¢ = 2 cos
2b 2b
2 2
p 2 h pq
y¢¢ =- 2 2 sin
( )
4 b 2b
2 2
We need velocity continuity at the end of the C1 curve and the beginning of the H2 curve
(Fig. 3.18)
h Ê pb 1 ˆ p h p 0
1 Á 1- cos ˜ = 2 cos
b Ë b ¯ 2b 2b
1 1 2 2
Acceleration, y"

Velocity, y'
y, y', y" (C1) Displacement, y

h 2

h 1
0
Dwell q

(H2)
b 1 b 2

FIGURE 3.18. Cycloidal harmonic compling example.