Page 77 - Cam Design Handbook

THB3 8/15/03 12:58 PM Page 65

MODIFIED CAM CURVES 65

Ê b ˆ
At point D i.e., when =q the total displacement can be found from this equation to be
Ë 2 ¯
Ê p ˆ
y = h¢ 1 + .
Ë 2 ¯
The displacement of the final segment is

y =- 1 y 2
y y -
3
or
Ê 1 p 1 ˆ
y = h¢ Ë 4 + 4 + 2p ¯ .
3
From the relationship
h
y + y + y = ,
2
1
3
2
we establish the relationship between h¢ and h
h
h ¢ = . (3.6)
2 + p
Therefore, the displacement equations of the first three segments are

h Ê 2q 1 q ˆ b (3.7)
££
y = Á - sin 4p ˜ 0 q
2 + p Ë b 2p b ¯ 8
h È1 1 2 Ê b ˆ 4p Ê b ˆ 2 ˘ b 3
q
y = Í - + q - + q - ¯ ˙ ££ b
2 + p Î 4 2p b Ë 8 ¯ b 2 Ë 8 ˚ 8 8
b ˘
q -
h È p q 1 ˙ 3 b
y = - + ( 21 p + sin 4p 2 ˙ ˙ bq .
+ )
££
2 + p Í Î 2 b 2p b 8 2
˙
˚
Evaluating all constants, characteristic curve equations are:
q 1
for q £ £ , (3.8)
b 8
Ê q 1 q ˆ
.
y = 009724613 hÁ4 - sin 4p ˜
Ë b p b ¯
h Ê q ˆ
.
y¢ = 03889845 Á1 - cos 4p ˜
b Ë b ¯
h q
y¢¢ = 4 888124 sin 4p
.
b 2 b
h q
.
y¢¢¢ = 61 425975 cos 4p
b 3 b