Page 93 - Cam Design Handbook

THB3 8/15/03 12:58 PM Page 81

MODIFIED CAM CURVES 81

Portion II
˙˙ y = A ˙
˙ y = Aq + ˙ y
2 1
2
˙ y ¢ +
q
y = A() 2 + q y 1
1
2
˙ y = Ab + 2 Ab p
2 2 1
y = Ab 22 Ab b p + 2 Ab p (1 - 2 p )
+
2
2
2 2 12 1
Portion III
˙˙ y = A cos(pq b 3 )
3
˙ y = Ab p sin(pq b 3 )+ ˙ y 2
3
3
2
¢¢
y =- A(bp ) [1 - cos(pq b )]+ q y
˙ y ¢¢ +
3 3 2 2
˙ y = ˙ y
3 2
(
2
+
y = 2 A(b p ) + Ab b + 2 Abb p + Ab 2 2 Abb p ( ( Ab p) -12 p )
2
+ 2
2
3 3 2 3 1 3 2 12 1
Portion IV
˙˙ y =- A
˙ y =- Aq + ˙ y
4 3
y =-[ q 2 2 ˙ y ¢¢¢ + y
A() ]+ q
4 3 3
˙ y =- Ab + ˙ y =- Ab + Ab + 2 Ab p = 0
4 2 3 4 2 1
b = b + b p
2
4 2 1
Total Rise
h = y = -( Ab 2 2 )+ A ( b + 2 Ab p )b + y
4 4 2 1 4 3
Substituting
h
A =
2
- [ b 2 + b b + bb p2 + (b p2 ) + b b + bb p + b 2 + bb p
2
2
2
2
4 2 4 1 4 3 2 3 1 3 2 12
+( bp2 1 2 ) - 2 p )]
(1
For a given total rise h for angle q 0 and any two of the b angles given one can solve
for all angles and all values of the derivative curves.
3.10 COUPLED CURVE SIMPLIFICATION
This section presents a convenient method for combining segments of basic curves to
produce the required design motion. This procedure was developed by Kloomok and
Muffley in Mabie and Ocvirk (1979), who selected three analytic functions of the simple
harmonic, the cycloidal, and the eighth-degree polynomial (the latter described in Chapter
4). These curves, having excellent characteristics, can be blended with constant accelera-
tion, constant velocity, and any other curve satisfying the boundary conditions stated in
Sec. 3.2. Figures 3.15, 3.16, and 3.17 show the three curves including both half curve seg-
ments and full curve action in which
h = total follower displacement for half curve or full curve action, and
b = cam angle for displacement h, in