Page 112 - Cam Design Handbook

THB4 8/15/03 1:01 PM Page 100

100 CAM DESIGN HANDBOOK

4-8-12-16
y"

4-6-8-10
4-5-6-7

Cam angle q

FIGURE 4.8. Acceleration of a family of seventh-order polynomial curves.

2-14-26-38-50

y" 2-10-18-26-34

2-6-10-14-18

Cam angle q

FIGURE 4.9. A family of high-order DRRD polynomial curves.

Eighth-Degree Polynomial Curve
The eighth-degree polynomial has acceleration characteristics between the harmonic
and cycloidal curves. It has an asymmetrical acceleration at the dwell rise or end. The
curve can also be blended conveniently with other curves at its maximum rise point.
For the rise action:
q
q
q
È Ê ˆ 3 Ê ˆ 5 Ê ˆ 6
y = h 6 09755 Á ˜ - 20 78040 Á ˜ + 26 73155 Á ˜
.
.
.
Í
b
b
b
Î Ë ¯ Ë ¯ Ë ¯
7 8
q
q
Ê ˆ Ê ˆ ˘
-13 60965 Á ˜ + 2 56095 Á ˜ ˙
.
.
b
b
Ë ¯ Ë ¯ ˚
q
q
h È Ê ˆ 2 Ê ˆ 4 Ê ˆ 5
q
y ¢ = Í 18 29265 Á ˜ =- 3 90200 Á ˜ +160 38930 Á ˜
.
.
1
.
b Î Ë ¯ Ë ¯ Ë ¯
b
b
b
7
q
q
Ê ˆ 6 Ê ˆ ˘
.
.
- 95 26755 Á ˜ + 2048760 Á ˜ ˙
b
b
Ë ¯ Ë ¯ ˚