This paper deals with the problem of designing dynamically compensated cam profiles to minimize residual vibrations in high-speed cam-follower systems. The traditional Polydyne method is modified and extended to achieve significant improvement in residual vibration characteristics. First, cam displacement curves are represented by Bernstein-Be´zier harmonic curves as opposed to polynomial curves. These recently developed harmonic curves are low in harmonic content and therefore the resulting cam profiles are less prone to induce resonant vibrations in the follower system. Second, the design procedure is expanded such that the residual vibrations of the resulting cam-follower system is not only extinguished at the design speed but also made insensitive to speed variations. Numerical examples are given in the end.

1.
Berzak, N., and Freudenstein, F., 1979, “Optimization Criteria in Polydyne Cam Design,” Proc. 5th World Congress on Theory of Machines and Mechanisms, pp. 1303–1306.
2.
Berzak
N.
,
1982
, “
Optimization of Cam-follower Systems With Kinematic and Dynamic Constraints
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
104
, pp.
29
33
.
3.
Chen, F. Y., 1982, Mechanics and Design of Cam Mechanisms, Pergamon Press.
4.
Chew
M.
,
Freudenstein
F.
, and
Longman
R. W.
,
1983
, “
Application of Optimal Control Theory to the Synthesis of High-Speed Cam-Follower Systems, Part 1: Optimality Criteria, Part 2: System Optimization
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
105
, pp.
576
591
.
5.
Chew
M.
, and
Chuang
C. H.
,
1995
, “
Minimizing Residual Vibrations in High-Speed Cam-Follower Systems Over a Range of Speeds
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
117
, March, pp.
166
172
.
6.
Fabien
B. C.
,
Longman
R. W.
, and
Freudenstein
F.
,
1994
, “
The Design of High-Speed Dwell-Rise-Dwell Tuned Cam Displacement Curves Using Linear Quadratic Optimal Control Theory
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, No.
3
, pp.
867
874
.
7.
Farin, G., 1993, Curves and Surfaces for Computer Aided Geometric Design, Third edition. Academic Press, Inc.
8.
Farouki
R. T.
, and
Shah
S.
,
1996
, “
Real-time CNC Interpolators for Pythagorean-Hodograph Curves
,”
Computer Aided Geometric Design
, Vol.
13
, pp.
583
600
.
9.
Farouki, R. T., Manjunathaiah, J., and Jee, S., 1997, “Design of Rational Cam Profiles With Pythagorean-Hodograph Curves,” Mechanism and Machine Theory, in press.
10.
Ge, Q. J., and Srinivasan, L., 1996, “C2 Piecewise Be´zier Harmonics for Motion Specifications of High-Speed Cam Mechanisms,” Proc. 1996 ASME Design Engineering Technical Conferences, 96-DETC/MECH-1173, Irvine, California, August, 1996.
11.
Ge
Q. J.
, and
Rastegar
J.
,
1996
, “
Bernstein-Be´zier Harmonics and Their Application to Robot Trajectory Synthesis with Minimal Vibrational Excitation
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
118
, No.
4
, pp.
509
514
.
12.
Ge
Q. J.
,
Srinivasan
L.
, and
Rastegar
J.
,
1997
, “
Low-Harmonic Rational Be´zier Curves For Trajectory Generation of High-Speed Machinery
,”
Computer Aided Geometric Design
, Vol.
14
, pp.
251
271
.
13.
Hoschek, J., and Lasser, D., 1993, Fundamentals of Computer Aided Geometric Design (translated by L. L. Schumaker), A K Peters, 727 pp.
14.
Kanzaki
K.
, and
Itao
K.
,
1972
, “
Polydyne Cam Mechanisms for Typehead Positioning
,”
ASME Journal of Engineering for Industry
, Vol.
94
, Feb., pp.
250
254
.
15.
Kelly, S. G., 1993, Fundamentals of Mechanical Vibrations, McGraw-Hill, New York.
16.
Kwakernaak
H.
, and
Smit
J.
,
1968
, “
Minimum Vibration Cam Profiles
,”
J. of Mech. Engr. Sci.
, Vol.
10
, No.
3
, pp.
219
227
.
17.
Meirovitch, L., 1975, Elements of Vibration Analysis, McGraw-Hill, New York.
18.
Neamtu, M., Pottmann, H., and Schumaker, L. L., 1996, “Designing NURBS Cam Profiles Using Trigonometric Splines,” preprint.
19.
Singer
N. C.
, and
Seering
W. P.
,
1990
, “
Preshaping Command Inputs to Reduce System Vibration
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
112
, March, pp.
76
82
.
20.
Srinivasan, L., and Ge, Q. J., 1997, “Designing Dynamically Compensated and Robust Cam Profiles With Bernstein-Be´zier Harmonic Curves,” Proc. 1997 ASME Design Automation Conference, Sacramento, CA, Paper Number DETC97/DAC-3960.
21.
Stoddart, D. A., 1953, “Polydyne Cam Design,” Machine Design, January, pp. 121–135; February, pp. 146–154; March, pp. 149–164.
22.
Tesar, D., and Matthew, G. K., 1976, The Dynamic Synthesis, Analysis, and Design of Modeled Cam Systems, Lexington Books.
23.
Wiederrich, J. L., and Roth, B., 1975, “Dynamic Synthesis of Tuned Cam Displacement Curves Using Finite Trigonometric Series,” ASME Journal of Engineering for Industry, Feb., pp. 287–293.
This content is only available via PDF.
You do not currently have access to this content.