A direct procedure, based on the generalized Lagrange multiplier method, will be presented for designing high-speed cam-follower systems over a range of cam speeds. With this method residual vibrations at the end of the rise of a Dwell-Rise-Dwell (DRD) cam motion are minimized for any specified range of rise times. A minimum of boundary conditions on the cam displacement function will be specified to reduce unnecessary constraints on the cam displacement function. The applicability of rules of thumb generally accepted in designing for minimum vibrations will be discussed and compared to the results from this approach.

Issue Section:
Research Papers
Topics:
Vibration, Design, Displacement, Boundary-value problems
1.
Chen
F. Y.
,
1977
, “
A Survey of the State of Art of Cam System Dynamics
,”
Mechanism and Machine Theory
, Vol.
12
, pp.
201
–
224
.
2.
Chen, F. Y., 1982, Mechanics and Design of Cam Mechanisms, Pergamon Press.
3.
Chew, M., Freudenstein, F., and Longman, R. W., 1983, “Application of Optimal Control Theory to the Synthesis of High-Speed Cam-Follower Systems, Part I: Optimality Criterion; Part II: System Optimization,” ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 104, September.
4.
Chew, M., and Chuang, C. H., 1990, “Designing for Lower Residual Vibrations in High-Speed Cam-Follower Systems Over a Range of Speeds,” Proceedings of the 1990 ASME Design Technical Conferences-21st Biennial Mechanisms Conference, Chicago, IL, DE-Vol 26.
5.
Freudenstein
F.
,
1960
, “
On the Dynamics of High-Speed Cam Profiles
,”
Int. J. Mech. Sci.
, Vol.
1
, pp.
342
–
349
.
6.
Gabriele
G. A.
, and
Ragsdell
K. M.
,
1977
, “
The Generalized Reduced Gradient Method: A Reliable Tool for Optimal Design
,”
ASME Journal of Engineering for Industry
, Vol.
99
, No.
2
, pp
394
–
400
.
7.
Hrones
J. A.
,
1948
, “
An Analysis of the Dynamic Forces in a Cam-Driven System
,”
Transactions of the ASME
, Vol.
70
, pp.
473
–
482
.
8.
Kanzaki
K.
, and
Itao
K.
,
1972
, “
Polydyne Cam Mechanisms for Type-head Positioning
,”
ASME Journal of Engineering for Industry
, Vol.
94
, Feb., pp.
250
–
254
.
9.
Kwakernaak
H.
, and
Smith
J.
,
1968
, “
Minimum Vibration Cam Profiles
,”
J. of Mech. Engr. Sci.
, Vol.
10
, No.
3
, pp.
219
–
227
.
10.
Stoddart
D. A.
,
1965
, “
Polydyne Cam Design
,”
Machine Design
, Vol.
25
, Jan., Feb., Mar., pp.
121
–
135
.
11.
Wiederrich
J. L.
, and
Roth
B.
,
1975
, “
Dynamic Synthesis of Cams Using Finite Trigonometric Series
,”
ASME Journal of Engineering for Industry
, Vol.
97
, Feb., pp.
287
–
293
.
12.
Yamada
I.
, and
Nakagawa
M.
,
1985
, “
Reduction of Residual Vibrations in Positioning Control Mechanism
,”
ASME Journal of Vibration, Acoustics, Stress and Reliability in Design
, Jan., Vol.
107
, pp.
47
–
52
.
13.
Zhou
J.
, and
Mayne
R. W.
,
1984
, “
Monotonicity Analysis and the Reduced Gradient Method in Constrained Optimization
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
106
, No.
1
, pp.
90
–
94
.
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