Input torque balancing through addition of an auxiliary, input torque balancing mechanism, is a well-known way for reducing drive speed fluctuations in high-speed cam-follower mechanisms. This paper develops a methodology to design and optimize the so-called inverted cam mechanism (ICM), a simple, cam-based input torque balancing mechanism. It was already introduced in the 1950s, but the design methodologies proposed by Meyer zur Capellen (1964) and Michelin (1979) are, respectively, erroneous or too rough an approximation, and are corrected here. The describing equation that governs the ICM cam design, is shown to be a second-order, nonlinear, ordinary differential equation. It is solved by parameterizing its solution as a finite Fourier series, the coefficients of which are determined through a nonlinear least-squares problem. Based on this methodology, an ICM is designed for input torque balancing a high-speed, industrial cam-follower mechanism. The ICM’s design parameters result from a design optimization, which aims at obtaining a compact and technologically feasible mechanism. The optimization problem is solved using a design chart, which is efficiently created based on a nondimensionalized analysis.

1.
Koster
,
M. P.
, 1975, “
Effect of flexibility of driving shaft on the dynamic behavior of a cam mechanism
,”
ASME J. Eng. Ind.
0022-0817,
97
, pp.
595
602
.
2.
Sarring
,
E. J.
, 1962, “
Torque compensation for cam systems
,”
Transactions of the 7th Conference on Mechanisms
,
Purdue University
, pp.
179
185
.
3.
Benedict
,
C. E.
, and
Tesar
,
D.
, 1970, “
Optimal torque balance for a complex stamping and indexing machine
,”
Mechanisms Conference
, Columbus, Ohio, Paper No. 70-Mech-82.
4.
Kirchhof
,
M.
, 1972, “
Ausgleichsgetriebe zur erhöhung der leistungsfähigkeit und betriebssicherheit von maschinen und geräten
,”
Wiss. Zeitschrift der Tech. Hochschule Karl-Marx-Stadt
,
14
, pp.
51
59
.
5.
Nishioka
,
M.
, 1995, “
State of the art of torque compensation cam mechanisms
,” in
Proceedings of the 9th World Congress on the Theory of Machines and Mechanisms
, Milan, Italy, pp.
713
717
.
6.
Demeulenaere
,
B.
, and
De Schutter
,
J.
, 2003, “
Synthesis of inertially compensated variable-speed cams
,”
ASME J. Mech. Des.
1050-0472,
125
, pp.
593
601
.
7.
Ogawa
,
K.
, and
Funabashi
,
H.
, 1969, “
On the balancing of the fluctuating input torques caused by inertia forces in the crank-and-rocker mechanisms
,”
ASME J. Eng. Ind.
0022-0817,
91
, pp.
97
102
.
8.
Kulitzscher
,
P.
, 1970, “
Leistungsausgleich von koppelgetrieben durch veränderung der massenverteilung oder zusatzkoppelgetriebe
,”
Maschinenbautechnik
,
19
, pp.
562
568
.
9.
Bagci
,
C.
, 1978, “
Synthesis of the plane four-bar mechanism for torque generation, and application to a case study for the design of a new balancing mechanism for rotary top brush in power wax car washing machines
,”
ASME Mechanisms Conference
, Paper No. 78-DET-71.
10.
Yong
,
L. D.
, and
Zhen
,
H.
, 1989, “
Input torque balancing of linkages
,”
Mech. Mach. Theory
0094-114X,
24
, pp.
99
103
.
11.
Kochev
,
I. S.
, 1990, “
General method for active balancing of combined shaking moment and torque fluctuations in planar linkages
,”
Mech. Mach. Theory
0094-114X,
25
, pp.
679
687
.
12.
Dooner
,
D. B.
, 1997, “
Use of noncircular gears to reduce torque and speed fluctuations in rotating shafts
,”
ASME J. Mech. Des.
1050-0472,
119
, pp.
299
306
.
13.
Barkah
,
D.
,
Shafiq
,
B.
, and
Dooner
,
D.
, 2002, “
3D mesh generation for static stress determination in spiral noncircular gears used for torque balancing
,”
ASME J. Mech. Des.
1050-0472,
124
, pp.
313
319
.
14.
Artobolewski
,
I. I.
, 1958, “
Das dynamische laufkriterium bei getrieben
,”
Maschinenbautechnik
,
7
, pp.
663
667
.
15.
Wu
,
C.-J.
, and
Angeles
,
J.
, 2001, “
The optimum synthesis of an elastic torque-compensating cam mechanism
,”
Mech. Mach. Theory
0094-114X,
36
, pp.
245
259
.
16.
Tsay
,
D. M.
,
Ho
,
H. C.
, and
Wang
,
K. C.
, 2002, “
Design of torque balancing cams for globoidal cam indexing mechanisms
,”
ASME J. Mech. Des.
1050-0472,
124
, pp.
441
447
.
17.
Tidwell
,
P. H.
,
Bandukwala
,
N.
,
Dhande
,
S. G.
,
Reinholtz
,
C. F.
, and
Webb
,
G.
, 1994, “
Synthesis of wrapping cams
,”
ASME J. Mech. Des.
1050-0472,
116
, pp.
634
638
.
18.
Funk
,
W.
, and
Han
,
J.
, 1996, “
On the complete balancing of the inertia-caused input torque for plane mechanisms
,”
Proceedings of the ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference
,
Irvine
, California, Paper No. 96-DETC/MECH-1570.
19.
Teng
,
G.
,
Fu
,
H.
, and
Zhou
,
W.
, 1999, “
A new method of torque compensation for high speed indexing cam mechanism
,”
ASME J. Mech. Des.
1050-0472,
121
, pp.
319
323
.
20.
Ullman
,
D.
, and
Velkoff
,
H.
, 1979, “
An introduction to the variable inertia flywheel (vif)
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
46
, pp.
186
190
.
21.
Dizioğlu
,
B.
, 1966,
Getriebelehre, Band 3: Dynamik
,
Vieweg und Sohn
, Braunschweig.
22.
Meyer zur Capellen
,
W.
, 1964, “
Die bewegung periodischer getriebe unter einfluß von kraft- und massenwirkungen
,”
Industrie-Anzeiger
,
86
, pp.
135
140
;
Meyer zur Capellen
,
W.
, 1964, “
Die bewegung periodischer getriebe unter einfluß von kraft- und massenwirkungen
,”
Industrie-Anzeiger
,
86
, pp.
282
289
.
23.
Michelin
,
V.
, 1979, European Patent No. 0 010 267,
European Patent Office
, pp.
1
16
.
24.
Berkof
,
R. S.
, 1979, “
The input torque in linkages
,”
Mech. Mach. Theory
0094-114X,
14
, pp.
61
73
.
26.
Demeulenaere
,
B.
,
Al-Bender
,
F.
, and
De Schutter
,
J.
, 2002, “
Input torque balancing using an inverted cam mechanism
,” in
Proceedings of the ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Montréal, Canada, Paper No. DETC2002/MECH-34313.
27.
Demeulenaere
,
B.
, 2004, “
Dynamic balancing of reciprocating machinery with application to weaving machines
,” Ph.D. thesis, Department of Mechanical Engineering, K.U. Leuven, Leuven, Belgium.
28.
Norton
,
R. L.
, 2002,
Cam Design and Manufacturing Handbook
,
Industrial Press, Inc.
29.
Benedict
,
C. E.
,
Matthew
,
G. K.
, and
Tesar
,
D.
, 1971, “
Torque balancing of machines by subunit cam systems
,”
2nd Applied Mechanism Conference
,
Oklahoma State University
, Stillwater, Oklahoma, Paper No. 15.
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