This paper deals with the solutions of the problem of the shaking force and shaking moment balancing of planar mechanisms by different methods based on the generation of the movements of counterweights. Some special cases are examined, such as balancing methods based on the copying properties of pantograph systems that carry the counterweights (formed by gears or by toothed-belt transmissions). The pantograph system executes a movement exactly opposite to the movement of the total center of the movable link masses. Such a solution provides the conditions for dynamic balancing with a relatively small increase of the total mass of the movable links. The methods are illustrated by many examples.

1.
Arakelian, V., Dahan, M., and Smith, M. R., 2000, “A Historical Review of the Evolution of the Theory on Balancing of Mechanisms,” International Symposium on History of Machines and Mechanisms—Proceedings HMM2000, Kluwer Academic, Dordrecht, pp. 291–300.
2.
Gheronimus
,
Y. L.
,
1968
, “
An Approximate Method of Calculating a Counterweight for the Balancing of Vertical Inertia Forces
,”
J. Mech.
,
3
(4), pp.
283
288
.
3.
Artobolevskii, I. I., 1968, Theory of Mechanisms and Machines, Nauka, Moscow, p. 644.
4.
1979, Balanced slider-crank mechanism, Patent FR 2421301, 1979-10-26.
5.
Shchepetilnikov, V. A., 1982, Balancing of Mechanisms, Mashinostroenie, Moscow, p. 256.
6.
Smith
,
M. R.
, and
Maunder
,
L.
,
1967
, “
Inertia Forces in a Four-Bar Linkage
,”
J. Mech. Eng. Sci.
,
9
(
3
), pp.
218
225
.
7.
Berkof, R. S., 1979, “Force Balancing of a Six-Bar Linkage,” Proceedings of the Fifth World Congress on Theory of Machines and Mechanisms, pp. 1082–1085.
8.
Lanchester
,
F. M.
,
1914
, “
Engine Balancing
,”
Horseless Age
,
33
(12–16), Mar. 25, Apr. 1, 8, 15, 22, pp.
494
498
, 536–538, 571–572, 608–610, 644–646.
9.
Grossley
,
F. R.
,
1965
, “
The Balancing of High-Speed Oscillating Feed Mechanisms
,”
Trans. ASME
,
64
(
28
), pp.
4
8
.
10.
Gappoev, T. T., 1970, Some Methods of the Balancing of Mechanisms on the Frame, Mashinostroenie, Moscow, pp. 313–319.
11.
Emo¨d
,
I.
,
1967
, “
Massenausgleich am Kurbelgetriebe von Sechszylinder-viertakt-V-motoren mit 6 Kurbeln und 60° Zylinderwinkeln
,”
Period. Polytechn. Engng.
,
11
(3–4), pp.
205
221
.
12.
1989, “Le Syste`me Bielle-Manivelle et l’E´quilibrage du Moteur,” Technique et Pratique Auto., Paris, 1, pp. 25–30.
13.
Tsai, L. W., and Walter, R., 1984, “Evaluation of the Oldham-Coupling Type Balancer on a 2.5 Liter In-Line Four-Cylinder Engine,” SEA paper 840456, SEA International Congress and Exposition, Detroit, MI.
14.
Davies
,
T. H.
,
1968
, “
The Kinematics and Design of Linkages, Balancing Mechanisms and Machines
,”
Machine Design Eng.
,
40
, pp.
40
51
.
15.
Arakelian
,
V.
,
1998
, “
Equilibrage Dynamique Complet des Me´canismes
,”
Mech. Mach. Theory
,
33
(
4
), pp.
425
436
.
16.
Turbin
,
B. I.
,
Koropetz
,
A. A.
, and
Koropetz
,
Z. A.
,
1978
, “
The Possibility of the Shaking Force Balancing in the System With Oscillating Links
,”
Mech. Mach. Theory
,
7
, pp.
87
90
.
17.
Koropetz
,
A. A.
,
1979
, “
Shaking Force and Shaking Moment Balancing of the Mechanisms of Machines for the Scouring Grain
,”
Moscow, Ed. NTVIM
,
13
, pp.
62
71
.
18.
Kamenski
,
V. A.
,
1968
, “
On the Question of the Balancing of Plane Linkages
,”
J. Mech.
,
3
(
4
), pp.
303
322
.
19.
Filonov, I. P., and Petrikovetz, I. P., 1987, “Balancing Device of Lever Mechanisms,” Patent SU1296762, 1987-03-15.
20.
Arakelian
,
V.
, and
Dahan
,
M.
,
2001
, “
Partial Shaking Moment Balancing of Fully Shaking Force Balanced Linkages
,”
Mech. Mach. Theory
,
36
(11–12), pp.
1241
1252
.
21.
Arakelian
,
V.
,
Dahan
,
M.
, and
Smith
,
M. R.
,
2001
, “
Complete Shaking Force and Partial Shaking Moment Balancing of Planar Four-Bar Linkages
,”
J. Multibody Syst. Dyn.
,
215
(
K
), pp.
31
34
.
22.
Frolov, K. V., 1987, Theory of Mechanisms and Machines, Vishaya shkola, Moscow, p. 496.
23.
Doronin, V. I., and Pospelov, A. I., 1991, “Balanced Slider-Crank Mechanism,” Patent SU1627769, 1991-02-15.
24.
Bagci
,
C.
,
1982
, “
Complete Shaking Force and Shaking Moment Balancing of Link Mechanisms Using Balancing Idler Loops
,”
Trans. ASME
,
104, pp.
482
493
.
25.
Hilpert
,
H.
,
1968
, “
Weight Balancing of Precision Mechanical Instruments
,”
J. Mech.
,
3
(
4
), pp.
289
302
.
26.
Ye
,
Z.
, and
Smith
,
M. R.
,
1994
, “
Complete Balancing of Planar Linkages by an Equivalence Method
,”
Mech. Mach. Theory
,
29
(
5
), pp.
701
712
.
27.
Arakelian
,
V. H.
, and
Smith
,
M. R.
,
1999
, “
Complete Shaking Force and Shaking Moment Balancing of Linkages
,”
Mech. Mach. Theory
,
34
(
8
), pp.
1141
1153
.
28.
Kochev
,
I. S.
,
1992
, “
Active Balancing of the Frame Shaking Moment in High Speed Planar Machines
,”
Mech. Mach. Theory
,
27
(
1
), pp.
53
58
.
29.
Berkof
,
R. S.
,
1973
, “
Complete Force and Moment Balancing of Inline Four-Bar Linkages
,”
Mech. Mach. Theory
,
8
(
3
), pp.
397
410
.
30.
Feng
,
G.
,
1991
, “
Complete Shaking Force and Shaking Moment Balancing of 17 Types of Eight-Bar Linkages Only With Revolute Pairs
,”
Mech. Mach. Theory
,
26
(
2
), pp.
197
206
.
31.
Berestov, L. V., 1977, “Comparative Analysis of the Reactions in the Kinematic Pairs of the Four-Bar Linkages for the Different Balancing Methods,” Mekhanika Machin, Nauka, Moscow, pp. 61–70.
32.
Berkof
,
R. S.
, and
Lowen
,
G. G.
,
1971
, “
Theory of Shaking Moment Optimization of Force-Balanced Four-Bar Linkages
,”
ASME J. Eng. Ind.
,
93B
, pp.
53
60
.
33.
Wiederrich
,
J. L.
, and
Roth
,
B.
,
1976
, “
Momentum Balancing of Four-Bar Linkages
,”
Trans. ASME
,
98B
(
4
), pp.
1289
1295
.
34.
Esat
,
I.
, and
Bahai
,
H.
,
1999
, “
A Theory of Complete Force and Moment Balancing of Planar Linkage Mechanisms
,”
Mech. Mach. Theory
,
34
(
6
), pp.
903
922
.
35.
Arakelian, V., and Dahan, M., Patent FR2817008, 24 May, 2002.
You do not currently have access to this content.