Abstract

This paper proposes a new solution to the problem of torque minimization of spatial parallel manipulators. The suggested approach involves connecting a secondary mechanical system to the initial structure, which generates a vertical force applied to the manipulator platform. Two versions of the added force are considered: constant and variable. The conditions for optimization are formulated by the minimization of the root-mean-square values of the input torques. The positioning errors of the unbalanced and balanced parallel manipulators are provided. It is shown that the elastic deformations of the manipulator structure, which are due to the payload, change the altitude and the inclination of the platform. A significant reduction of these errors is achieved by using the balancing mechanism. The efficiency of the suggested solution is illustrated by numerical simulations and experimental verifications. The prototype of the suggested balancing mechanism for the Delta robot is also presented.

References

1.
Lowen
,
G. G.
,
Tepper
,
F. R.
, and
Berkof
,
R. S.
, 1983, “
Balancing of Linkages: Update
,”
Mech. Mach. Theory
0094-114X,
18
(
3
), pp.
213
230
.
2.
Arakelian
,
V.
, and
Smith
,
M. R.
, 2005, “
Shaking Force and Shaking Moment Balancing of Mechanisms: An Historical Review With New Examples
,”
ASME J. Mech. Des.
1050-0472,
127
, pp.
334
339
;
Arakelian
,
V.
, and
Smith
,
M. R.
, 2005,
ASME J. Mech. Des.
1050-0472,
127
, pp.
1034
1035
.
3.
Agrawal
,
S. K.
, and
Fattah
,
A.
, 2004, “
Reactionless Space and Ground Robots: Novel Designs and Concept Studies
,”
Mech. Mach. Theory
0094-114X,
39
, pp.
25
40
.
4.
Wang
,
J.
, and
Gosselin
,
C. M.
, 1999, “
Static Balancing of Spatial Three-Degree-of-Freedom Parallel Mechanisms
,”
Mech. Mach. Theory
0094-114X,
34
, pp.
437
452
.
5.
Newman
,
W. S.
, and
Hogan
,
N.
, 1986, “
The Optimal Control of Balanced Manipulators
,”
Proceedings of the Winter Annual Meeting of the ASME
, Anaheim, CA.
6.
Laliberté
,
T.
,
Gosselin
,
C. M.
, and
Jean
,
M.
, 1999, “
Static Balancing of 3-DOF Planar Parallel Mechanisms
,”
IEEE/ASME Trans. Mechatron.
1083-4435,
4
(
4
), pp.
363
377
.
7.
Fujikoshi
,
K.
, 1976, “
Balancing Apparatus for Jointed Robot
,” Patent No. JP51–122254.
8.
Arakelian
,
V.
, 1989, “
Manipulator
,” S.U. Patent No. 1,465,298.
9.
Wang
,
J.
, and
Gosselin
,
C. M.
, 2000, “
Static Balancing of Spatial Four-Degree-of-Freedom Parallel Mechanisms
,”
Mech. Mach. Theory
0094-114X,
35
, pp.
563
592
.
10.
Russo
,
A.
,
Sinatra
,
R.
, and
Xi
,
F.
, 2005, “
Static Balancing of Parallel Robots
,”
Mech. Mach. Theory
0094-114X,
40
, pp.
191
202
.
11.
Carwardine
,
G.
, 1940, “
Elastic Force and Equipoising Mechanism
,” S.U. Patent No. 2,204,301.
12.
Ebert-Uphoff
,
I.
,
Gosselin
,
C. M.
, and
Laliberté
,
T.
, 2000, “
Static Balancing of Spatial Parallel Mechanisms: Revisited
,”
ASME J. Mech. Des.
1050-0472,
122
, pp.
43
51
.
13.
Herder
,
J. L.
, 2001, “
Energy-Free Systems: Theory, Conception and Design of Statically Balanced Mechanisms
,” Ph.D. thesis, Delf University of Technology.
14.
Streit
,
D. A.
, and
Shin
,
E.
, 1993, “
Equilibrators for Planar Linkages
,”
ASME J. Mech. Des.
1050-0472,
115
, pp.
604
611
.
15.
Vrijlandt
,
N.
, and
Herder
,
J. L.
, 2002, “
Seating Unit for Supporting a Body or Part of a Body
,” Patent No. NL1018178.
16.
Vladov
,
I. L.
,
Danilevskij
,
V. N.
, and
Rassadkin
,
V. D.
, 1981, “
Module of Linear Motion of Industrial Robot
,” S.U. Patent Application No. 848,350.
17.
Ebert-Uphoff
,
I.
, and
Johnson
,
K.
, 2002, “
Practical Considerations for the Static Balancing of Mechanisms of Parallel Architecture
,”
Proc. Inst. Mech. Eng. Part K: Journal of Multi-Body Dynamics
,
216
(
1
), pp.
73
85
.
18.
Tuda
,
G.
, and
Mizuguchi
,
O.
, 1983, “
Arm With Gravity-Balancing Function
,” S.U. Patent No. 4,383,455.
19.
Herder
,
J. L.
, 2002, “
Some Considerations Regarding Statically Balanced Parallel Mechanisms
,”
Proceedings of the Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators
,
Quebec City, QB, Canada
, Oct. 3 and 4.
20.
Leblond
,
M.
, and
Gosselin
,
C. M.
, 1998, “
Static Balancing of Spatial and Planar Parallel Manipulators With Prismatic Actuators
,”
Proceedings of DETC’98
, Atlanta, GA, pp.
1
12
.
21.
Popov
,
M.
, and
Tyurin
,
V.
, 1988, “
Balanced Manipulator
,” S.U. Patent No. 1,379,105.
22.
Agrawal
,
A.
, and
Agrawal
,
S. K.
, 2005, “
Design of Gravity Balancing Leg Orthosis Using Non-Zero Free Length Springs
,”
Mech. Mach. Theory
0094-114X,
40
, pp.
693
709
.
23.
Simionescu
,
I.
, and
Ciupitu
,
L.
, 2000, “
The Static Balancing of the Industrial Arms. Part I: Discrete Balancing
,”
Mech. Mach. Theory
0094-114X,
35
, pp.
1287
1298
.
24.
Segla
,
S.
,
Kalker-Kalkman
,
C. M.
, and
Schwab
,
A. L.
, 1998, “
Statical Balancing of A Robot Mechanism With the Aid of A Genetic Algorithm
,”
Mech. Mach. Theory
0094-114X,
33
2
, pp.
163
174
.
25.
Minotti
,
P.
, and
Pracht
,
P.
, 1988, “
Ressort et Mécanismes: Une Solution aux Problèmes D’équilibrage
,”
Mech. Mach. Theory
0094-114X,
23
, pp.
157
168
.
26.
Dzhavakhyan
,
R. P.
, and
Dzhavakhyan
,
N. P.
, 1989, “
Balanced Manipulator
,” S.U. Patent No. 1,521,579.
27.
Hervé
,
J.
, 1985, “
Device for Counter-Balancing the Forces Due to Gravity in a Robot Arm
,” Patent No. FR2565153.
28.
Bartlett
,
D. S.
,
Freed
,
D. I.
, and
Poynter
,
W. H.
, 1988, “
Robot With Spring Pivot Balancing Mechanism
,” S.U. Patent No. 4,753,128.
29.
Popov
,
M. V.
,
Tyurin
,
V. N.
, and
Druyanov
,
B. A.
, 1984, “
Counterbalanced Manipulator
” S.U. Patent No. 1,065,186.
30.
Simionescu
,
I.
, and
Ciupitu
,
L.
, 2000, “
The Static Balancing of the Industrial Arms. Part I: Continuous Balancing
,”
Mech. Mach. Theory
0094-114X,
35
, pp.
1299
1311
.
31.
Lakota
,
N. A.
, and
Petrov
,
L. N.
, 1985, “
Manipulators for Assembly Tasks
,”
Automation of Assembly Tasks
,
D. E.
Okhotsimskij
, ed.,
Nauka
,
Moscow
, pp.
137
153
.
32.
Kondrin
,
A. T.
,
Petrov
,
L. N.
, and
Polishchuk
,
N. F.
, 1990, “
Pivoted Arm Balancing Mechanism
” S.U. Patent No. 1,596,154.
33.
Petrov
,
L. N.
, and
Polishchuk
,
N. F.
, 1979, “
Vertical Displacement Device
,” S.U. Patent Application No. 643,323.
34.
Popov
,
M. V.
, and
Tyurin
,
V. N.
, 1983, “
Balanced Manipulator
,” S.U. Patent No. 1,000,271.
35.
Gvozdev
,
Y. F.
, 1992, “
Manipulator
,” S.U. Patent No. 1,777,993.
36.
Gvozdev
,
Y. F.
, 1990, “
Manipulator
,” S.U. Patent No. 1,537,512.
37.
Gvozdev
,
Y. F.
, 1987, “
Manipulator
,” S.U. Patent No. 1,308,463.
38.
Belyanin
,
P. N.
, 1988,
Balanced Manipulators
,
Mashinostroynie
,
Moscow
, p.
263
.
39.
Wildenberg
,
F.
, 2002, “
Compensating System for a Hexapod
,” S.U. Patent No. 6,474,915.
40.
Dzhavakhyan
,
R. P.
, and
Dzhavakhyan
,
N. P.
, 1987, “
Balanced Manipulator
,” S.U. Patent No. 1,357,218.
41.
Segawa
,
Y.
,
Yamamoto
,
M.
, and
Shimada
,
A.
, 2000, “
Parallel Link Mechanism
,” Patent No. JP2000120824.
42.
Agrawal
,
S. K.
, and
Fattah
,
A.
, 2004, “
Gravity-Balancing of Spatial Open-Chain Manipulators
,”
Mech. Mach. Theory
0094-114X,
39
, pp.
1331
1344
.
43.
Clavel
,
R.
, 1990, “
Device for Movement and Displacing of an Element In Space
,” S.U. Patent No. 4,976,582.
44.
Miller
,
K.
, and
Clavel
,
R.
, 1992, “
The Lagrange-Based Model of Delta-4 Robot Dynamics
,”
Robotersysteme
,
8
(
1
), pp.
49
54
.
45.
Baradat
,
C.
,
Arakelian
,
V.
, and
Maurine
,
P.
, 2006, “
Parallel Robot Including of Load-Compensation System
,” Patent No. FR2880575.
You do not currently have access to this content.