An optimum design of an industrial robot can be achieved from different point of views. For example, a robot can be conceived from the standpoint achieving maximum workspace or minimum weight, etc. In this paper, the objective is to arrive at a robot design that will require optimum driving torques/forces at its joints to perform tasks within its workspace. Such a design will automatically save energy. Note that these torques/forces at the joints are highly dependent on the mass and the inertia properties of the robot’s links. Therefore, these quantities were minimized by determining the optimum masses and optimum mass centers and finding out the corresponding inertia properties of the moving links. Such an approach was briefly introduced earlier by the authors with the help of a simple two-link planar arm. In this paper, the concept is generalized and demonstrated with the help of a complex robot, a 6-degrees-of-freedom PUMA robot. To achieve the design for optimum driving torques/forces at the joints, the concept of equimomental system of point masses was introduced, which helped to obtain the optimum locations of the mass centers of each link quite conveniently. However, to compute the driving torques/forces recursively for such equivalent point mass systems, the decoupled natural orthogonal complement matrices for point masses (DeNOC-P) was derived. It has led to a simplified algorithm for obtaining driving torques/forces. The proposed algorithm for optimization is illustrated with the help of a PUMA robot.

References

References
1.
Khan
,
W. A.
, and
Angeles
,
J.
,
2005
, “
The Kinetostatic Optimization of Robotic Manipulators: The Inverse and the Direct Problems
,”
ASME J. Mech. Des.
,
128
(
1
), pp.
168
178
.
2.
Ceccarelli
,
M.
, and
Lanni
,
C.
,
2004
, “
A Multi-Objective Optimum Design of General 3R Manipulators for Prescribed Workspace Limits
,”
Mech. Mach. Theory
,
39
(
2
), pp.
119
132
.
3.
Jin
,
L.
,
Li
,
S.
,
La
,
H. M.
, and
Luo
,
X.
,
2017
, “
Manipulability Optimization of Redundant Manipulators Using Dynamic Neural Networks
,”
IEEE Trans. Ind. Electron.
,
64
(
6
), pp.
4710
4720
.
4.
Yoshikawa
,
T.
,
1985
, “
Manipulability of Robotic Mechanisms
,”
Int. J. Rob. Res.
,
4
(
2
), pp.
3
9
.
5.
Gosselin,
,
C.
,
2008
, “
Gravity Compensation, Static Balancing and Dynamic Balancing of Parallel Mechanisms
,”
Smart Devices and Machines for Advanced Manufacturing,
,
L.
Wang
, and
J.
Xi
, eds.,
Springer
,
London
, pp.
27
48
.
6.
Agrawal
,
S. K.
,
Gardner
,
G.
, and
Pledgie
,
S.
,
1999
, “
Design and Fabrication of an Active Gravity Balanced Planar Mechanism Using Auxiliary Parallelograms
,” ASME
J. Mech. Des.
,
123
(
4
), pp.
525
528
.
7.
Agrawal
,
S. K.
, and
Fattah
,
A.
,
2004
, “
Gravity-Balancing of Spatial Robotic Manipulators
,”
Mech. Mach. Theory
,
39
, pp.
1331
1344
.
8.
Arakelian
,
V.
, and
Briot
,
S.
,
2015
,
Balancing of Linkages and Robot Manipulators
,
Springer
,
Swizerland
.
9.
Kolarski
,
M.
,
Vukobratovic
,
M.
, and
Borovac
,
B.
,
1994
, “
Dynamic Analysis of Balanced Robot Mechanisms
,”
Mech. Mach. Theory
,
29
(
3
), pp.
427
454
.
10.
Coelho
,
T. A. H.
,
Yong
,
L.
, and
Alves
,
V. F. A.
,
2004
, “
Decoupling of Dynamic Equations by Means of Adaptive Balancing of 2-dof Open-Loop Mechanisms
,”
Mech. Mach. Theory
,
39
, pp.
871
881
.
11.
Moradi
,
M.
,
Nikoobin
,
A.
, and
Azadi
,
S.
,
2010
, “
Adaptive Decoupling for Open Chain Planar Robots
,”
Trans. B: Mech. Eng.
,
17
(
5
), pp.
376
386
.
12.
Sherwood
,
A. A.
, and
Hockey
,
B. A.
,
1968
, “
The Optimization of Mass Distribution in Mechanism Using Dynamically Similar Systems
,”
J. Mech.
,
4
(
3
), pp.
243
260
.
13.
Arakelian
,
V.
,
Baron
,
J.-P. L.
, and
Mottu
,
P.
,
2011
, “
Torque Minimisation of the 2-DOF Serial Manipulators Based on Minimum Energy Consideration and Optimum Mass Redistribution
,”
Mechatronics
,
21
(
1
), pp.
310
314
.
14.
Routh
,
E. J.
,
1905
,
Treatise on the Dynamics of a System of Rigid Bodies. Elementary Part-I
,
Dover Publication Inc.
,
New York
.
15.
Haung
,
N. C.
,
1993
, “
Equimomental System of Rigidly Connected Equal Particles
,”
J. Guid. Control Dyn.
,
16
(
6
), pp.
1194
1196
.
16.
Hang
,
W. J.
,
Li
,
Q.
, and
Guo
,
L. S.
,
1999
, “
Integrated Design of Mechanical Structure and Control Algorithm for a Programmable Four-Bar Linkage
,”
IEEE/ASME Trans. Mechatron.
,
4
(
4
), pp.
354
362
.
17.
Verschuure
,
M.
,
Demeulenaere
,
B.
,
Aertbelien
,
E.
,
Swevers
,
J.
, and
De Schutter
,
J.
,
2008
, “
Optimal Counterweight Balancing of Spatial Mechanisms Using Voxel-Based Discretization
,”
Proc. ISMA, Katholieke Universiteit Leuven, Belgium
, pp.
2159
2173
.
18.
Illarreal-Cervantes
,
M. G.
,
Cruz-Villar
,
C. A.
,
Alvarez-Gallegos
,
J.
, and
Portilla-Flores
,
E. A.
,
2013
, “
Robust Structure-Control Design Approach for Mechatronic Systems
,”
IEEE/ASME Trans. Mechatron.
,
18
(
5
), pp.
1592
1601
.
19.
Chaudhary
,
H.
, and
Saha
,
S. K.
,
2009
,
Dynamics and Balancing of Multibody Systems
,
Springer-Verlag
,
Berlin
.
20.
Chaudhary
,
K.
, and
Chaudhary
,
H.
,
2015
, “
Optimal Dynamic Balancing and Shape Synthesis of Links in Planar Mechanisms
,”
Mech. Mach. Theory
,
93
, pp.
127
146
.
21.
Molian
,
S.
,
1973
, “
Kinematics and Dynamics of the RSSR Mechanism
,”
Mech. Mach. Theory
,
8
(
2
), pp.
271
282
.
22.
Attia
,
H. A.
,
2003
, “
A Matrix Formulation for the Dynamic Analysis of Spatial Mechanism Using Point Coordinates and Velocity Transformation
,”
Acta Mech.
,
165
(
3
), pp.
207
222
.
23.
Gherman
,
B.
,
Pisla
,
D.
,
Vaida
,
C.
, and
Plitea
,
N.
,
2012
, “
Development of Inverse Dynamic Model for a Surgical Hybrid Parallel Robot With Equivalent Lumped Masses
,”
Rob. Comp. Integr. Manuf.
,
28
(
3
), pp.
402
415
.
24.
Hockey
,
B. A.
,
1972
, “
The Minimization of the Fluctuation of Input-Shaft Torque in Plane Mechanisms
,”
Mech. Mach. Theory
,
7
(
3
), pp.
335
346
.
25.
Lee
,
T. W.
, and
Cheng
,
C.
,
1984
, “
Optimum Balancing of Combined Shaking Force, Shaking Moment and Torque Fluctuations in High Speed Linkages
,” ASME
J. Mech. Des.
,
106
(
2
), pp.
242
251
.
26.
Qi
,
N. M.
, and
Pennestri
,
E.
1991
, “
Optimum Balancing of Four-bar Linkages. Mechanism and Machine Theory
,”
Mech. Mach. Theory,
26
(
3
), pp.
337
348
.
27.
Diken
,
H.
,
1995
, “
Effect of Mass Balancing on the Actuator Torques of a Robot
,”
Mech. Mach. Theory
,
30
(
4
), pp.
495
500
.
28.
Gupta
,
V.
,
Chaudhary
,
H.
, and
Saha
,
S. K.
,
2015
, “
Dynamics and Actuating Torque Optimization of Planar Robots
,”
KSME J. Mech. Sci. Technol.
,
29
(
7
), pp.
2699
2704
.
29.
Saha
,
S. K.
,
1999
, “
Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices
,”
Trans. ASME
,
66
(
4
), pp.
986
996
.
30.
Saha
,
S. K.
,
2014
,
Introduction to Robotics
,
2nd ed
.,
Tata McGraw Hill, Higher Education
,
New Delhi
.
31.
Angeles
,
J.
, and
Lee
,
S.
,
1988
, “
The Formulation of Dynamical Equations of Holonomic Mechanical Systems Using a Natural Orthogonal Complement
,”
ASME J. Appl. Mech.
,
55
(
1
), pp.
243
244
.
32.
Luh
,
J. Y. S.
,
Walker
,
M. W.
, and
Paul
,
R. P. C.
,
1980
, “
Online Computational Scheme for Mechanical Manipulators,”
ASME J. Dyn. Syst. Meas. Control
,
102
, pp.
69
76
.
33.
RoboAnalyzer V6
,
2013
,
http://www.roboanalyzer.com, Indian Institute of Technology Delhi, New Delhi, India
.
34.
Arakelian
,
V.
,
Samsonyan
,
A.
, and
Arakelyan
,
N.
(
2015
). “
Optimum Shaking Force Balancing of Planar 3-RRR Parallel Manipulators by Means of an Adaptive Counterweight System,”
Proceedings of the 14th IFToMM World Congress
,
Taipei, Taiwan
.
35.
Allison
,
J. T.
,
2013
, “
Plant-Limited Co-Design of an Energy-Efficient Counterbalanced Robotic Manipulator
,”
ASME J. Mech. Des.
,
135
(
10
), pp.
3
13
.
36.
matlab, Version R2013a,
2013
.
37.
Marler
,
R. T.
, and
Arora
,
J. S.
,
2010
, “
The Weighted Sum Method for Multi-Objective Optimization: New Insights
,”
Struct. Multidisc. Optim.
,
41
(
6
), pp.
853
862
.
38.
Gill
,
P. E.
,
Murray
,
W.
, and
Wright
,
M. H.
,
1981
,
Practical Optimization
,
Academic Press Inc.
,
San Diego
.
39.
Paplambros
,
P. Y.
, and
Wilde
,
D. J.
,
2000
,
Principle of Optimal Deisgn: Modeling and Computation
,
Cambridge University Press
,
Spain
.
40.
Feng
,
B.
,
Morita
,
N.
,
Torii
,
T.
, and
Yoshida
,
S.
,
2000
, “
Optimum Balancing of Shaking Force and Shaking Moment for Spatial RSSR Mechanism Using Genetic Algorithm
,”
JSME Int. J. C
,
43
(
3
), pp.
691
696
.
You do not currently have access to this content.