In mechanism design and in the particular case of the parallel manipulator, most optimization problems involve simultaneously optimizing more than one objective function. In this paper, a method to identify Pareto-optimal solutions for the design of low-mobility parallel manipulators is presented. A 4-degree-of-freedom symmetric parallel manipulator for Schönflies-motion generation is taken as a case study. The design goals used are workspace volume and manipulator dexterity based on a dispersion weighted Frobenius norm. In addition, an expression for energy per cycle has been defined for different types of trajectory to evaluate the power drive. Finally, the set of Pareto-optimal solutions of the design parameters are represented in the design parameter space.

References

References
1.
Zhao
,
T. S.
,
Dai
,
J. S.
, and
Huang
,
Z.
, 2002,
“Geometric Analysis of Overconstrained Parallel Manipulators With Three and Four Degrees of Freedom,”
JSME Int. J., Ser. C
,
45
(
3
), pp.
730
740
.
2.
Huang
,
Z.
, and
Li
,
Q.
, 2002,
“General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators,”
Int. J. Robot. Res.
,
21
(
2
), pp.
131
145
.
3.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004,
“Type Synthesis of 3T1R 4-DOF Parallel Manipulators Based on Screw Theory,”
IEEE Trans. Rob. Autom.
,
20
(
2
), pp.
181
190
.
4.
Company
,
O.
,
Marquet
,
F.
, and
Pierrot
,
F.
, 2003,
“A New High-Speed 4-DoF Parallel Robot Synthesis and Modelling Issues,”
IEEE Trans. Rob. Autom.
,
19
(
3
), pp.
411
420
.
5.
Angeles
,
J.
,
Caro
,
S.
,
Khan
,
W.
, and
Morozov
,
A.
, 2006,
“Kinetostatic Design of an Innovative Schönflies-Motion Generator,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
220
(
7
), pp.
935
943
.
6.
Stamper
,
R. E.
,
Tsai
,
L.-W.
, and
Walsh
,
G. C.
, 1997,
“Optimization of a Three DOF Translational Platform for Well-Conditioned Workspace,”
Proc. IEEE Int. Conf. Robot. Autom.
,
4
, pp.
3250
3255
.
7.
Liu
,
X.-J.
,
Guan
,
L.
, and
Wang
,
J.
, 2007,
“Kinematics and Closed Optimal Design of a Kind of PRRRP Parallel Manipulator,”
ASME J. Mech. Des.
,
129
(
5
), pp.
558
563
.
8.
Liu
,
X.-J.
,
Wang
,
J.
, and
Zheng
,
H.-J.
, 2006,
“Optimum Design of the 5R Symmetrical Parallel Manipulator With a Surrounded and Good-Condition Workspace,”
Robot. Auton. Syst.
,
54
(
3
), pp.
221
233
.
9.
Rao
,
A. B. K.
,
Rao
,
P.V. M.
, and
Saha
,
S. K.
, 2005,
“Dimensional Design of Hexaslides for Optimal Workspace and Dexterity,”
IEEE Trans. Rob.
,
21
(
3
), pp.
444
449
.
10.
Pashkevich
,
A.
,
Wenger
,
P.
, and
Chablat
,
D.
, 2005,
“Design Strategies for the Geometric Synthesis of Orthoglide-Type Mechanisms,”
Mech. Mach. Theory
,
40
(
8
), pp.
907
930
.
11.
Mastinu
,
G.
,
Gobbi
,
M.
, and
Miano
,
C.
, 2006,
Optimal Design of Complex Mechanical Systems
,
Springer
,
Berlin
.
12.
Kim
,
I. Y.
, and
de Weck
,
O. L.
, 2005,
“Adaptive Weighted-Sum Method for Bi-Objective Optimization: Pareto Front Generation,”
Struct. Multidiscip. Optim.
,
29
(
2
), p.
149
158
.
13.
Lin
,
J. G.
, 1976,
“Multiple-Objective Problems: Pareto-Optimal Solutions by Method of Proper Equality Constraints,”
IEEE Trans. Autom. Control
,
21
(
5
), pp.
641
650
.
14.
Giesy
,
D. P.
, 1978,
“Calculation of Pareto Optimal Solutions to Multiple Objective Problems Using Threshold of Acceptability Constraints,”
IEEE Trans. Autom. Control
,
23
(
6
), pp.
1114
1115
.
15.
Chen
,
Y.-L.
, and
Liu
,
C.-C.
, 1994,
“Multiobjective VAR Planning Using the Goal-Attainment Method,”
IEE Proc.: Gener. Transm. Distrib.
,
141
(
3
), pp.
227
232
.
16.
Pentzaropoulos
,
G. C.
, and
Giokas
,
D. I.
, 1993,
“Cost-Performance Modeling and Optimization of Network Flow Balance via Linear Goal Programming Analysis,”
Comput. Commun.
,
16
(
10
), pp.
645
652
.
17.
Srinivas
,
N.
, and
Deb
,
K.
, 1994,
“Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms,”
J. Evol. Comput.
,
2
(
3
), pp.
221
248
.
18.
Fonseca
,
C. M.
, and
Fleming
,
P. J.
, 1995,
“An Overview of Evolutionary Algorithms in Multiobjective Optimization,”
J. Evol. Comput.
,
3
(
1
), pp.
1
16
.
19.
Altuzarra
,
O.
,
Hernández
,
A.
,
Salgado
,
O.
, and
Angeles
,
J.
, 2009,
“Multiobjective Optimum Design of a Symmetric Parallel Schönflies-Motion Generator,”
ASME J. Mech. Des.
,
131
(
3
), p.
031002
.
20.
Salgado
,
O.
,
Altuzarra
,
O.
,
Petuya
,
V.
, and
Hernández
,
A.
, 2008,
“Synthesis and Design of a Novel 3T1R Fully-Parallel Manipulator,”
ASME J. Mech. Des.
,
130
(
4
), p.
042305
.
21.
Pierrot
,
F.
,
Nabat
,
V.
,
Company
,
O.
,
Krut
,
S.
, and
Poignet
,
P.
, 2009,
“Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry,”
IEEE Trans. Rob.
,
25
, pp.
213
224
.
22.
Yoshikawa
,
T.
, 1985,
“Manipulability of Robotic Mechanisms,”
Int. J. Robot. Res.
,
4
(
2
), pp.
3
9
.
23.
Schwartz
,
E.
,
Manseur
,
R.
, and
Doty
,
K.
, 2002,
“Noncommensurate Systems in Robotics,”
Int. J. Rob. Autom.
,
17
(
2
), pp.
1
6
.
24.
Golub
,
G. H.
, and
Van Loan
,
C. F.
, 1996,
Matrix Computations
,
3rd ed.
,
The Johns Hopkins University Press
,
Baltimore, MD
.
25.
Khan
,
W. A.
, and
Angeles
,
J.
, 2006,
“The Kinetostatic Optimization of Robotic Manipulators: The Inverse and the Direct Problems,”
ASME J. Mech. Des.
,
128
(
1
), pp.
168
178
.
26.
Merlet
,
J. P.
, 2006,
Parallel Robots
,
2nd ed.
,
Springer
,
The Netherlands
.
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