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.
Issue Section:
Research Papers
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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by American Society of Mechanical Engineers
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