The singularity-free workspace of parallel mechanisms is highly desirable in a context of robot design. This work focuses on analyzing the effects of the orientation angles on the singularity-free workspace of the Gough–Stewart platform in order to determine the optimal orientation. In any orientation with and , the singularity surface becomes a plane coinciding with the base plane. Hence, an analytic algorithm is presented in this work to determine the singularity-free workspace. The results show that the singularity-free workspace in some orientations can be larger than that in the reference orientation with . However, the global optimal orientation is difficult to determine. Only an approximate optimal orientation is available. The results obtained can be applied to the design or parameter setup of the Gough–Stewart platform.
Issue Section:
Research Papers
1.
Gosselin
, C.
, 1990, “Determination of the Workspace of 6-DOF Parallel Manipulators
,” ASME J. Mech. Des.
0161-8458, 112
, pp. 331
–336
.2.
Merlet
, J. P.
, 1999, “Determination of 6D Workspaces of Gough-Type Parallel Manipulator and Comparison Between Different Geometries
,” Int. J. Robot. Res.
0278-3649, 18
(9
), pp. 902
–916
.3.
Pernkopf
, F.
, and Husty
, M.
, 2006, “Workspace Analysis of Stewart–Gough-Type Parallel Manipulators
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062, 220
(7
), pp. 1019
–1032
.4.
Gosselin
, C.
, and Angeles
, J.
, 1990, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE Trans. Rob. Autom.
1042-296X, 6
(3
), pp. 281
–290
.5.
Zlatanov
, D.
, Fenton
, R. G.
, and Behhabid
, B.
, 1994, “Singularity Analysis of Mechanisms and Robots Via a Velocity-Equation Model of the Instantaneous Kinematics
,” Proceedings of the IEEE International Conference on Robotics and Automation
, San Diego, CA, pp. 986
–991
.6.
Sefrioui
, J.
, and Gosselin
, C.
, 1995, “On the Quadratic Nature of the Singularity Curves of Planar Three-Degree-of-Freedom Parallel Manipulators
,” Mech. Mach. Theory
0094-114X, 30
(4
), pp. 533
–551
.7.
Collins
, C. L.
, and McCarthy
, J. M.
, 1998, “The Quartic Singularity Surfaces of Planar Platforms in the Clifford Algebra of the Projective Plane
,” Mech. Mach. Theory
0094-114X, 33
(7
), pp. 931
–944
.8.
Fichter
, E. F.
, 1986, “A Stewart Platform-Based Manipulator: General Theory and Practical Construction
,” Int. J. Robot. Res.
0278-3649, 5
(2
), pp. 157
–182
.9.
Merlet
, J. P.
, 1989, “Singular Configurations of Parallel Manipulators and Grassmann Geometry
,” Int. J. Robot. Res.
0278-3649, 8
(5
), pp. 45
–56
.10.
Hunt
, K. H.
, and McAree
, P. R.
, 1998, “The Octahedral Manipulator: Geometry and Mobility
,” Int. J. Robot. Res.
0278-3649, 17
(8
), pp. 868
–885
.11.
McAree
, P. R.
, and Daniel
, R. W.
, 1999, “An Explanation of Never-Special Assembly Changing Motions for 3-3 Parallel Manipulators
,” Int. J. Robot. Res.
0278-3649, 18
(6
), pp. 556
–574
.12.
Mayer St-Onge
, B.
, and Gosselin
, C.
, 2000, “Singularity Analysis and Representation of the General Gough–Stewart Platform
,” Int. J. Robot. Res.
0278-3649, 19
(3
), pp. 271
–288
.13.
Li
, H.
, Gosselin
, C.
, Richard
, M.
, and Mayer-St-Onge
, B.
, 2006, “Analytic Form of the Six-Dimensional Singularity Locus of the General Gough–Stewart Platform
,” ASME J. Mech. Des.
0161-8458, 128
(1
), pp. 279
–287
.14.
Jiang
, Q.
, and Gosselin
, C.
, 2008, “Singularity Equations of Gough–Stewart Platforms Using a Minimal Set of Geometric Parameters
,” ASME J. Mech. Des.
0161-8458, 130
(11
), p. 112303
.15.
Merlet
, J. P.
, 1994, “Trajectory Verification in the Workspace for Parallel Manipulator
,” Int. J. Robot. Res.
0278-3649, 13
(4
), pp. 326
–333
.16.
Bhattacharya
, S.
, Hatwal
, H.
, and Ghosh
, A.
, 1998, “Comparison of an Exact and an Approximate Method of Singularity Avoidance in Platform Type Parallel Manipulators
,” Mech. Mach. Theory
0094-114X, 33
(7
), pp. 965
–974
.17.
Dash
, A. K.
, Chen
, I. M.
, Yeo
, S. H.
, and Yang
, G.
, 2003, “Singularity-Free Path Planning of Parallel Manipulators Using Clustering Algorithm and Line Geometry
,” Paper No. ICRA-2003.18.
Sen
, S.
, Dasgupta
, B.
, and Mallik
, A. K.
, 2003, “Variational Approach for Singularity-Free Path-Planning of Parallel Manipulators
,” Mech. Mach. Theory
0094-114X, 38
(11
), pp. 1165
–1183
.19.
Merlet
, J. P.
, and Daney
, D.
, 2001, “A Formal-Numerical Approach to Determine the Presence of Singularity Within the Workspace of a Parallel Robot
,” Proceedings of the International Workshop on Computational Kinematics
, Seoul, May 20–22, pp. 167
–176
.20.
Li
, H.
, Gosselin
, C.
, and Richard
, M.
, 2007, “Determination of the Maximal Singularity-Free Zones in the Six-Dimensional Workspace of the General Gough–Stewart Platform
,” Mech. Mach. Theory
0094-114X, 42
(4
), pp. 497
–511
.21.
Jiang
, Q.
, and Gosselin
, C.
, 2008, “The Maximal Singularity-Free Workspace of the Gough–Stewart Platform for a Given Orientation
,” ASME J. Mech. Des.
0161-8458, 130
(11
), p. 112304
.22.
Jiang
, Q.
, and Gosselin
, C.
, 2009, “Geometric Optimization of the MSSM Gough–Stewart Platform
,” ASME J. Mech. Rob.
1942-4302, 1
(3
), p. 031006
.23.
Jiang
, Q.
, and Gosselin
, C.
, 2009, “Maximal Singularity-Free Total Orientation Workspace of the Gough–Stewart Platform
,” ASME J. Mech. Rob.
1942-4302, 1
(3
), p. 034501
.24.
Merlet
, J. P.
, 2002, Parallel Robots
, Kluwer
, Dordrecht
.25.
Press
, W. H.
, Teukolsky
, S. A.
, Vetterling
, W. T.
, and Flannery
, B. P.
, 1992, Numerical Recipes in C: The Art of Scientific Computing
, 2nd ed., Cambridge University Press
, New York
.26.
Jiang
, Q.
, and Gosselin
, C.
, 2008, “Evaluation and Representation of the Orientation Workspace of the Gough–Stewart Platform
,” ASME J. Mech. Rob.
1942-4302, 1
(2
), p. 021004
.27.
Jiang
, Q.
, and Gosselin
, C.
, 2008, “Determination of the Maximal Singularity-Free Orientation Workspace for the Gough–Stewart Platform
,” Mech. Mach. Theory
0094-114X, 44
, pp. 1281
–1293
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
