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A Vector Expression of the Constant-Orientation Singularity Locus of the Gough–Stewart Platform

[+] Author and Article Information
Clément Gosselin

e-mail: gosselin@gmc.ulaval.ca

Philippe Cardou

Département de Génie Mécanique,
Université Laval,
1065 Avenue de la Médecine Québec,
QC G1V 0A6, Canada

This condition is a special case which corresponds also to a type I singularity.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received October 17, 2012; final manuscript received April 11, 2013; published online June 10, 2013. Assoc. Editor: J. M. Selig.

J. Mechanisms Robotics 5(3), 034502 (Jun 24, 2013) (4 pages) Paper No: JMR-12-1168; doi: 10.1115/1.4024295 History: Received October 17, 2012; Revised April 11, 2013

This paper presents a vector expression of the constant-orientation singularity locus of the general Gough–Stewart platform. The third-degree vector expression obtained does not contain a constant term, which allows the factorization of an instance of the position vector, thereby leading to a very compact form. Additionally, an expression of the vector orthogonal to the singularity locus is obtained as a byproduct. An alternative expression that reduces the number of times that the position vector appears in the expression is also presented. It is shown that a simplified architecture such as that of the Minimal Simplified Symmetric Manipulator (MSSM) can significantly reduce the complexity of the coefficients appearing in the expression.

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Gosselin, C. M., and Angeles, J., 1990, “Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Dasgupta, B., and Mruthyunjaya, T. S., 1998, “Singularity-Free Path Planning for the Stewart Platform Manipulator,” Mech. Mach. Theory, 33(6), pp. 711–725. [CrossRef]
Merlet, J.-P., 1989, “Singular Configurations of Parallel Manipulators and Grassmann Geometry,” Int. J. Robot. Res., 8(5), pp. 45–56. [CrossRef]
Verhoeven, R., Hiller, M., and Tadokoro, S., 1998, “Workspace, Stiffness, Singularities and Classification of Tendon-Driven Stewart Platforms,” Advances in Robot Kinematics: Analysis and Control, J. Lenarčič and M. L. Husty eds, Springer, Dordrecht, The Netherlands, pp. 105–114.
Ben-Horin, P., and Shoham, M., 2009, “Application of Grassmann-Cayley Algebra to Geometrical Interpretation of Parallel Robot Singularities,” Int. J. Robot. Res., 28(1), pp. 127–141. [CrossRef]
Cao, Y., Zhou, H., Shen, L., and Li, B., 2011, “Singularity Kinematics Principle and Position-Singularity Analyses of the 6-3 Stewart-Gough Parallel Manipulators,” J. Mech. Sci. Technol., 25(2), pp. 513–522. [CrossRef]
Bohigas, O., Manubens, M., and Ros, L., 2012, “Planning Singularity-Free Force Feasible Paths on the Stewart Platform,” Latest Advances in Robot Kinematics, J.Lenarčič and M.Husty, eds, Springer, Dordrect, The Netherlands, pp. 245–252.
Bohigas, O., Zlatanov, D., Ros, L., Manubens, M., and Porta, J. M., 2012, “Numerical Computation of Manipulator Singularities,” Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1351–1358.
Li, H., Gosselin, C. M., Richard, M. J., and Mayer St-Onge, B., 2006, “Analytic Form of the Six-Dimensional Singularity Locus of the General Gough-Stewart Platform,” ASME J. Mech. Des., 128, pp. 279–287. [CrossRef]
Mayer St-Onge, B., and Gosselin, C. M., 2000, “Singularity Analysis and Representation of the General Gough-Stewart Platform,” Int. J. Robot. Res., 19(3), pp. 271–288. [CrossRef]
Shanker, V., and Bandyopadhay, S., 2012, “Singular Manifold of the General Hexagonal Stewart Platform Manipulator,” Latest Advances in Robot Kinematics, J.Lenarčič and M.Husty, eds, Springer, Dordrect, The Netherlands, pp. 397–404.
Cao, Y., Wu, M., and Zhou, H., 2013, “Position-Singularity Characterization of a Special Class of the Stewart Parallel Mechanisms,” Int. J. Rob. Autom., 28(1), pp. 57–64. [CrossRef]
Strang, G., 2006, Linear Algebra and its Applications, 4th ed., Brooks/Cole, Belmont, CA.
Petersen, K. B., and Pedersen, M. S., 2008, The Matrix Cookbook, November 2008 Version, Technical University of Denmark, Denmark, p. 71.
Doyon, K., 2012, “Analyse Vectorielle des Lieux de Singularité de la Plate-Forme de Gough-Stewart,” M.S. thesis, Université Laval, Québec, QC.
Di Gregorio, R., 2002, “Singularity-Locus Expression of a Class of Parallel Mechanisms,” Robotica, 20, pp. 323–328.
Merlet, J.-P., 2006, Parallel Robots, 2nd ed., Springer, Dordrecht, The Netherlands.
Merlet, J.-P., 2004, “Solving the Forward Kinematics of a Gough-Type Parallel Manipulator With Interval Analysis,” Int. J. Robot. Res., 23(3), pp. 221–235. [CrossRef]


Grahic Jump Location
Fig. 1

A generic Gough–Stewart platform




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