Geometric characterization and parametric representation of the singularity manifold of a 6-6 Stewart platform manipulator

Mechanism and Machine Theory

Volumn 41, Issue 11, 2006, Pages 1377-1400

  Bandyopadhyay, Sandipan ^a   Ghosal, Ashitava ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; HAND TOOLS; INDUSTRIAL APPLICATIONS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; RESEARCH AND DEVELOPMENT MANAGEMENT;

EXPLICIT PARAMETERIZATION; GEOMETRIC CHARACTERIZATION; PARAMETRIC REPRESENTATION; TRIGONOMETRIC FUNCTIONS;

AUTOMOBILE ENGINE MANIFOLDS;

EID: 33746676211     PISSN: 0094114X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmachtheory.2005.12.006     Document Type: Article

References (24)

1. Basu D., and Ghosal A. Singularity analysis of platform-type multi-loop spatial mechanisms. Mechanism and Machine Theory 32 (1997) 375-389
2. J.S. Cohen, Computer Algebra and Symbolic Computation: Mathematical Methods, AK Peters, Natick, 2002.
3. Cox D., Little J., and O'Shea D. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (1991), Springer-Verlag, New York
4. Fichter E.F. A Stewart platform-based manipulator: general theory and practical construction. International Journal of Robotics Research 5 2 (1986) 157-182
5. Geddes K.O., Czapor S.R., and Labahn G. Algorithms for Computer Algebra (1992), Kluwer Academic Publishers, Boston
6. Gosselin C., and Angeles J. Singularity analysis of closed loop kinematic chains. IEEE Transactions on Robotics and Automation 6 3 (1990) 281-290
7. Gregorio R.D. Analytic formulation of the 6-3 fully-parallel manipulator's singularity determination. Robotica 19 (2001) 663-667
8. R.D. Gregorio, Statics and singularity loci of the 3-UPU wrist, in: 2001 IEEE/ASME International Conference on Advanced Intelligent Mechatronics Proceedings, Italy, 2001, pp. 470-475.
9. Gregorio R.D. Singularity-locus expression of a class of parallel mechanisms. Robotica 20 (2002) 323-328
10. Herstein I.N. Topics in Algebra (1975), John Wiley & Sons, New York
11. Hunt K.H. Kinematic Geometry of Mechanism (1978), Clarendon Press, Oxford
12. Kim D., and Chung W. Analytic singularity equation and analysis of six-dof parallel manipulators using local structurization method. IEEE Transactions on Robotics and Automation 15 4 (1999) 612-622
13. H. Li, C. Gosselin, M.J. Richard, B.M. St-Onge, Analytic form of the six-dimensional singularity locus of the general Gough-Stewart platform, in: Proceedings of ASME 28th Biennial Mechanisms and Robotics Conference, Salt Lake City, Utah, USA, 2004.
14. O. Ma, J. Angeles, Architectural singularities of platform manipulators, in: Proceedings of International Conference on Robotics and Automation, 1991, pp. 1542-1547.
15. McCarthy J.M. Geometric Design of Linkages (2002), Springer, New York
16. Merlet J.-P. Singularity configurations of parallel manipulators and Grassman geometry. International Journal of Robotics Research 8 (1989) 45-56
17. Merlet J.-P. Parallel Robots (2001), Kluwer Academic Press, Dordrecht
18. Miscehnko A., and Fomenko A. A Course of Differential Geometry and Topology (1988), Mir Publishers, Moscow
19. Murray R.M., Li Z., and Sastry S.S. A Mathematical Introduction to Robotic Manipulation (1994), CRC Press, Boca Raton
20. Press W.H., Teukolsky S.A., Vetterling W., and Flannery B.P. Numerical Recipies in C++: The Art of Scientific Computing (2002), Cambridge University Press, Cambridge
21. Sefrioui J., and Gosselin C.M. On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators. Mechanism and Machine Theory 30 (1995) 533-551
22. St-Onge B.M., and Gosselin C. Singularity analysis and representation of spatial six-dof parallel manipulators. Recent Advances in Robot Kinematics (1996) 389-398
23. St-Onge B.M., and Gosselin C. Singularity analysis and representation of the general Gough-Stewart platform. International Journal of Robotics Research 19 3 (2000) 271-288
24. Wolfram S. The Mathematica Book (2004), Cambridge University Press, Cambridge