Singularity analysis of lower mobility parallel manipulators using Grassmann-Cayley algebra

IEEE Transactions on Robotics

Volumn 25, Issue 5, 2009, Pages 995-1004

  Kanaan, Daniel ^a,b   Wenger, Philippe ^a,c   Caro, Stéphane ^a   Chablat, Damien ^a  

^a CNRS   (France)

^b THALES ALENIA SPACE   (France)

^c ECOLE CENTRALE DE NANTES   (France)

Author keywords

Grassmann Cayley algebra (GCA); Infinite elements; Parallel manipulator; Screw theory; Singularity

Indexed keywords

GRASSMANN-CAYLEY ALGEBRA (GCA); INFINITE ELEMENTS; PARALLEL MANIPULATOR; SCREW THEORY; SINGULARITY;

ALGEBRA; ELECTROSTATIC ACTUATORS;

MANIPULATORS;

EID: 70350221804     PISSN: 15523098     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRO.2009.2017132     Document Type: Article

References (28)

1. J. Angeles, S. Caro, W. Khan, and A. Morozov, "The design and prototyping of an innovative schonflies motion generator," Proc. IMechE Part C, J. Mech. Eng. Sci., vol. 220, no. C7, pp. 935-944, Jul. 2006.
2. J. P. Merlet, "A formal-numerical approach for robust in-workspace singularity detection," IEEE Trans. Robot., vol. 23, no. 3, pp. 393-402, Jun. 2007.
3. J. P. Merlet, "Singular configurations of parallel manipulators and grassmann geometry," Int. J. Robot. Res., vol. 8, no. 5, pp. 45-56, 1989.
4. J. P. Merlet, Parallel Robots, 2nd ed. New York: Springer-Verlag, 2006.
5. F. Hao and J. M. McCarthy, "Conditions for line-based singularities in spatial platform manipulators," J. Robot. Syst., vol. 15, no. 1, pp. 43-55, 1998.
6. P. Ben-Horin and M. Shoham, "Singularity analysis of parallel robots based on Grassmann-Cayley algebra," presented at the Int. Workshop Comput. Kinematics, Cassino, Italy, May 4-6, 2005.
7. P. Ben-Horin and M. Shoham, "Singularity condition of six degree-of freedom three-legged parallel robots based on Grassmann-Cayley algebra," IEEE Trans. Robot., vol. 22, no. 4, pp. 577-590, Aug. 2006.
8. S. A. Joshi and L. W. Tsai, "Jacobian analysis of limited-DOF parallel manipulators," ASME J. Mech. Des., no. 124, pp. 254-258, 2002.
9. E. Staffetti and F. Thomas, "Analysis of rigid body interactions for compliant motion tasks using the Grassmann-Cayley algebra," in Proc. IEEE/RSJ Int. Conf. Intell. Robot. Syst., 2000, pp. 2325-2332.
10. N. White, "Grassmann-Cayley algebra and robotics," J. Intell. Robot. Syst., vol. 11, pp. 91-107, 1994.
11. N. White, "Grassmann-Cayley algebra and robotics applications," in Handbook of Geometric Computing (Part VIII , E. B. Corrochano, Ed. Berlin, Heidelberg: Springer-Verlag, 2005, pp. 629-656.
12. N. White, "The bracket ring of a combinatorial geometry I," Trans. Amer. Math. Soc., vol. 202, pp. 79-95, 1975.
13. N. White, "The bracket of 2-extensors," Congr. Numerantium, vol. 40, pp. 419-428, 1983.
14. T. McMillan, "Invariants of antisymmetric tensors," Ph.D. dissertation, Univ. Florida, Gainesville, FL, 1990.
15. P. Ben-Horin and M. Shoham, "Application of Grassmann-Cayley algebra to geometrical interpretation of parallel robot singularities," Int. J. Robot. Res., vol. 28, no. 1, pp. 127-141, 2009.
16. S. R. S. Ball, Theory of Screws. Cambridge, U.K.: Cambridge Univ. Press, 1900.
17. K. H. Hunt, Kinematic Geometry of Mechanisms. London, U.K.: Oxford Univ. Press, 1978.
18. H. Lipkin and J. Duffy, "The elliptic polarity of screws," ASME J. Mech. Transmiss. Autom. Des., vol. 107, no. 3, pp. 377-387, 1985.
19. T.-S. Zhao, J. S. Dai, and Z. Huang, "Geometric analysis of over-constrained parallel manipulators with three and four degrees of freedom," JSME Int. J. Ser C Mech. Syst., Mach. Elements Manuf., vol. 45, no. 3, pp. 730-740, 2002.
20. H. Pottmann, M. Peternell, and B. Ravani, "An introduction to line geometry with applications," Comput. Aided Des., vol. 31, no. 1, pp. 3-16, 1999.
21. A. Wolf and M. Shoham, "Investigation of parallel manipulators using linear complex approximation," ASME J. Mech. Des., vol. 125, pp. 564-572, 2003.
22. R. Clavel, "DELTA, a fast robot with parallel geometry," in Proc. 18th Int. Symp. Ind. Robots, Lausanne, Switzerland, 1988, pp. 91-100.
23. P. Ben-Horin, M. Shoham, S. Caro, D. Chablat, and Ph. Wenger, "A graphical user interface for the singularity analysis of parallel robots based on Grassmann-Cayley algebra," in Advances in Robot Kinematics New York: Springer-Verlag, 2008, pp. 49-58.
24. R. Di Gregorio and V. Parenti-Castelli, "A translational 3-DOF parallel manipulator," in Advances in Robot Kinematics. Boston, MA: Kluwer, 1998, pp. 49-58.
25. A. Cammarata, J. Angeles, and R. Sinatra, "The dynamics of parallel schönflies motion generators: The case of a two-limb system," in Proc. IMechE Part I, J. Syst. Control Eng., 2009, vol. 223, no. 1, pp. 29-52.
26. D. Kanaan, Ph. Wenger, and D. Chablat, "Workspace analysis of the parallel module of the VERNE machine," Problems Mech., vol. 4, no. 25, pp. 26-42, 2006.
27. D. Kanaan, Ph. Wenger, and D. Chablat, "Singularity analysis of limited-DOF parallel manipulators using Grassmann-Cayley algebra," in Advances in Robot Kinematics. New York: Springer-Verlag, 2008, pp. 59-68.
28. M. Zoppi, L. E. Bruzzone, R. M. Molfino, and R. C. Michelini, "Constraint singularities of force transmission in nonredundant parallel robots with less than six degrees of freedom," ASME J. Mech. Des., vol. 125, pp. 557-563, 2003.