Synthesis on forward kinematics problem algebraic modeling for the planar parallel manipulator: Displacement-based equation systems

Advanced Robotics

Volumn 20, Issue 9, 2006, Pages 1035-1065

  Rolland, L U C ^a  

^a UNIVERSITY OF CENTRAL LANCASHIRE   (United Kingdom)

Author keywords

Certified results; Displacement based models; Exact algebraic method; Forward kinematics; Parallel planar manipulator; Real root isolation

Indexed keywords

ALGEBRA; COMPUTATIONAL GEOMETRY; KINEMATICS; MATHEMATICAL MODELS; POLYNOMIALS; PROBLEM SOLVING;

CERTIFIED RESULTS; DISPLACEMENT BASED MODELS; EXACT ALGEBRAIC METHODS; FORWARD KINEMATIC PROBLEMS (FKP); PARALLEL PLANAR MANIPULATORS; REAL ROOT ISOLATION;

MANIPULATORS;

EID: 33750174384     PISSN: 01691864     EISSN: None     Source Type: Journal    
DOI: 10.1163/156855306778394003     Document Type: Article

References (24)

1. D. Stewart, A platform with 6 degrees of freedom, Proc. IMechE 180, 371-386 (1965).
2. J. P. Merlet, Les Robots Parallèles, Herm̀s, Paris (1997).
3. C. Gosselin and J.-P. Merlet, The direct kinematics of planar parallel manipulators: special architectures and number of solutions, J. Mech. Machine Theory 29, 1083-1097 (1994).
4. E. J. F. Primrose and F. Freudenstein, Spatial motions, part 1: point paths of mechnisms with four or fewer links, ASME J. Eng. Ind. 91, 103-114 (1969).
5. K. H. Hunt, Structural kinematics of in-parallel-actuated robot-arms, J. Mech. Transmiss. Automat. Des. 105, 705-712 (1983).
6. C. Gosselin and J. Angeles, The optimum kinematic design of a planar three-dof parallel manipulator, J. Mech. Transmiss. Automat. Des. 110, 35-41 (1988).
7. L. Rolland, Outils algébriques pour la résolution de problèmes géométriques et l'analyse de trajectoire de robots parallèles prévus pour des applications à haute cadence et grande précision, PhD thesis, Université Henri Poincaré, Nancy (2003).
8. L. Rolland, Certified solving of the forward kinematics problem with an exact method for the general parallel manipulator, Adv. Robotics 19, 995-1025 (2005).
9. J. P. Merlet, Parallel manipulators: state of the art and perspectives, J. Adv. Robotics 8, 589-596 (1994).
10. M. Raghavan and B. Roth, Solving polynomial systems for the kinematic analysis and synthesis of mechanisms and robot manipulators, Trans. ASME 117, 71-79 (1995).
11. R. Parrish, E. Dieudonné and R. Bardusch, An actuator extension transormation for a motion simulator and an inverse transformation applying newton-raphson's method, Technical report D-7067, NASA, Washington, DC (1972).
12. D. Lazard, Solving zero-dimensional algebraic systems, J. Symbolic Comput. 13, 117-131 (1992).
13. M. Griffis and J. Duffy, A forward displacement analysis of a class of stewart platform, J. Robotic Syst. 6, 703-720 (1989).
14. C. Innocenti and V. Parenti-Castelli, Direct position analysis of the stewart platform mechanism, IFTOMM Mech. Machine Theory 25, 611-621 (1990).
15. K. Waldron, P. Nanua and V. Murthy, Direct kinematic solution of a stewart platform, IEEE Trans. Robotics Automat. 6, 438-444 (1991).
16. M. Petitot, O. Didrit and E. Walter, Guaranteed solution od direct kinematics problems for general configurations of parallel manipulators, IEEE Trans. Robotics Automat. 14, 259-265 (1998).
17. J. Little, D. Cox and D. O'Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer, New York, NY (1992).
18. S. Czapor, K. Geddes and G. Labahn, Algorithms for Computer Algebra, Kluwer, Dordrecht (1994).
19. G. E. Collins, B. Buchberger and R. Loos, Computer Algebra Symbolic and Algebraic Computation. Springer, Berlin (1982).
20. B. Buchberger, Gröbner bases: an algorithmic method in polynomial ideal theory, in: Recent Trends in Multidimensional Systems Theory, N. K. Bose (Ed.). Reidel, Dordrecht (1985).
21. J.-C. Faugère, A new efficient algorithm for computing gröbner bases (f4), J. Pure Appl. Algebra 139, 61-88 (1999).
22. F. Rouillier, Solving zero-dimensional systems through the rational univariate representation, J. Appl. Algebra Eng. Commun. Comput. 9, 433-461 (1999).
23. F. Rouillier and P. Zimmermann, Efficient isolation of a polynomial real roots, Technical report RR-4113, INRIA (2001).
24. D. Lazard, Stewart platforms and gröbner basis, in: Proc. of Advances in Robotics Kinematics, Ferrara, pp. 136-142 (1992).