Generalized Stewart-Gough platforms and their direct kinematics

IEEE Transactions on Robotics

Volumn 21, Issue 2, 2005, Pages 141-151

  Gao, Xiao Shan ^a   Lei, Deli ^a   Liao, Qizheng ^b   Zhang, Gui Fang ^c  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^c TSINGHUA UNIVERSITY   (China)

Author keywords

Closed form solution; Decoupled mechanisms; Direct kinematics; Generalized Stewart Gough platform (GSP); Parallel manipulator

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; GEOMETRY; KINEMATICS; LINEAR EQUATIONS; MATRIX ALGEBRA; POLYNOMIALS; THEOREM PROVING; VECTORS;

CLOSED FORM SOLUTION; DECOUPLED MECHANISMS; DIRECT KINEMATICS; GENERALIZED STEWART-GOUGH PLATFORMS (GSP); PARALLEL MANIPULATOR;

MANIPULATORS;

EID: 18144396562     PISSN: 15523098     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRO.2004.835456     Document Type: Article

References (27)

1. F. Artigue, M. Y. Amirat, and J. Pontnau, "Isoelastic behavior of parallel robots," Robotica, vol. 7, pp. 323-325, 1989.
2. L. Baron and J. Angles, "The direct kinematics of parallel manipulators under joint-sensor redundancy," IEEE Trans. Robot. Autom., vol. 16, pp. 12-19, Feb. 2000.
3. I. A. Bonev, J. Ryu, S. G. Kim, and S. K. Lee, "A closed-form solution to the direct kinematics of nearly general parallel manipulators with optimally located three linear extra sensors," IEEE Trans. Robot. Autom., vol. 17, pp. 148-156, Apr. 2001.
4. E. M. Dafaoui. Y. Amirat, F. Pontnau, and C. Francois, "Analysis and design of a six-DOF parallel manipulator: Modeling, singular configurations and workspace," IEEE Trans. Robot. Autom., vol. 14, pp. 78-91, Feb. 1998.
5. B. Dasgupta and T. S. Mruthyunjaya, "The Stewart platform manipulator: A review," Mech. Machine Theory, vol. 35, pp. 15-40, 2000.
6. P. Dietmaier, "The Stewart-Gough platform of general geometry can have 40 real postures," in Advances in Robot Kinematics: Analysis and Control, J. Lenarcic and M. L. Hust, Eds. Norwell, MA: Kluwer, 1998, pp. 7-16.
7. J. C. Faugere and D. Lazard, "Combinatorial classes of parallel manipulators," Mech. Machine Theory, vol. 30, no. 6, pp. 765-776, 1995.
8. W. Fulton, Intersection Theory. Berlin, Germany: Springer-Verlag, 1984.
9. X. S. Gao, X. R. Hou, J. Tang, and H. Cheng, "Complete solution classification for the perspective-three-point problem," IEEE Trans. Pattern Anal. Machine Intell., vol. 25, no. 8, pp. 930-943, Aug. 2003.
10. X. S. Gao and G. Zhang, "Geometric constraint solving via c-tree decomposition," in Proceedings of ACM Solid Modeling Conference. Seattle, WA: ACM Press, 2003, pp. 45-55.
11. X. S. Gao, D. Lei, Q. Liao, and G. Zhang. (2003) Generalized Stewart platforms and their direct kinematics. MM Preprints [Online], vol (22), pp. 64-85. Available: http://www.mmrcass.ac.cn/xgao/publ.html
12. V. E. Gough, "Automobile stability, control, and tyre performance," Automobile Div., Inst. Mech. Eng., 1956.
13. K. H. Hunt, "Structural kinematics of in parallel actuated robot arms," J. Mechan., Transmission Autom. Design, vol. 105, pp. 705-712, 1983.
14. M. L. Husty, "An algorithm for solving the direct kinematics of general Stewart-Gough platforms," Mech. Machine Theory, vol. 31, no. 4, pp. 365-379, 1996.
15. D. Lazard, "Generalized Stewart platform: How to compute with rigid motions?," in Proc. IMACS ACA, Lille, France, Jun. 1993, pp. 85-88.
16. J. P. Merlet, Parallel Robots. Dordrecht, The Netherlands: Kluwer, 2000.
17. B. Mishra, Algorithmic Algebra. Berlin, Germany: Springer, 1993, pp. 297-381.
18. B. Mourrain, "The 40 generic positions of a parallel robot," in Proc. ISSAC, M. Bronstein, Ed., 1993, pp. 173-182.
19. B. Mourrain, "Enumeration problems in geometry, robotics and vision," in Algorithms in Algebraic Geometry and Applications, L. Gonzalez and T. Recio, Eds. Cambridge, MA: Birkhäuser, 1996, vol. 143, pp. 285-306.
20. G. Pritschow, C. Eppler, and W.-D. Lehner, "Highly dynamic drives for parallel kinematic machines with constant arm length," in Proc. 1st Int. Colloq., Collaborative Res. Center, vol. 562, Braunschweig, Germany, 2002, pp. 199-211.
21. M. Raghavan, "The Stewart platform of general geometry has 40 configurations," ASME J. Mech. Design, vol. 115, pp. 277-282, 1993.
22. F. Ronga and T. Vust, "Stewart platforms without computer?," in Proc. Int. Conf. Real Analytic and Algebraic Geom.. New York: Walter de Gruyter, 1995, pp. 196-212.
23. D. Stewart, "A platform with six degrees of freedom," Proc. Inst. Mech. Eng., vol. 180, no. 1, pp. 371-386, 1965.
24. F. Wen and C. G. Liang, "Displacement analysis of the 6-6 Stewart platform mechanism," Mech. Machine Theory, vol. 29, no. 4, pp. 547-557, 1994.
25. W. T. Wu, Basic Principles of Mechanical Theorem Proving in Geometries. Berlin, Germany: Springer, 1995.
26. C. Zhang and S. M. Song, "Forward position analysis of nearly general Stewart platforms," ASME J. Mech. Des., vol. 116, pp. 54-60, 1994.
27. H. Zhang, "Self-calibration of parallel mechanisms: A case study on Stewart platform," IEEE Trans. Robot. Autom., vol. 13, no. 3, pp. 387-397, Jun. 1997.