Numerical continuation methods for solving polynomial systems arising in kinematics

Journal of Mechanical Design, Transactions of the ASME

Volumn 112, Issue 1, 1990, Pages 59-68

  Wampler, C W ^a   Morgan, A P ^a   Sommese, A J ^b  

^a GM Research Lab   (United States)

^b UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84988473168     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2912579     Document Type: Article

References (23)

1. Allgower, E. L., 1981, “A Survey of Homotopy Methods for Smooth Mappings,” Numerical Solution of Nonlinear Equations, E. L. Allgower, K. Glash off, and H.-O. Peitgen, eds., Lecture Notes in Mathematics No. 878, SpringerVerlag, New York.
2. Allgower, E. L., and Georg, K., 1980, “Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations,” SIAM Rev., Vol. 22, pp. 28-85.
3. Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland, New York.
4. Duffy, J., and Crane, C., 1980, “A Displacement Analysis of the General 7R Spatial Mechanism,” Mechanism and Machine Theory, Vol. 15, pp. 153-169. '
5. Forsythe, G. E., Malcolm, M. A., and Moler, C. B., 1977, Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs, NJ.
6. Garcia, C. B., and Zangwill, W. I., 1981, Pathways to Solutions, Fixed Points, and Equilibria, Prentice-Hall, Englewood Cliffs, NJ.
7. Lee, H.-Y., and Liang, C.-G., 1988, “Displacement Analysis of the General 7-Link 7R Mechanism,” Mechanism and Machine Theory, Vol. 21, pp. 219-226.
8. Li, T. Y., Sauer, T., and Yorke, J. A., 1988, “Numerically Determining Solutions of Systems of Polynomial Equations,” Bull. Amer. Math. Soc., Vol. 18, pp. 173-177.
9. Morgan, A. P., 1986, “A Transformation to Avoid Solutions at Infinity for Polynomial Systems,” Appl. Math. Comput., Vol. 18, pp. 77-86.
10. Morgan, A. P., 1987, Solving Polynomial Systems Using Continuation for Scientific and Engineering Problems, Prentice-Hall, Englewood Cliffs, NJ.
11. Morgan, A. P., and Sommese, A. J., 1987a, “A Homotopy for Solving General Polynomial Systems that Respects Af-homogeneous Structures,” Appl. Math. Comput., Vol. 24, pp. 101-113.
12. Morgan, A. P., and Sommese, A. J. 1987b, “Computing All Solutions to Polynomial Systems Using Homotopy Continuation,” Appl. Math. Comput., Vol. 24, pp. 115-138.
13. Morgan, A. P., and Sommese, A. J., 1989, “Coefficient Parameter Polynomial Continuation,” Appl. Math. Comput., Vol. 29, pp. 123-160.
14. Primrose, E. J. F., 1986, “On the Input-Output Equation of the General 7R Mechanism,” Mechanism and Machine Theory, Vol. 21, pp. 509-510.
15. Raghavan, M., and Roth, B., 1989, “Kinematic Analysis of the 6R Manipulator of General Geometry,” preprint.
16. Rheinboldt, W. C., 1986, Numerical Analysis of Parameterized Nonlinear Equations, John Wiley & Sons, New York.
17. Roth, B., 1967, “The Kinematics of Motion through Finitely Separated Positions,” ASME Journal of Applied Mechanics Vol. 34E-3, pp. 591-598.
18. Roth, B., and Freudenstein, F., 1963a, “Synthesis of Path-Generating Mechanisms by Numerical Methods,” ASME Journal of Engineering for Industry, Vol. 85B-3, pp. 298-306.
19. Roth, B., and Freudenstein, F., 1963b, “Numerical Solution of Systems of Nonlinear Equations,” J. Assoc. Computing Machinery, Vol. 10, pp. 550-556.
20. Tsai, L.-W., and Morgan, A. P., 1985, “Solving the Kinematics of the Most General Six-and Five-Degree-of-Freedom Manipulators by Continuation Methods,” ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 107, pp. 189-200.
21. Wampler, C. W., and Morgan, A. P., 1989, “Solving the 6R Inverse Position Problem Using a Generic-Case Solution Methodology,” General Motors Research Publication GMR-6702, Warren, MI.
22. Watson, L. T., Billups, S. C., and Morgan, A. P., 1987, “HOMPACK: A Suite of Codes for Globally Convergent Homotopy Algorithms,” ACM Trans. Math. Software, Vol. 13, pp. 281-310.
23. van der Waerden, B. L., 1970, Algebra, Vols. 1, 2, Translated by F. Blum and J. Schulenberger, Frederick Ungar Pub. Co., New York.