Advances on the simplification of sine-cosine equations

Journal of Symbolic Computation

Volumn 26, Issue 1, 1998, Pages 31-70

  Gutierrez, Jaime ^a   Recio, Tomas ^a  

^a UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032119183     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1998.0200     Document Type: Article

References (36)

1. Alonso, C., Gutierrez, J., Recio, T. (1995a). A rational function decomposition algorithm by near-separated polynomials. J. Symb. Comput., 19, 527-544.
2. Alonso, C., Gutierrez, J., Recio. T. (1995b). An implicitization algorithm with fewer variables. Comput. Aided Geomet. Design, 12, 1-8.
3. Atiyah, M.F., MacDonald, I.G. (1969). Introduction to Commutative Algebra. Addison-Wesley.
4. Becker, E., Neuhaus, R. (1993). Computation of real radicals of polynomials ideals. Proc. of MEGA-92, Computational Algebraic Geometry, Eysette, F., Galligo, A., eds, Progress in Mathematics, 109. Birkhäuser.
5. Bochnak, J., Coste, M., Roy, M-F. (1986). Géometrie Algébrique Réelle. Ergeb. Math. Vol. 12. Springer-Verlag.
6. Buchberger, B. (1989). Applications of Gröbner bases in non-linear computational geometry. Trends in Computer Algebra. Lect. Notes in Computer Science, 296. Springer-Verlag.
7. Canny, J.F., Manocha, D. (1994). Efficient inverse kinematics for general 6R manipulators. IEEE Trans. Robot. Autom. 10-5, 648-657.
8. Craig, J. (1989) Introduction to Robotics Mechanics and Control, 2nd edn. Addison-Wesley.
9. Cox, D., Little, J., O' Shea, D. (1992). Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics, Springer-Verlag.
10. Duffly, J., Lipkin, H. (1985). A vector analysis of robot manipulators. In Beni, G., Hackwood, S.J., eds, Recent Advances in Robotics, pp. 175-242. Wiley.
11. Duval, D. (1990). Calculs avec discussion automatique: descriptions et applications. Publ. du depart. de Mathematiques, Limoges. N. 12.
12. von zur Gathen, J., Weiss, J. (1995). Homogeneus bivariate decompositions. J. Symb. Comput. 19, 409-434.
13. Gonzalez-Lopez, M.J., Recio, T. (1993). The ROMIN inverse geometric model and the dynamic evaluation method. In Cohen, A., ed., Computer Algebra in Industry. Wiley.
14. Gonzalez-Lopez, M.J., Recio, T. (1994). On the symbolic insimplification of the general 6R-manipulator kinematic equations. Proc. ISSAC-94, pp. 354-358. ACM Press.
15. Gonzalez-Lopez, M.J., Recio, T. (1995a). On the reality of inverse kinematic ideals. Contributions to General Algebra, 9, 183-195. Verlag Holder-Pichler-Tempsky, Teubner.
16. Gonzalez-Lopez, M.J., Recio, T. (1995b). Symbolic simplification of kinematic equations. Rigid motion representation and the Stewart platform case. Actas del Congreso Internacional de Teoria de Anillos. Universidad de Almeria. Servicio de Publicaciones.
17. Gonzalez-Vega, L. (1989). La sucesion de Sturm-Habicht y sus aplicaciones al algebra computacional. Thesis. Universidad de Cantabria.
18. Gutierrez, J. (1991). A polynomial decomposition algorithm over factorial domains. C.R. Math. Rep. Acad. Sci. Canada. XIII, 2-3, 81-86.
19. Kovács, P. (1991). Minimum degree solutions for the inverse kinematics problem by application of the Buchberger algorithm. In Stifter, S., Lenarcie, J., eds, Proc. 2nd. Intl. Conf. on Adv. in Robot Kinematics, pp. 326-334. Springer-Verlag.
20. Kovács, P. (1993). Rechnergestützte Symbolische Roboterkinematik. Vieweg Verlag.
21. Kovács, P., Hommel, G. (1990). Factorization and decomposition in kinematic equation systems. Techn. Report 90-23, Inst. für Technische Informatik. Technische Universität Berlin.
22. Kovács, P., Hommel, G. (1992). Simplification of symbolic inverse kinematic transformations through functional decomposition. In Parenti-Castelli, V., Lenarcic, J., eds, Proc. 3rd. Intl. Conf. on Adv. in Robot Kinematics, pp. 88-95. Ferrara.
23. Kovács, P., Hommel, G. (1993a). On the tangent-half-angle substitution. In Angeles, J., et al., eds, Proc. Computational Kinematics, pp. 27-39. Kluwer.
24. Kovács, P., Hommel, G. (1993b). Fast functional decomposition of Sine-Cosine-Polynomials. Proc. IEEE Robotics and Automation. Atlanta.
25. Lee, H-Y., Liang, C-G. (1988a). A new vector theory for the analysis of spatial mechanisms. Mechanisms and Machine Theory 23-3, 209-217.
26. Lee, H-Y., Liang, C-G. (1988b). Displacement analysis of the general spatial 7-link 7R. Mechanisms and Machine Theory 23-3, 219-226.
27. Licciardi, S., Mora, T. (1994). Implicitization of hypersurfaces and curves by the Primbasissatz and basis conversion. Proc. ISSAC-94, pp. 191-196. ACM Press.
28. Loos, R. (1982). Computing in algebraic extensions. In Buchberger, B., Collins, G., Loos, R., eds, Computer Algebra and Algebraic Computation, Computing. Supplementum 4, pp. 115-138. Springer-Verlag.
29. Merlet, J.P., Lazard, D. (1994). The (true) Stewart plataform has 12 configurations. Proc. IEEE Conference on Robotics-92.
30. Mourrain, M. (1994). Enumeration problems in geometry, robotics and vision. In González Vega, L., Recio, T., eds, Proc. MEGA-94. Algorithms in Algebraic Geometry and Applications. Progress in Mathematics, 143. Birkhäuser.
31. Pieper, D., Roth, B. (1969). The kinematics of manipulators under computer control. Proc. of 2nd. Intl. Congress on Theory of Machines and Mechanisms. Vol. 2, pp. 159-169. Zakopane, Poland.
32. Raghavan, M., Roth, B. (1989). Kinematic Analysis of the 6R Manipulator of General Geometry. Proc. Intl. Symposium on Robotic Research, Tokyo, pp. 314-320.
33. Recio, T. (1994). Simplification of SC-equations. Abstracts of 2nd Workshop on Planning Robot Motion PROMOTION, L'Escala (Spain).
34. Smith, D., Lipkin, H. (1990). A summary of the Theory and Applications of the conics method in robot kinematics. Proc. 2nd. Intl. Conf. on Adv. in Robot Kinematics. Linz pp. 81-88. Springer-Verlag.
35. th powers of polynomials. Proc. ISSAC-76, pp. 351-355. ACM Press.
36. Zippel, R. (1993). Effective Polynomial Computation. Kluwer Academic Press.