Investigation of parallel manipulators using linear complex approximation

Journal of Mechanical Design

Volumn 125, Issue 3, 2003, Pages 564-572

  Wolf, A ^a   Shoham, M ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; DEGREES OF FREEDOM (MECHANICS); KINEMATICS; MATHEMATICAL MODELS; MATRIX ALGEBRA; SCREWS;

LINEAR COMPLEX APPROXIMATION; PARALLEL MANIPULATORS;

MANIPULATORS;

EID: 0141842688     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1582876     Document Type: Article

References (37)

1. Merlet, J. P., 1992, "Singular Configurations of Parallel Manipulators and Grassman Geometry," Int. J. Robot. Res., 8(5), pp. 45-56.
2. Hunt, K. H., 1983, "Structural Kinematics of In-Parallel-Actuated Robot Arms," ASME J. Mech. Des., 105(4), pp. 705-712.
3. St-Onge, B. M., and Gosselin, C. M., 2000, "Singularity Analysis and Representation of the General Gaugh-Stewart Platform," Int. J. Robot. Res., 19(3), pp. 271-288.
4. Dasgupta, B., and Mruthyunjaya, T. S., 1998, "Singularity-Free Path Planning for the Stewart Platform Manipulator," Mech. Mach. Theory, 33(6), pp. 711-725.
5. Gosselin, C., and Angeles, J., 1990, "Singularity Analysis of Closed-Loop Kinematic Chains," IEEE Trans. Rob. Autom., 6(3), pp. 281-290.
6. Zlatanov, D., Fenton, R. G., and Benhabib, B., 1994, "Singularity Analysis of Mechanisms and Robots via a Motion-Space Model of the Instaneous Kinematics," Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 2, pp. 980-991.
7. Ma, O., and Angeles, J., 1992, "Architecture Singularities of Parallel Manipulators," Int. J. Robot. Res., 7(1), pp. 23-29.
8. Mohammadi Daniali, H. R., Zsomobor-Murray, P. J., and Angeles, J., 1955, "The Isotropic Design of Two General Classes of Planar Parallel Manipulators," J. Rob. Syst., 12(2), pp. 795-805.
9. Zlatanov, D., Fenton, R. G., and Benhabib, B., 1995, "A Unifying Framework for Classification and Interpretation of Mechanisms Singularities," ASME J. Mech. Des., 117, pp. 566-572.
10. Mayer St-Onge, B., and Gosselin, C. M., 1996, "Singularity Analysis and Representation of Spatial Six-Degree of Freedom Parallel Manipulator," Advances in Robot Kinematics (ARK), J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 389-398.
11. Sefroui, J., and Gosselin, C. M., 1995, "On the Quadratic Nature of the Singularity Curves of Planar Three-Degree-of-Freedom Parallel Manipulators," Mech. Mach. Theory, 30(4), pp. 533-551.
12. Collins, C. L., and McCarthy, J. M., 1998, "The Quartic Singularity Surface of Planar Platforms in the Clifford Algebra of the Projective Plane," Mech. Mach. Theory, 33(7), pp. 931-944.
13. Feng-Cheng, Y., and Haug, E. J., 1994, "Numerical Analysis of the Kinematic Working Capability of Mechanisms," ASME J. Mech. Des., 116, pp. 111-117.
14. Funabashi, H., and Takeda, Y., 1995, "Determination of Singular Points and Their Vicinity in Parallel Manipulators Based on the Transmission Index," Ninth World Congress on the Theory of Machines and Mechanisms, pp. 1977-1981.
15. Karger, A., and Husty, M., 1996, "On Self-Motion of a Class of Parallel Manipulators," Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 339-348.
16. Karger, A., 1998, "Architecture Singular Parallel Manipulators," Advanced in Robot Kinematics: Analysis and Control, J. Lenarcic and M. L. Husty, eds., Kluwer Academic Publisher, pp. 445-454.
17. Merlet, J. P., 1989, "Parallel Manipulators Part 2: Theory, Singular Configurations and Grassmann Geometry," Rapport de Recherche INRIA No 791, F'evrier.
18. Merlet, J. P., 1992, "On the Infinitesimal Motion of a Parallel Manipulator in Singular Configurations," IEEE Int. Conf. on Robotics and Automation, pp. 320-325, Nice, France.
19. Fichter, E. F., 1986, "A Stewart Platform-Based Manipulator: General Theory and Practical Construction," Int. J. Robot. Res., 5(2), pp. 155-182.
20. Collins, C. L., and Long, G. L., 1995, "The Singularity Analysis of an In-Parallel Hand Controller for Force-Reflected Teleoperation," IEEE Trans. Rob. Autom., 11(5), pp. 661-669.
21. Dandurand, A., 1984, "The Rigidity of Compound Spatial Grid," Structural Topology, 10, pp. 41-55.
22. Ben Horin, R., 1997, "Criteria for Analysis of Parallel Robots," Doctoral Dissertation, Technion-Israeli Institute of Technology.
23. Simaan, N., and Shoham, M., 2001, "Singularity Analysis of a Class of Composite Serial In-Parallel Robots," IEEE Trans. Rob. Autom., 17(3), pp.301-311.
24. Hao, F., and McCarthy, J. M., 1998, "Conditions for Line-Based Singularities in Spatial Platform Manipulators," J. Rob. Syst., 15(1), pp. 43-55.
25. Hunt, K. H., 1978, "Kinematic Geometry of Mechanisms," Department of Mechanical Engineering, Monash University, Clayton, Victoria, Australia.
26. Pottmann, H., Peternell, M., and Ravani, B., 1999, "An Introduction to Line Geometry With Applications," Comput.-Aided Des., 31, pp. 3-16.
27. Klein, F., 1871, "Uber Liniengeometrie und Metrische Geometrie," Mathematische Annalen, pp. 257-303.
28. Ball, R. S., 1990, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge.
29. Ciblak, N., and Lipkin, H., 1999, "Synthesis of Cartesian Stiffness for Robotic Applications," Proceedings of the 1999 IEEE International Conference on Robotics and Automation, Detroit, Michigan., pp. 2147-2152.
30. Tsai, L.-W., and Joshi, S., 2000, "Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator," ASME J. Mech. Des., 122(4), pp. 439-446.
31. Tsai, L.-W., 1996, "Kinematics of a Three-DOF Platform With Three Extensible Limbs," Advances in Robot Kinematics (ARK), J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 401-410.
32. Di Gregorio, R., and Parenti-Castelli, V., 2002, "Mobility Analysis of the 3-UPU Parallel Mechanism Assembled in a Pure Translational Motion," ASME J. Mech. Des., 124, pp. 259-264.
33. Tsai, L.-W., 1998, "The Jacobian Analysis of a Parallel Manipulator Using Reciprocal Screws," Advances in Robot Kinematics (ARK): Analysis and Control, Lenarcic, J., and Husty, M. L., eds., Kluwer Academic Publishers, pp. 327-336.
34. Parenti-Castelli, V., Di Gregorio, R., and Bubani, F., 2000, "Workspace and Optimal Design of a Pure Translation Parallel Manipulator," Meccanica 35, pp. 203-214; (anche presentato al 14th Italian Congress on Theoretical and Applied Mechanics AIMETA, Como, Italy, October 6-9, 1999).
35. Sommerville, D. M. Y., 1934, Analytical Geometry of Three Dimensions, Cambridge University press.
36. Bonev, I., and Zlatanov, D., 2001, "The Mystery of the Singular SNU Translational Parallel Robot," http://www.parallemic.org/Reviews/Review004.html.
37. Zlatanov, D., Bonev, I., and Gosselin, C., 2001, "Constraint Singularities as Configuration Space Singularities," http://www.parallemic.org/Reviews/Review008.html.