Abstract
A new geometric decomposition is introduced that diagonalizes the 6 × 6 stiffness and compliance matrices which model robot elasticity. Using screw theory, a congruence transformation is developed from the three orthogonal wrench-compliant axes and the three orthogonal twist-compliant axes. The diagonal elements are the stationary values of linear and rotational compliance and stiffness. This generalizes and is analogous to principal axes and principal values for stress, strain, and rotational inertia. It is proved that the decomposition always exists for both the nonsingular and singular cases.
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References
Ball, R. S., 1900, A Treatise on the Theory of Screws. Cambridge at the University Press.
Bunse-Gerstner, A., 1984, “An Algorithm for the Symmetric Generalized Eigenvalue Problem,” Linear Algebra and Its Applications, Vol. 58, pp. 43–68.
Dimentberg, F. M., 1965, “The Screw Calculus and its Applications in Mechanics.” Foreign Technology Division, Wright-Patterson Air Force Base, Ohio. Document No. FTD-HT-23-1632-67.
Griffis, M. and Duffy, J., 1990, “Kinestatic Control: A Novel Theory for Simultaneously Regulating Force and Displacement,” 21st ASME Mechanisms Conference and ASME Journal of Mechanical Design
Joh, J. and Lipkin, H., 1991, “A Unified Framework for Analysis of Cooperating Robotic Mechanisms,” 8th World Congress on the Theory of Machines and Mechanisms, Prague, August.
Lipkin, H. and Patterson, T., 1992, “Center-of-Elasticity,” 18th NSF Design and Manufacturing Systems Conference, Atlanta, January 8–10.
Loncaric, J., 1985, Geometrical Analysis of Compliant Mechanisms in Robotics. Ph.D. Dissertation. Harvard University.
Patterson, T. and Lipkin, H., 1990A, “Structure of Manipulator Compliance Matrices,” 21st ASME Mechanisms Conference, Chicago and ASME Journal of Mechanical Design (To appear)
Patterson, T. and Lipkin, H., 1990B, “A Classification of Manipulator Compliance Matrices,” 21st ASME Mechanisms Conference, Chicago ASME Journal of Mechanical Design (To appear).
Patterson, T. and Lipkin, H., 1991, “Duality of Constrained Elastic Manipulation,” IEEE Conference on Robotics and Automation, and Journal of Laboratory Robotics and Automation (To appear).
West, H., 1985, “Kinematic Analysis for the Design and Control of Braced Manipulators,” Ph.D. Dissertation, Massachusetts Institute of Technology.
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© 1993 Springer-Verlag London Limited
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Lipkin, H., Patterson, T. (1993). Geometrical decomposition of robot elasticity. In: Morecki, A., Bianchi, G., Jaworek, K. (eds) RoManSy 9. Lecture Notes in Control and Information Sciences, vol 187. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031436
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DOI: https://doi.org/10.1007/BFb0031436
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