A spherical wrist of the serial type with n revolute (R) joints is said to be isotropic if it can attain a posture whereby the singular values of its Jacobian matrix are all equal to What isotropy brings about is robustness to manufacturing, assembly, and measurement errors, thereby guaranteeing a maximum orientation accuracy. In this paper we investigate the existence of redundant isotropic architectures, which should add to the dexterity of the wrist under design by virtue of its extra degree of freedom. The problem formulation, for leads to a system of eight quadratic equations with eight unknowns. The Bezout number of this system is thus its BKK bound being 192. However, the actual number of solutions is shown to be 32. We list all solutions of the foregoing algebraic problem. All these solutions are real, but distinct solutions do not necessarily lead to distinct manipulators. Upon discarding those algebraic solutions that yield no new wrists, we end up with exactly eight distinct architectures, the eight corresponding manipulators being displayed at their isotropic postures.
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June 2003
Technical Papers
The Computation of All 4R Serial Spherical Wrists With an Isotropic Architecture
Damien Chablat,
Damien Chablat
Institut de Recherche en Communications et Ecole Centrale de Nantes, Universite´ de Nantes, 44321 Nantes, France
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Jorge Angeles
Jorge Angeles
Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, Montreal, Canada H3A 2K6
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Damien Chablat
Institut de Recherche en Communications et Ecole Centrale de Nantes, Universite´ de Nantes, 44321 Nantes, France
Jorge Angeles
Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, Montreal, Canada H3A 2K6
Contributed by the Mechanisms Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 2001. Associate Editor: G. S. Chirikjian.
J. Mech. Des. Jun 2003, 125(2): 275-280 (6 pages)
Published Online: June 11, 2003
Article history
Received:
September 1, 2001
Online:
June 11, 2003
Citation
Chablat, D., and Angeles, J. (June 11, 2003). "The Computation of All 4R Serial Spherical Wrists With an Isotropic Architecture ." ASME. J. Mech. Des. June 2003; 125(2): 275–280. https://doi.org/10.1115/1.1561041
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