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.
Skip Nav Destination
Article navigation
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
Search for other works by this author on:
Jorge Angeles
Jorge Angeles
Department of Mechanical Engineering & Centre for Intelligent Machines, McGill University, Montreal, Canada H3A 2K6
Search for other works by this author on:
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
Download citation file:
Get Email Alerts
Related Articles
A Temperature-based Controller for a Shape Memory Alloy Actuator
J. Vib. Acoust (June,2005)
Determination of Singularity-Free Zones in the Workspace of Planar 3 - P ̱ RR Parallel Mechanisms
J. Mech. Des (June,2007)
Singularity Equations of Gough–Stewart Platforms Using a Minimal Set of Geometric Parameters
J. Mech. Des (November,2008)
A Locking Compliant Device Inspired by the Anatomy of the Spine
J. Mech. Des (January,2009)
Related Proceedings Papers
Related Chapters
Feedback-Aided Minimum Joint Motion
Robot Manipulator Redundancy Resolution
Fault-Tolerant Control of Sensors and Actuators Applied to Wind Energy Systems
Electrical and Mechanical Fault Diagnosis in Wind Energy Conversion Systems
Out-Of-Order Matrix Processor: Implementation and Performance Evaluation
International Conference on Advanced Computer Theory and Engineering (ICACTE 2009)