Publication
A distance geometry approach to the singularity analysis of 3R robots
Journal Article (2015)
Journal
Journal of Mechanisms and Robotics
Pages
1-11
Volume
8
Number
1
Doc link
http://dx.doi.org/10.1115/1.4029500
File
Authors
Abstract
This paper shows how the computation of the singularity locus of a 3R robot can be reduced to the analysis of the relative position of two coplanar ellipses. Since the relative position of two conics is a projective invariant, and the basic projective geometric invariants are determinants, it is not surprising that, using Distance Geometry, the computation of the singularity locus of a 3R robot can be fully expressed in terms of determinants. Geometric invariants have the benefit of simplifying symbolic manipulations. This paper shows how their use leads to a simpler characterization, compared to previous approaches, of the cusps and nodes in the singularity loci of 3R robots.
Categories
automation.
Author keywords
wrist-partitioned robots, 3R robots, cuspidal robots, singularities, cusps, nodes, distance geometry, coordinate-free formulations
Scientific reference
F. Thomas. A distance geometry approach to the singularity analysis of 3R robots. Journal of Mechanisms and Robotics, 8(1): 1-11, 2015.
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