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.
A Distance Geometry Approach to the Singularity Analysis of 3R Robots
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 23, 2014; final manuscript received December 23, 2014; published online August 18, 2015. Assoc. Editor: Yuefa Fang.
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Thomas, F. (August 18, 2015). "A Distance Geometry Approach to the Singularity Analysis of 3R Robots." ASME. J. Mechanisms Robotics. February 2016; 8(1): 011001. https://doi.org/10.1115/1.4029500
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