We report some recent advances in kinematics and singularity analysis of the mirrorsymmetric N-UU parallel wrists using symmetric space theory. We show that both the finite displacement and infinitesimal singularity kinematics of a N-UU wrist are governed by the mirror symmetry property and half-angle property of the underlying motion manifold, which is a symmetric submanifold of the special Euclidean group SE(3). Our result is stronger than and may be considered a closure of Hunt's argument for instantaneous mirror symmetry in his pioneering exposition of constant velocity shaft couplings. Moreover, we show that the wrist can, to some extent, be treated as a spherical mechanism, even though dependent translation exists, and the singularity-free workspace of a N-UU wrist may be analytically derived. This leads to a straightforward optimal design for maximal singularity-free workspace.

Wu, Y., Carricato, M. (2017). Synthesis and singularity analysis of N-UU parallel wrists: A symmetric space approach. JOURNAL OF MECHANISMS AND ROBOTICS, 9(5), 1-11 [10.1115/1.4037547].

Synthesis and singularity analysis of N-UU parallel wrists: A symmetric space approach

WU, YUANQING;CARRICATO, MARCO
2017

Abstract

We report some recent advances in kinematics and singularity analysis of the mirrorsymmetric N-UU parallel wrists using symmetric space theory. We show that both the finite displacement and infinitesimal singularity kinematics of a N-UU wrist are governed by the mirror symmetry property and half-angle property of the underlying motion manifold, which is a symmetric submanifold of the special Euclidean group SE(3). Our result is stronger than and may be considered a closure of Hunt's argument for instantaneous mirror symmetry in his pioneering exposition of constant velocity shaft couplings. Moreover, we show that the wrist can, to some extent, be treated as a spherical mechanism, even though dependent translation exists, and the singularity-free workspace of a N-UU wrist may be analytically derived. This leads to a straightforward optimal design for maximal singularity-free workspace.
2017
Wu, Y., Carricato, M. (2017). Synthesis and singularity analysis of N-UU parallel wrists: A symmetric space approach. JOURNAL OF MECHANISMS AND ROBOTICS, 9(5), 1-11 [10.1115/1.4037547].
Wu, Yuanqing; Carricato, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/607546
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