Symmetric subspaces of SE(3)-Reference-Cited by-同舟云学术

Symmetric subspaces of SE(3)

Published:2016-06-27 Issue:3 Volume:16 Page:381-388
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Löwe Harald¹,Wu Yuanqing²,Carricato Marco²

Affiliation:

1. Technische Universität Braunschweig, Institut Computational Mathematics, 38106 Braunschweig, Germany

2. Department Industrial Engineering, University of Bologna, 40136 Bologna, Italy

Abstract

Abstract Being a Lie group, the group SE(3) of orientation preserving motions of the real Euclidean 3-space becomes a symmetric space (in the sense of O. Loos) when endowed with the multiplication µ(g, h) = gh −1 g. In this note we classify all connected symmetric subspaces of SE(3) up to conjugation. Moreover, we indicate some of its important applications in robot kinematics.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2016-0015/pdf

Reference18 articles.

1. J. Beckers, J. Patera, M. Perroud, P. Winternitz, Subgroups of the euclidean group and symmetry breaking in nonrelativistic quantum mechanics. Journal of Mathematical Physics 18 (1977),72–83.

2. R. Behrens, C. Kuchler, T. Forster, N. Elkmann, Kinematics analysis of a 3-dof joint for a novel hyper-redundant robot arm. 2011 IEEE International Conferenceon Roboticsand Automation (ICRA),3224–3229.

3. F. Bullo, A. D. Lewis, Geometric control of mechanical systems, volume 49 of Texts in Applied Mathematics. Springer 2005. MR2099139 Zbl1066.70002

4. S. S. Canfield, A. Ganino, C. Reinholtz, R. Salerno, Spatial, parallel-architecture robotic carpal wrist. 23 December, 1997. USPatent5,699,695.

5. J. M. Hervé, The Lie group of rigid body displacements, a fundamental tool for mechanism design. Mech. Mach. Theory 34 (1999),719–730. MR1750554 Zbl1049.70506

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