Quadratic constraints on rigid-body displacements

Journal article


Selig, JM (2010). Quadratic constraints on rigid-body displacements. Journal of Mechanisms and Robotics. 2 (4). https://doi.org/10.1115/1.4002344
AuthorsSelig, JM
Abstract

In this work, the solution to certain geometric constraint problems are studied. The possible rigid displacements allowed by the constraints are shown to be intersections of the Study quadric of rigid-body displacements with quadratic hypersurfaces. The geometry of these constraint varieties is also studied and is found to be isomorphic to products of subgroups in many cases. This information is used to find extremely simple derivations for general solutions to some problems in kinematics. In particular, the number of assembly configurations for RRPS and RRRS mechanisms are found in this way. In order to treat planes and spheres on an equal footing, the Clifford algebra for the Möbius group is introduced. © 2010 American Society of Mechanical Engineers.

Year2010
JournalJournal of Mechanisms and Robotics
Journal citation2 (4)
PublisherAmerican Society of Mechanical Engineers
ISSN1942-4302
Digital Object Identifier (DOI)https://doi.org/10.1115/1.4002344
Publication dates
Print30 Sep 2010
Publication process dates
Deposited01 Jun 2016
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