Half-turns and line symmetric motions

Journal article

Selig, JM and Husty, M (2011). Half-turns and line symmetric motions. Mechanism and Machine Theory. 46 (2), pp. 156 - 167. https://doi.org/10.1016/j.mechmachtheory.2010.10.001
AuthorsSelig, JM and Husty, M
Abstract

A line symmetric motion is the motion obtained by reflecting a rigid body in the successive generator lines of a ruled surface. In this work we review the dual quaternion approach to rigid body displacements, in particular the representation of the group SE(3) by the Study quadric. Then some classical work on reflections in lines or half-turns is reviewed. Next two new characterisations of line symmetric motions are presented. These are used to study a number of examples one of which is a novel line symmetric motion given by a rational degree five curve in the Study quadric. The rest of the paper investigates the connection between sets of half-turns and linear subspaces of the Study quadric. Line symmetric motions produced by some degenerate ruled surfaces are shown to be restricted to certain 2-planes in the Study quadric. Reflections in the lines of a linear line complex lie in the intersection of the Study quadric with a 4-plane. © 2010 Elsevier Ltd. All rights reserved.

Year2011
JournalMechanism and Machine Theory
Journal citation46 (2), pp. 156 - 167
PublisherElsevier
ISSN0094-114X
Digital Object Identifier (DOI)https://doi.org/10.1016/j.mechmachtheory.2010.10.001
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Print01 Feb 2011
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Deposited21 Jun 2016
Accepted01 Oct 2010
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