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Symmetry 2014, 6(3), 516-550; https://doi.org/10.3390/sym6030516

Symmetry Adapted Assur Decompositions

1
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada
2
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK
3
Department of Physics, Ryerson University, Toronto, ON M5B 2K3, Canada
4
Department of Psychology and Neuroscience, University of Colorado, Boulder, CO 80309, USA
*
Author to whom correspondence should be addressed.
Received: 31 March 2014 / Revised: 5 June 2014 / Accepted: 12 June 2014 / Published: 27 June 2014
(This article belongs to the Special Issue Rigidity and Symmetry)
Full-Text   |   PDF [1266 KB, uploaded 27 June 2014]

Abstract

Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools. View Full-Text
Keywords: Assur decomposition; pinned framework; forced symmetry; symmetric infinitesimal motion; isostatic graph; gain graph; orbit matrix Assur decomposition; pinned framework; forced symmetry; symmetric infinitesimal motion; isostatic graph; gain graph; orbit matrix
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Nixon, A.; Schulze, B.; Sljoka, A.; Whiteley, W. Symmetry Adapted Assur Decompositions. Symmetry 2014, 6, 516-550.

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