On the Self-Mobility of Point-Symmetric Hexapods

In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally...

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Bibliographic Details
Main Author:	Georg Nawratil
Format:	Article
Language:	English
Published:	MDPI AG 2014-11-01
Series:	Symmetry
Subjects:	hexapod self-motion bond theory Borel–Bricard problem
Online Access:	http://www.mdpi.com/2073-8994/6/4/954

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spelling	doaj-3adc3852ea334206a78502dcd7dc091b2020-11-25T00:17:34ZengMDPI AGSymmetry2073-89942014-11-016495497410.3390/sym6040954sym6040954On the Self-Mobility of Point-Symmetric HexapodsGeorg Nawratil0Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10/104, Vienna 1040, AustriaIn this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries.http://www.mdpi.com/2073-8994/6/4/954hexapodself-motionbond theoryBorel–Bricard problem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Georg Nawratil
spellingShingle	Georg Nawratil On the Self-Mobility of Point-Symmetric Hexapods Symmetry hexapod self-motion bond theory Borel–Bricard problem
author_facet	Georg Nawratil
author_sort	Georg Nawratil
title	On the Self-Mobility of Point-Symmetric Hexapods
title_short	On the Self-Mobility of Point-Symmetric Hexapods
title_full	On the Self-Mobility of Point-Symmetric Hexapods
title_fullStr	On the Self-Mobility of Point-Symmetric Hexapods
title_full_unstemmed	On the Self-Mobility of Point-Symmetric Hexapods
title_sort	on the self-mobility of point-symmetric hexapods
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2014-11-01
description	In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries.
topic	hexapod self-motion bond theory Borel–Bricard problem
url	http://www.mdpi.com/2073-8994/6/4/954
work_keys_str_mv	AT georgnawratil ontheselfmobilityofpointsymmetrichexapods
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On the Self-Mobility of Point-Symmetric Hexapods

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