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Symmetry 2014, 6(4), 954-974; doi:10.3390/sym6040954

On the Self-Mobility of Point-Symmetric Hexapods

Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10/104, Vienna 1040, Austria
Received: 3 October 2014 / Revised: 27 October 2014 / Accepted: 6 November 2014 / Published: 18 November 2014
(This article belongs to the Special Issue Rigidity and Symmetry)
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Abstract

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. View Full-Text
Keywords: hexapod; self-motion; bond theory; Borel–Bricard problem hexapod; self-motion; bond theory; Borel–Bricard problem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Nawratil, G. On the Self-Mobility of Point-Symmetric Hexapods. Symmetry 2014, 6, 954-974.

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