Correcting Duporcq's theorem()

In 1898, Ernest Duporcq stated a famous theorem about rigid-body motions with spherical trajectories, without giving a rigorous proof. Today, this theorem is again of interest, as it is strongly connected with the topic of self-motions of planar Stewart–Gough platforms. We discuss Duporcq's the...

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Autor principal: Nawratil, Georg
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier Ltd 2014
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4270477/
https://www.ncbi.nlm.nih.gov/pubmed/25540467
http://dx.doi.org/10.1016/j.mechmachtheory.2013.11.012
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author Nawratil, Georg
author_facet Nawratil, Georg
author_sort Nawratil, Georg
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description In 1898, Ernest Duporcq stated a famous theorem about rigid-body motions with spherical trajectories, without giving a rigorous proof. Today, this theorem is again of interest, as it is strongly connected with the topic of self-motions of planar Stewart–Gough platforms. We discuss Duporcq's theorem from this point of view and demonstrate that it is not correct. Moreover, we also present a revised version of this theorem.
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spelling pubmed-42704772014-12-22 Correcting Duporcq's theorem() Nawratil, Georg Mech Mach Theory Article In 1898, Ernest Duporcq stated a famous theorem about rigid-body motions with spherical trajectories, without giving a rigorous proof. Today, this theorem is again of interest, as it is strongly connected with the topic of self-motions of planar Stewart–Gough platforms. We discuss Duporcq's theorem from this point of view and demonstrate that it is not correct. Moreover, we also present a revised version of this theorem. Elsevier Ltd 2014-03 /pmc/articles/PMC4270477/ /pubmed/25540467 http://dx.doi.org/10.1016/j.mechmachtheory.2013.11.012 Text en © 2014 The Author https://creativecommons.org/licenses/by/3.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Article
Nawratil, Georg
Correcting Duporcq's theorem()
title Correcting Duporcq's theorem()
title_full Correcting Duporcq's theorem()
title_fullStr Correcting Duporcq's theorem()
title_full_unstemmed Correcting Duporcq's theorem()
title_short Correcting Duporcq's theorem()
title_sort correcting duporcq's theorem()
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4270477/
https://www.ncbi.nlm.nih.gov/pubmed/25540467
http://dx.doi.org/10.1016/j.mechmachtheory.2013.11.012
work_keys_str_mv AT nawratilgeorg correctingduporcqstheorem

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