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Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan

We present a study on planar equilibria of a terminally loaded elastic rod wrapped around a rigid circular capstan. Both frictionless and frictional contact between the rod and the capstan are considered. We identify three cases of frictionless contact – namely where the rod touches the capstan at o...

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Autor principal: Singh, Harmeet
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9581844/
https://www.ncbi.nlm.nih.gov/pubmed/36274652
http://dx.doi.org/10.1007/s10659-022-09939-8
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author Singh, Harmeet
author_facet Singh, Harmeet
author_sort Singh, Harmeet
collection PubMed
description We present a study on planar equilibria of a terminally loaded elastic rod wrapped around a rigid circular capstan. Both frictionless and frictional contact between the rod and the capstan are considered. We identify three cases of frictionless contact – namely where the rod touches the capstan at one point, along a continuous arc, and at two points. We show that, in contrast to a fully flexible filament, an elastic rod of finite length wrapped around a capstan does not require friction to support unequal loads at its two ends. Furthermore, we classify rod equilibria corresponding to the three aforementioned cases in a limit where the length of the rod is much larger than the radius of the capstan. In the same limit, we incorporate frictional interaction between the rod and the capstan, and compute limiting equilibria of the rod. Our solution to the frictional case fully generalizes the classic capstan problem to include the effects of finite thickness and bending elasticity of a flexible filament wrapped around a circular capstan. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10659-022-09939-8.
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spelling pubmed-95818442022-10-21 Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan Singh, Harmeet J Elast Article We present a study on planar equilibria of a terminally loaded elastic rod wrapped around a rigid circular capstan. Both frictionless and frictional contact between the rod and the capstan are considered. We identify three cases of frictionless contact – namely where the rod touches the capstan at one point, along a continuous arc, and at two points. We show that, in contrast to a fully flexible filament, an elastic rod of finite length wrapped around a capstan does not require friction to support unequal loads at its two ends. Furthermore, we classify rod equilibria corresponding to the three aforementioned cases in a limit where the length of the rod is much larger than the radius of the capstan. In the same limit, we incorporate frictional interaction between the rod and the capstan, and compute limiting equilibria of the rod. Our solution to the frictional case fully generalizes the classic capstan problem to include the effects of finite thickness and bending elasticity of a flexible filament wrapped around a circular capstan. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10659-022-09939-8. Springer Netherlands 2022-10-14 2022 /pmc/articles/PMC9581844/ /pubmed/36274652 http://dx.doi.org/10.1007/s10659-022-09939-8 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Singh, Harmeet
Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan
title Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan
title_full Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan
title_fullStr Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan
title_full_unstemmed Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan
title_short Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan
title_sort planar equilibria of an elastic rod wrapped around a circular capstan
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9581844/
https://www.ncbi.nlm.nih.gov/pubmed/36274652
http://dx.doi.org/10.1007/s10659-022-09939-8
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