More views of a one-sided surface: Mechanical models and stereo vision techniques for Möbius strips

Kumar, A and Handral, P and Bhandari, D and Rangarajan, R (2021) More views of a one-sided surface: Mechanical models and stereo vision techniques for Möbius strips. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477 (2250).

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Abstract

Möbius strips are prototypical examples of ribbon-like structures. Inspecting their shapes and features provides useful insights into the rich mechanics of elastic ribbons. Despite their ubiquity and ease of construction, quantitative experimental measurements of the three-dimensional shapes of Möbius strips are surprisingly non-existent in the literature. We propose two novel stereo vision-based techniques to this end - a marker-based technique that determines a Lagrangian description for the construction of a Möbius strip, and a structured light illumination technique that furnishes an Eulerian description of its shape. Our measurements enable a critical evaluation of the predictive capabilities of mechanical theories proposed to model Möbius strips. We experimentally validate, seemingly for the first time, the developable strip and the Cosserat plate theories for predicting shapes of Möbius strips. Equally significantly, we confirm unambiguous deficiencies in modelling Möbius strips as Kirchhoff rods with slender cross-sections. The experimental techniques proposed and the Cosserat plate model promise to be useful tools for investigating a general class of problems in ribbon mechanics. © 2021 The Author(s).

Item Type:	Journal Article
Publication:	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher:	Royal Society Publishing
Additional Information:	The copyright for this article belongs to Royal Society Publishing
Keywords:	Plates (structural components); Stereo image processing, Critical evaluation; Eulerian description; Experimental techniques; Lagrangian description; Mechanical theory; Predictive capabilities; Ribbon-like structures; Three-dimensional shape, Stereo vision
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	20 Nov 2021 11:35
Last Modified:	20 Nov 2021 11:35
URI:	http://eprints.iisc.ac.in/id/eprint/69894

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