The Hanging Drape: a Vertex Analogy
- 13 October 2021
- journal article
- research article
- Published by ASME International in Journal of Mechanisms and Robotics
- Vol. 14 (3), 1-12
- https://doi.org/10.1115/1.4052742
Abstract
We present a novel, rigidly folding vertex inspired by the shape of the simplest hanging drape. Fold lines in the vertex correspond to pleats and ridges in the drape, and are symmetrically arranged to enable synchronised at folding of facet pairs. We calculate the folded rotation angles exactly using a spherical image specialised for inextensible vertex folding. We show that the vertex shape is bounded by a pair of conical surfaces whose apex semi-angles directly correspond with fold-line rotations, which expresses a geometrical equivalence between the external shape and internal folding motion of the vertex. We discuss how the vertex viz. drape perform as a novel type of conical defect based on its spherical image topography; and we highlight the meaning of bistable behaviour for the vertex, in analytical- and practical terms.Keywords
This publication has 10 references indexed in Scilit:
- Forms and Concepts for Lightweight StructuresPublished by Cambridge University Press (CUP) ,2020
- Calculating the Fold Angles of Any Vertex Roof Using a Spherical Image TechniqueJournal of Mechanisms and Robotics, 2020
- Static bistability of spherical capsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2018
- Localization in Thin Metallic Annuli due to Diametrical ExtensionAIAA Journal, 2017
- Fundamental conical defects: The d-cone, its e-cone, and its p-conePhysical Review E, 2016
- Elastic theory of origami-based metamaterialsPhysical Review E, 2016
- Generic Bistability in Creased Conical SurfacesPhysical Review Letters, 2015
- Draping Films: A Wrinkle to Fold TransitionPhysical Review Letters, 2010
- Geometry of “developable cones”International Journal of Mechanical Sciences, 2005
- The elements of drapingProceedings of the National Academy of Sciences of the United States of America, 2004