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Research Papers: Design Automation

Miura-Base Rigid Origami: Parametrizations of Curved-Crease Geometries

[+] Author and Article Information
Joseph M. Gattas

School of Civil Engineering,
University of Queensland,
St. Lucia QLD 4072, Australia
e-mail: j.gattas@uq.edu.au

Zhong You

Department of Engineering Science,
University of Oxford,
Oxford, Oxfordshire OX1 3PJ, UK
e-mail: zhong.you@eng.ox.ac.uk

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 5, 2013; final manuscript received September 1, 2014; published online October 20, 2014. Assoc. Editor: Karthik Ramani.

J. Mech. Des 136(12), 121404 (Oct 20, 2014) (10 pages) Paper No: MD-13-1509; doi: 10.1115/1.4028532 History: Received November 05, 2013; Revised September 01, 2014

Curved-crease (CC) origami differs from prismatic, or straight-crease origami, in that the folded surface of the pattern is bent during the folding process. Limited studies on the mechanical performance of such geometries have been conducted, in part because of the difficulty in parametrizing and modeling the pattern geometry. This paper presents a new method for generating and parametrizing rigid-foldable, CC geometries from Miura-derivative prismatic base patterns. The two stages of the method, the ellipse creation stage and rigid subdivision stage, are first demonstrated on a Miura-base pattern to generate a CC Miura pattern. It is shown that a single additional parameter to that required for the straight-crease pattern is sufficient to completely define the CC variant. The process is then applied to tapered Miura, Arc, Arc-Miura, and piecewise patterns to generate CC variants of each. All parametrizations are validated by comparison with physical prototypes and compiled into a matlab Toolbox for subsequent work.

Copyright © 2014 by ASME
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Figures

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Fig. 1

Straight-crease Miura-base unit geometries and relevant parameters. Crease pattern, on left and folded configuration, on right. (a) Miura, (b) tapered Miura, (c) Arc, and (d) Arc-Miura.

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Fig. 2

CC surfaces from developable surface inversion. (a) Cylindrical inversion and (b) conical inversion.

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Fig. 3

Ellipse creation on a prismatic Miura-base pattern. (a) Ellipse through three points, (b) longitudinal axes projection, (c) base and ellipse parameters, and (d) lower and upper bounds of ϕ .

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Fig. 4

Crease pattern unrolled from a folded configuration. (a) Perpendicular projected ellipse and (b) unrolled pattern.

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Fig. 5

Rigid subdivision of CC pattern. (a) S = 1, 2, and 4 divisions, (b) straight-line segments between subdivided points, and (c) K rigid strips.

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Fig. 6

Maximum and minimum limits of CC foldability. (a) Isometric view and (b) top view.

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Fig. 7

Comparison of folding motion of simulated (left) and aluminum prototype (right) CC-Miura pattern

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Fig. 8

Two tessellations of the CC-Miura pattern unit geometry. (a) Tessellation 1 and (b) tessellation 2.

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Fig. 9

Curved crease tapered Miura geometry creation. (a) Three point ellipse, (b) projected surface, (c) divisor lines and exploded rigid strips, and (d) crease pattern.

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Fig. 10

Comparison of folding motion of simulated (left) and paper prototype (right) CC-tapered Miura pattern

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Fig. 11

CC Arc geometry creation. (a) Three point ellipse, (b) projected curved surface, (c) divisor lines and exploded rigid panels, and (d) crease pattern.

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Fig. 12

Comparison of folding motion of simulated (left) and plastic prototype (right) CC-Arc pattern

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Fig. 13

CC Arc-Miura geometry creation. (a) Three point ellipse, (b) projected curved surface, (c) divisor lines and exploded rigid panels, and (d) crease pattern.

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Fig. 14

Comparison of folding motion of simulated (left) and paper prototype (right) CC-Arc-Miura pattern

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Fig. 15

Formation of complex CC geometries from by conversion of straight-crease geometries. (a) Preserved closure condition in prismatic and CC Tapered Miura patterns and (b) CC piecewise geometries formed from Miura/Arc-Miura assemblies.

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