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Research Papers

Miura-Base Rigid Origami: Parameterizations of First-Level Derivative and Piecewise Geometries

[+] Author and Article Information
Joseph M. Gattas

e-mail: joe.gattas@eng.ox.ac.uk

Zhong You

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

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 1, 2013; final manuscript received June 20, 2013; published online October 9, 2013. Assoc. Editor: Alexander Slocum.

J. Mech. Des 135(11), 111011 (Oct 09, 2013) (11 pages) Paper No: MD-13-1051; doi: 10.1115/1.4025380 History: Received February 01, 2013; Revised June 20, 2013

Miura and Miura-derivative rigid origami patterns are increasingly used for engineering and architectural applications. However, geometric modelling approaches used in existing studies are generally haphazard, with pattern identifications and parameterizations varying widely. Consequently, relationships between Miura-derivative patterns are poorly understood, and widespread application of rigid patterns to the design of folded plate structures is hindered. This paper explores the relationship between the Miura pattern, selected because it is a commonly used rigid origami pattern, and first-level derivative patterns, generated by altering a single characteristic of the Miura pattern. Five alterable characteristics are identified in this paper: crease orientation, crease alignment, developability, flat-foldability, and rectilinearity. A consistent parameterization is presented for five derivative patterns created by modifying each characteristic, with physical prototypes constructed for geometry validation. It is also shown how the consistent parameterization allows first-level derivative geometries to be combined into complex piecewise geometries. All parameterizations presented in this paper have been compiled into a matlab Toolbox freely available for research purposes.

Copyright © 2013 by ASME
Topics: Geometry
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Figures

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Fig. 1

Folding sequence of a Miura pattern

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Fig. 2

Parameters of the Miura pattern

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Fig. 3

Arc pattern geometry

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Fig. 4

Arc pattern folding motion

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Fig. 5

Arc-Miura pattern geometry

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Fig. 6

Arc-Miura folding motion

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Fig. 7

Non-developable Miura pattern geometry

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Fig. 8

Non-developable Miura pattern folding motion

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Fig. 9

Partially-folded and near fully-folded half-units of non-flat foldable Miura variants

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Fig. 10

Non-flat foldable Miura pattern geometry

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Fig. 11

Non-flat foldable Miura folding motion

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Fig. 12

Tapered Miura pattern geometry

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Fig. 13

Tapered Miura pattern folding motion

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Fig. 14

Piecewise geometries formed from Miura/Arc-Miura assemblies

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Fig. 15

Piecewise geometries formed from Miura/non-developable Miura assemblies

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Fig. 16

Piecewise geometries formed from Tapered Miura pattern assemblies

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