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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Tachi, T., 2009, “Generalization of Rigid-Foldable Quadrilateral-Mesh Origami,” J. Int. Assoc. Shell Spatial Struct., 50(162), pp. 173–179. Available at http://www.iass-structures.org/index.cfm/journal.article?aID=266
Schenk, M., Allwood, J., and Guest, S., 2011, “Cold Gas-Pressure Folding of Miura-Ori Sheets,” Proceedings of International Conference on Technology of Plasticity (ICTP 2011), Sept. 25–30th, Aachen, Germany.
Zakirov, I. M., and Alekseev, K. A., 2007, “Parameters of a Creasing-Bending Machine as Applied to the Scheme of Transverse Rotary Shaping of Chevron Structures,” Russ. Aeronaut. (Iz VUZ), 50(2), pp. 186–192. [CrossRef]
Huffman, D. A., 1976, “Curvature and Creases: A Primer on Paper,” IEEE Trans. Electron. Comput.C-25(10), pp. 1010–1019. [CrossRef]
Tachi, T., 2010, “Freeform Rigid-Foldable Structure Using Bidirectionally Flat-Foldable Planar Quadrilateral Mesh,” Advances in Architectural Geometry 2010 SE - 6, C.Ceccato, L.Hesselgren, M.Pauly, H.Pottmann, and J.Wallner, eds., Springer, Vienna pp. 87–102.
Hull, T., 2006, “Exploring Flat Vertex Folds,” Project Origami: Activities for Exploring Mathematics, A K Peters, Ltd., Wellesley, MA, pp. 215–230.
Miura, K., 2009, “The Science of Miura-Ori: A Review,” Origami4: Fourth International Meeting of Origami Science, Mathematics, and Education, R. J.Lang, ed., A K Peters, Ltd., Natick, MA, pp. 87–99.
Miura, K., 1972, “Zeta-Core Sandwich-Its Concept and Realization,” Inst. Space Aeronaut. Sci., Univ. Tokyo, 480, pp. 137–164.
Fischer, S., Drechsler, K., Kilchert, S., and Johnson, A., 2009, “Mechanical Tests for Foldcore Base Material Properties,” Composites, Part A, 40(12), pp. 1941–1952. [CrossRef]
Heimbs, S., 2013, “Foldcore Sandwich Structures and Their Impact Behaviour: An Overview,” Dynamic Failure of Composite and Sandwich Structures SE - 11, Solid Mechanics and Its Applications, Springer, Netherlands, Vol. 192, pp. 491–544.
Khaliulin, V. I., 2005, “A Technique for Synthesizing the Structures of Folded Cores of Sandwich Panels,” Russ. Aeronaut., 48(1), pp. 8–16.
Zakirov, I., and Alexeev, K., 2006, “New Folded Structures for Sandwich Panels,” Proceedings of SAMPE Conference, pp. 1–11.
Talakov, M. A., 2010, “Investigation of Folded Structure Geometry With Double Curvature,” Russ. Aeronaut., 53(3), pp. 334–338. [CrossRef]
Alekseev, K. A., 2011, “Geometrical Simulation of Regular and Irregular Folded Structures,” Russ. Aeronaut. (Iz VUZ), 54(1), pp. 84–88. [CrossRef]
De Temmerman, N., Mollaert, M., Van Mele, T., and De Laet, L., 2007, “Design and Analysis of a Foldable Mobile Shelter System,” Int. J. Space Struct., 22(3), pp.161–168. [CrossRef]
Weinand, Y., 2009, “Innovative Timber Constructions,” Symposium of the International Association for Shell and Spatial Structures (50th. 2009. Valencia). Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures: Proceedings, Editorial de la Universitat Politécnica de Valencia.
Künstler, A., and Trautz, M., 2011, “Deployable Folding Patterns Using Stiff Plate Elements,” Bautechnik88(2), pp. 86–93. [CrossRef]
Gioia, F., Dureisseix, D., Motro, R., and Maurin, B., 2012, “Design and Analysis of a Foldable/Unfoldable Corrugated Architectural Curved Envelop,” ASME J. Mech. Des., 134(3), p. 031003. [CrossRef]
Albermani, F., Khalilpasha, H., and Karampour, H., 2011, “Propagation Buckling in Deep Sub-Sea Pipelines,” Eng. Struct., 33(9), pp. 2547–2553. [CrossRef]
Ma, J., and You, Z., 2011, “The Origami Crash Box,” Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education, P.Wang-Iverson, R. J.Lang, and M.Yim, eds., Taylor & Francis Group, pp. 277–290.
Tachi, T., 2011, “Rigid-Foldable Thick Origami,” Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education, P.Wang-Iverson, R. J.Lang, and M.Yim, eds., Taylor & Francis, pp. 253–264.
Nguyen, M. Q., Jacombs, S. S., Thomson, R. S., Hachenberg, D., and Scott, M. L., 2005, “Simulation of Impact on Sandwich Structures,” Compos. Struct., 67(2), pp. 217–227. [CrossRef]
Klett, Y., and Drechsler, K., 2011, “Designing Technical Tessellations,” Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education, P.Wang-Iverson, R. J.Lang, and M.Yim, eds., Taylor & Francis Group, pp. 305–322.
Lebée, A., and Sab, K., 2012, “Homogenization of Thick Periodic Plates: Application of the Bending-Gradient Plate Theory to a Folded Core Sandwich Panel,” Int. J. Solids Struct., 49(19), pp. 2778–2792. [CrossRef]
Tessellated Group, 2013, www.tessellated.com
Kawasaki, T., 1989, “On the Relation Between Mountain-Creases and Valley-Creases of a Flat Origami,” Proceedings of the 1st International Meeting of Origami Science and Technology, pp. 229–237.
Gattas, J. M., 2013, Rigid Origami Toolbox, Available at: http://joegattas.com/rigid-origami-toolbox/


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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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