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Research Papers

Geometry of Transformable Metamaterials Inspired by Modular Origami

[+] Author and Article Information
Yunfang Yang

Department of Engineering Science,
University of Oxford Magdalen College,
Oxford OX1 4AU, UK
e-mail: yunfang.yang@eng.ox.ac.uk

Zhong You

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

1Corresponding author.

Manuscript received September 12, 2017; final manuscript received December 13, 2017; published online January 29, 2018. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 10(2), 021001 (Jan 29, 2018) (10 pages) Paper No: JMR-17-1291; doi: 10.1115/1.4038969 History: Received September 12, 2017; Revised December 13, 2017

Modular origami is a type of origami where multiple pieces of paper are folded into modules, and these modules are then interlocked with each other forming an assembly. Some of them turn out to be capable of large-scale shape transformation, making them ideal to create metamaterials with tuned mechanical properties. In this paper, we carry out a fundamental research on two-dimensional (2D) transformable assemblies inspired by modular origami. Using mathematical tiling and patterns and mechanism analysis, we are able to develop various structures consisting of interconnected quadrilateral modules. Due to the existence of 4R linkages within the assemblies, they become transformable, and can be compactly packaged. Moreover, by the introduction of paired modules, we are able to adjust the expansion ratio of the pattern. Moreover, we also show that transformable patterns with higher mobility exist for other polygonal modules. The design flexibility among these structures makes them ideal to be used for creation of truly programmable metamaterials.

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Figures

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Fig. 1

Modular origami models: (a) a snapology ball and (b) an interlinked cube assembly

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Fig. 2

An arrangement of identical quadrilateral modules

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Fig. 3

The second arrangement of identical quadrilateral modules: (a) mathematical model and assemblies consisting of (b) trapezium and (c) arbitrary quadrilateral modules

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Fig. 4

The third arrangement of identical quadrilateral modules: (a) mathematical model and assemblies made from (b) quadrilateral modules with two opposite right angles and (c) general quadrilateral modules

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Fig. 5

Transformable assemblies made from alternative modules: (a) modules with mirror symmetry and (b) modules with rotational symmetry

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Fig. 6

Orientation of modules in a transformable assembly and its dual

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Fig. 7

Paired modules based on the arrangement of type 1: (a) jigsaw puzzle pair and (b) pair of square modules with different sizes

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Fig. 8

Comparison between an assembly with paired modules and that with square modules: (a) parameters of two assemblies and (b) their respective expansion ratios

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Fig. 9

Other transformable tiling patterns with (a) triangles and hexagons, (b) triangles, trapezium, and hexagons, (c) triangles, and (d) squares and triangles

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