Research Papers

Multitransformable Leaf-Out Origami With Bistable Behavior

[+] Author and Article Information
Hiromi Yasuda

Aeronautics and Astronautics,
University of Washington,
Seattle, WA 98195-2400
e-mail: hiromy@uw.edu

Zhisong Chen

Aeronautics and Astronautics,
University of Washington,
Seattle, WA 98195-2400
e-mail: chimatsu@uw.edu

Jinkyu Yang

Assistant Professor
Aeronautics and Astronautics,
University of Washington,
Seattle, WA 98195-2400
e-mail: jkyang@aa.washington.edu

1Corresponding author.

Manuscript received July 7, 2015; final manuscript received September 29, 2015; published online March 7, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(3), 031013 (Mar 07, 2016) (6 pages) Paper No: JMR-15-1187; doi: 10.1115/1.4031809 History: Received July 07, 2015; Revised September 29, 2015

We study the kinematics of leaf-out origami and explore its potential usage as multitransformable structures without the necessity of deforming the origami's facets or modifying its crease patterns. Specifically, by changing folding/unfolding schemes, we obtain various geometrical configurations of the leaf-out origami based on the same structure. We model the folding/unfolding motions of the leaf-out origami by introducing linear torsion springs along the crease lines, and we calculate the potential energy during the shape transformation. As a result, we find that the leaf-out structure exhibits distinctive values of potential energy depending on its folded stage, and it can take multiple paths of potential energy during the transformation process. We also observe that the leaf-out structure can show bistability, enabling negative stiffness and snap-through mechanisms. These unique features can be exploited to use the leaf-out origami for engineering applications, such as space structures and architectures.

Copyright © 2016 by ASME
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Grahic Jump Location
Fig. 1

Leaflike origami pattern composed of four unit cells (shaded): (a) leaf-out pattern and (b) leaf-in pattern

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Fig. 2

Unfolding motion of leaf-out origami which consists of (a) three unit cells (ncell = 3), (b) four unit cells (ncell = 4), and (c) five unit cells (ncell = 5)

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Fig. 3

Geometry of leaf-out origami which consists of four unit cells (n = 4). (a) Flat configuration is folded into (b). Dark area is a unit cell. Global (i1, i2, i3) and local (e1, e2, e3) coordinates are used to define ψ. (c) Single unit cell where folding angles (θM and θS) are defined.

Grahic Jump Location
Fig. 4

Symmetric deployment of the square leaf-out origami (ncell = 4) case

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Fig. 5

Multiple configurations of the leaf-out pattern with ncell = 4. The crease pattern of the flat state is shown in (a), and it can be folded into (b)–(f).

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Fig. 6

(Left) Folding angle change and (right) energy change of the leaf-out pattern with (top) ncell = 3, (middle) ncell = 4, and (bottom) ncell = 5

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Fig. 7

(a) Folding angle change and (b) normalized energy change of the four unit cell case (ncell = 4). Unfolding/folding sequence is shown in Fig. 4.



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