Research Papers: Design Automation

New Deployable Structures Based on an Elastic Origami Model

[+] Author and Article Information
Kazuya Saito

Department of Mechanical and
Biofunctional Systems,
Institute of Industrial Science,
The University of Tokyo,
4-6-1 Komaba,
Tokyo 153-8505, Japan
e-mail: saito-k@iis.u-tokyo.ac.jp

Akira Tsukahara

Department of Systems Innovation,
School of Engineering,
The University of Tokyo,
4-6-1 Komaba,
Tokyo 153-8505, Japan
e-mail: tsuka-hr@iis.u-tokyo.ac.jp

Yoji Okabe

Department of Mechanical and
Biofunctional Systems,
Institute of Industrial Science,
The University of Tokyo,
4-6-1 Komaba,
Tokyo 153-8505, Japan
e-mail: okabey@iis.u-tokyo.ac.jp

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 18, 2013; final manuscript received November 20, 2014; published online December 4, 2014. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 137(2), 021402 (Feb 01, 2015) (5 pages) Paper No: MD-13-1414; doi: 10.1115/1.4029228 History: Received September 18, 2013; Revised November 20, 2014; Online December 04, 2014

Traditionally, origami-based structures are designed on the premise of “rigid folding,” However, every act of folding and unfolding is accompanied by elastic deformations in real structures. This study focuses on these elastic deformations in order to expand origami into a new method of designing morphing structures. The authors start by proposing a simple model for evaluating elastic deformation in nonrigid origami structures. Next, these methods are applied to deployable plate models. Initial strain is introduced into the elastic parts as actuators for deployment. Finally, by using the finite element method (FEM), it is confirmed that the proposed system can accomplish the complete deployment in 3 × 3 Miura-or model.

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Grahic Jump Location
Fig. 1

Examples of rigid foldable origami. (a) Miura-ori. (b) DCS. (c) Pleated hyperbolic paraboloid.

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Fig. 2

Origami models and their corresponding 3D trusses. (a) and (b): 3 × 3 quadrilateral mesh origami. (c) and (d): 2 × 3 quadrilateral mesh origami.

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Fig. 3

Relation between line angles (α, β, γ, and δ) and folding angles (Θ, θ1, θ2, and θ3). ϕ0 = ∠BEH. ϕ1, ϕ2, ϕ3, and ϕ4 are dihedral angles between BEH and plate EFIH, BCFE, ABED, and DEHG, respectively. They correlate with each other in a one DOF origami.

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Fig. 4

Rigid folding simulation

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Fig. 5

Schematic of partially elastic origami model based on 3 × 3 quadrilateral mesh origami and the truss model of the rigid part. Eight gray plates R are assumed as rigid plates and have a one DOF mechanism. Only the upper right plate is replaced with an elastic plate.

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Fig. 6

Partially elastic origami model with single elastic truss member-A. The folding process of the gray rigid parts can be simulated using the method shown in Rigid Origami Models section. In nonrigid foldable patterns, truss-A is forced to deform and the resultant strain can be calculated by the trajectories of vertexes B and C.

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Fig. 7

Elastic strains of member-A as calculated by the partially elastic origami model. (a) Mura-ori (rigid foldable case). (b) Monotonically increase type. (c) Monotonically decrease type. (d) Bistable type. The strains are assumed to be zero in the completely folded and deployed conditions.

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Fig. 8

Simulated model. (a) Coordinate values of the x-y surface. (b) Fold line pattern. The model is similar to Miura-ori, but has slight misalignment in vertex V23 and V32. (c) Relation between degree of deployment D and strain of truss-A.

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Fig. 9

Deployment simulation using LS-DYNA




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