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# Analyses of Morphological Properties of a Generalized Miura Origami Structure

[+] Author and Article Information
Wei Ye

School of Engineering Science,
University of Science and Technology of China,
Hefei 230026, China
e-mail: weiye128@mail.ustc.edu.cn

Feng Wei

School of Engineering Science,
University of Science and Technology of China,
Hefei 230026, China
e-mail: fw153059@mail.ustc.edu.cn

Jin Yi

School of Engineering Science,
University of Science and Technology of China,
Hefei 230026, China
e-mail: jinyi08@ustc.edu.cn

Zhu Chang'an

School of Engineering Science,
University of Science and Technology of China,
Hefei 230026, China
e-mail: changan@ustc.edu.cn

1Corresponding authors.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 29, 2016; final manuscript received June 13, 2017; published online July 13, 2017. Assoc. Editor: James K. Guest.

J. Mech. Des 139(9), 094502 (Jul 13, 2017) (6 pages) Paper No: MD-16-1084; doi: 10.1115/1.4037184 History: Received January 29, 2016; Revised June 13, 2017

## Abstract

In this paper, we generalize Miura origami and propose a method for analyzing a generalized Miura origami structure. Morphological properties of the generalized Miura origami element during the deploy motion are analyzed using the proposed method, which mainly utilizes the principle of spherical trigonometry and is verified in the folding limit state. The longitudinal length, horizontal length, and height of the generalized Miura origami element are defined and obtained using the proposed method. Results show the relationship between the range of deployment and the element parameters as well as the changes of the folding plane angles in the deployment process. During the deploy motion, both the longitudinal and horizontal length increased while the height decreased. However, the change speed of horizontal length decreased, whereas those of longitudinal length and height initially increased and then decreased. The increment of the folding element angle difference $Δα$ reduced folding range and put off the severe change time of longitudinal length and height. The length parameters $Ka$, $Kb$, and $Kab$ had slight effects on the results, but their changes did not alter the change trends. These results are useful to the design of fold structure and analysis of errors in standard Miura-ori structures.

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## References

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## Figures

Fig. 1

The Miura-ori element: (a) standard form of the Miura-ori element and (b) generalized Miura-ori element

Fig. 2

Process of the fully collapsible element

Fig. 3

Paper model of Miura origami: (a) Miura-ori in standard form, (b) semideployed state of standard Miura-ori, (c) folded state of standard Miura-ori, (d) Miura-ori in generalized form, (e) folded state of generalized Miura-ori, and (f) ultimate folded state of a generalized Miura-ori unit

Fig. 4

The generalized Miura-ori element: (a) parameters of the generalized Miura-ori element and (b) solid structure of the generalized Miura-ori element

Fig. 5

Spherical diagram of the folded structure

Fig. 6

The parameters change during the deployment: (a) values of χ and ψ and (b) values of MN, PQ, and H

Fig. 8

Results produced using different parameters: (a) results of different Δα, (b) results of different Ka, (c) results of different Kb, and (d) results of different Kab

Fig. 7

Validation of δ1

## Errata

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