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Research Papers: Design Automation

The Foldability of Cylindrical Foldable Structures Based on Rigid Origami

[+] Author and Article Information
Jianguo Cai

Mem. ASME
Key Laboratory of C & PC Structures of
Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Si Pai Lou 2#,
Nanjing 210096, China
e-mails: j.cai@seu.edu.cn; caijg_ren@hotmail.com

Yuting Zhang

School of Civil Engineering,
Southeast University,
Nanjing 210096, China
e-mail: 472661724@qq.com

Yixiang Xu

Department of Civil Engineering,
Strathclyde University,
Glasgow G12 8QQ, UK
e-mail: Yixiang.xu@strath.ac.uk

Ya Zhou

School of Civil Engineering,
Southeast University,
Nanjing 210096, China
e-mail: zhouya5166@126.com

Jian Feng

School of Civil Engineering,
Southeast University,
Nanjing 210096, China
e-mail: fengjian@seu.edu.cn

1Corresponding author.

2Current address: Wuxi Architectural Design & Research Institute Co., Ltd., Wuxi 214001, Jiangsu, China.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 23, 2015; final manuscript received November 17, 2015; published online January 6, 2016. Assoc. Editor: Nam H. Kim.

J. Mech. Des 138(3), 031401 (Jan 06, 2016) (8 pages) Paper No: MD-15-1249; doi: 10.1115/1.4032194 History: Received March 23, 2015; Revised November 17, 2015

Foldable structures, a new kind of space structures developed in recent decades, can be deployed gradually to a working configuration and also can be folded for transportation, thus have potentially broad application prospects in the fields of human life, military, aerospace, building structures, and so on. Combined with the technology of origami folding, foldable structures derive more diversified models, and the foldable structures in cylindrical shape are mainly studied in this paper. Some researchers use the theory of quaternion representing spatial fixed-point rotation and construct the rotating vector model to obtain the quaternion rotation sequence method (QRS method) analyzing origami, but the method is very limited and not suitable for the cylindrical foldable structures. In order to solve the problem, a new method is developed, which combines the QRS method and the dual quaternion method. After analyzing the folding angle via the QRS method for multivertex crease system and calculating the coordinates of all vertices via the dual quaternion, the rigid foldability can be checked. Finally, two examples are carried out to confirm validity and versatility of the method.

FIGURES IN THIS ARTICLE
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Copyright © 2016 by ASME
Topics: Rotation , Cylinders
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References

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Figures

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Fig. 1

Origami crease pattern: (a) the initially flat state and (b) a folding configuration

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Fig. 2

The closed-loop rotation sequence of the characteristic vectors decomposed into eight steps in the rotating vector model of the single-vertex fourfold system

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Fig. 3

The modified Miura origami pattern

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Fig. 4

The cylinder configuration

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Fig. 5

The serial numbers of the vertex and fold lines

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Fig. 6

The coordinates of vertex 0

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Fig. 7

Tachi origami model: (a) formation of Tachi origami and (b) a typical unit

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Fig. 8

The coordinate changes of P1P4

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Fig. 9

Crease pattern of a deployable cylinder

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Fig. 10

Vertices of the deployable cylinder: (a) vertex P1, (b) vertex P2P5, (c) vertex P6, and (d) vertex P7P8

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Fig. 11

The coordinate changes of P1P8

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