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Technical Briefs

Geometric Analysis of a Foldable Barrel Vault With Origami

[+] Author and Article Information
Jianguo Cai

Lecturer Key Laboratory of
C & PC Structures of Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Nanjing 210096, China
e-mail: j.cai@seu.edu.cn

Yixiang Xu

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

Jian Feng

Professor
Key Laboratory of C & PC Structures
of Ministry of Education,
National Prestress Engineering Research Center,
Southeast University,
Nanjing 210096, China
e-mail: fengjian@seu.edu.cn

1Corresponding author.

Contributed by the Design Innovation and Devices of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 8, 2012; final manuscript received August 14, 2013; published online September 24, 2013. Assoc. Editor: Alexander Slocum.

J. Mech. Des 135(11), 114501 (Sep 24, 2013) (6 pages) Paper No: MD-12-1552; doi: 10.1115/1.4025369 History: Received November 08, 2012; Revised August 14, 2013

This paper investigates the geometry of a foldable barrel vault with modified Miura-ori patterns, which displays a curvature during the motion. The principal of spherical trigonometry was used to obtain the relationship of the inclined angles between adjacent folded papers of Miura-ori. Then, the radius, span, rise, and longitudinal length of the foldable barrel vault in all configurations throughout the motion are determined. The results show that the radius of curvature grows exponentially and the span increases during deployment. Furthermore, the rise increases first, followed by a decrease with increasing deployment angle.

FIGURES IN THIS ARTICLE
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Copyright © 2013 by ASME
Topics: Geometry
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References

Figures

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Fig. 1

Modified modules of Miura-ori

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Fig. 2

Foldable structure with modified modules of Miura-ori

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Fig. 3

3D figures of the folded barrel vault during the motion

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Fig. 4

The analytical model of Miura-ori elements

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Fig. 5

Spherical triangles of Miura-ori elements

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Fig. 6

Foldable barrel vault with two modified Miura-ori modules

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Fig. 7

Turned Miura-ori module

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Fig. 8

The foldable barrel vault during the motion

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Fig. 9

The model for the span and rise

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Fig. 10

The model for the longitudinal length

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Fig. 11

R/l against the deployment angle ψ

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Fig. 12

S/l against the deployment angle ψ

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Fig. 13

H/l against the deployment angle ψ

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Fig. 14

d/b against the deployment angle ψ

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