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Technical Brief

Mobility and Kinematic Analysis of Foldable Plate 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 210018, China
e-mails: j.cai@seu.edu.cn; caijg_ren@hotmail.com

Zelun Qian

School of Civil Engineering,
Southeast University,
Nanjing 210018, China
e-mail: 1610935058@qq.com

Chao Jiang

School of Civil Engineering,
Southeast University,
Nanjing 210018, China
e-mail: jiangc_2008@126.com

Jian Feng

School of Civil Engineering,
Southeast University,
Nanjing 210018, China
e-mail: fengjian@seu.edu.cn

Yixiang Xu

Department of Civil Engineering,
Strathclyde University,
Glasgow G1 1XQ, UK
e-mail: yixiang.xu@strath.ac.uk

1Corresponding author.

Manuscript received April 5, 2016; final manuscript received July 26, 2016; published online October 11, 2016. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 8(6), 064502 (Oct 11, 2016) (6 pages) Paper No: JMR-16-1090; doi: 10.1115/1.4034578 History: Received April 05, 2016; Revised July 26, 2016

As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, spherical joints, and the boundary conditions of linkages were first used to generate the system constraint equations. Then, the degree-of-freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method, and multiple kinematic paths existing in origami structures were studied by obtaining all the solutions of constraint equations. Different solutions represent different kinematic configurations. The DOF and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in detail.

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References

Figures

Grahic Jump Location
Fig. 2

The rectangular plate

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Fig. 1

Definition of the triangle plate

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Fig. 4

Deployable shell antenna

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Fig. 3

The typical element of Miura-ori

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Fig. 5

Two possible configurations of Miura-ori: (a) z7 = 25, (b) z7 = 50, and (c) z7 = 0

Grahic Jump Location
Fig. 6

Kinematic path of rigid deployable antenna: (a) z7 = 1104, (b) z7 = 1400, and (c) z7 = 1800

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