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Research Papers

Nonrigidly Foldability Analysis of Kresling Cylindrical Origami

[+] Author and Article Information
Cai Jianguo

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

Liu Yangqing

School of Civil Engineering,
Southeast University,
Nanjing 210096, China
e-mail: iamliuyangqing163@163.com

Ma Ruijun

School of Civil Engineering,
Southeast University,
Nanjing 210096, China
e-mail: 1175455218@qq.com

Feng Jian

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

Zhou Ya

Wuxi Architectural Design &
Research Institute Co. Ltd.,
Wuxi 214001, Jiangsu, China
e-mail: zhouya5166@126.com

1Corresponding author.

Manuscript received August 1, 2016; final manuscript received April 26, 2017; published online June 14, 2017. Assoc. Editor: Guimin Chen.

J. Mechanisms Robotics 9(4), 041018 (Jun 14, 2017) (10 pages) Paper No: JMR-16-1224; doi: 10.1115/1.4036738 History: Received August 01, 2016; Revised April 26, 2017

Rigid origami is seen as a fundamental model in many self-folding machines. A key issue in designing origami is the rigid/nonrigid foldability. The kinematic and foldability of Kresling origami, which is based on an origami pattern of the vertex with six creases, are studied in this paper. The movement of the single-vertex is first discussed. Based on the quaternion method, the loop-closure equation of the vertex with six creases is obtained. Then, the multitransformable behavior of the single vertex is investigated. Furthermore, the rigid foldability of origami patterns with multivertex is investigated with an improved dual quaternion method, which is based on studying the folding angle and the coordinates of all vertices. It can be found that the Kresling cylinder is not rigidly foldable.

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Figures

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Fig. 1

Kresling origami pattern

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Fig. 2

One vertex with six creases

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Fig. 3

The rotation of a vector

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Fig. 4

The first four steps of the rotation of the edge and normal vectors: (a) the first step, (b) the second step, (c) the third step, and (d) the fourth step

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Fig. 5

Output folding angles t6 versus input folding angles t3

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Fig. 6

Output folding angles t4, t5, t6 versus input folding angles t1 and t3: (a) t4, (b) t5, and (c) t6

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Fig. 7

A typical configuration in which every crease can fold

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Fig. 13

The origami pattern of a cylinder

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Fig. 14

Crease vectors in vertex P1

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Fig. 15

Vertex coordinate transfer along a closed path

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Fig. 16

Coordinate changes of the last vertex

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