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Research Papers

Chirality Induced by Structural Transformation in a Tensegrity: Theory and Experiment

[+] Author and Article Information
Li-Yuan Zhang

School of Mechanical Engineering,
University of Science and Technology Beijing,
Beijing 100083, China;
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Zi-Long Zhao

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Qing-Dong Zhang

School of Mechanical Engineering,
University of Science and Technology Beijing, Beijing 100083, China

Xi-Qiao Feng

AML & CNMM,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: fengxq@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 4, 2015; final manuscript received December 25, 2015; published online January 18, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(4), 041003 (Jan 18, 2016) (7 pages) Paper No: JAM-15-1654; doi: 10.1115/1.4032375 History: Received December 04, 2015; Revised December 25, 2015

Chiral structures have many technologically significant applications in engineering. In this paper, we investigate, both theoretically and experimentally, the structural transformation from a symmetric X-shaped tensegrity to a chiral structure under uniaxial tension. When the applied tensile force exceeds a critical value, the initially achiral structure would exhibit snap-through buckling. At the critical state, the in-plane deformation mode of the tensegrity switches into an off-plane one. The critical condition of the structural transformation is provided in terms of structural parameters. An experiment was performed to validate the theoretical model. This work may not only deepen our understanding of the stability of tensegrities but also help design chiral structures for engineering applications.

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Figures

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Fig. 1

Configuration of X-shaped tensegrity in the absence of external load. The spheres, thin lines, and thick lines denote the nodes, strings, and bars, respectively.

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Fig. 2

Two possible deformation modes of X-shaped tensegrity under uniaxial tension: (a) in-plane mode (α=0) and (b) off-plane mode (0<α<π), with α denoting the relative twist angle between the top and bottom strings

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Fig. 3

Curves of the uniaxial force f¯, incremental stiffness Δf¯/Δλ¯, and twist angle α with respect to relative elongation λ¯ for X-shaped tensegrity with k¯s2=1, k¯b=100, L¯s2=1, and L¯b=1.5

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Fig. 4

Curves of the critical force f¯cr and critical elongation λ¯cr with respect to the axial stiffness k¯s2 of the horizontal strings for an X-shaped tensegrity with k¯b=100, L¯s2=1, and L¯b=1.5. The inset shows the details of f¯cr – k¯s2 and λ¯cr – k¯s2 curves in a subrange.

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Fig. 5

Curves of the critical force f¯cr and critical elongation λ¯cr with respect to the axial stiffness k¯b of the bars for an X-shaped tensegrity with k¯s2=1, L¯s2=1, and L¯b=1.5. The inset shows the details of f¯cr – k¯b and λ¯cr – k¯b curves in a subrange.

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Fig. 6

Curves of the critical force f¯cr and critical elongation λ¯cr with respect to the natural length L¯s2 of the horizontal strings for an X-shaped tensegrity with k¯s2=1, k¯b=100, and L¯b=1.5

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Fig. 7

Curves of the critical force f¯cr and critical elongation λ¯cr with respect to the natural length L¯b of the bars for an X-shaped tensegrity with k¯s2=1, k¯b=100, and L¯s2=1. The inset shows the details of f¯cr – L¯b and λ¯cr – L¯b curves in a subrange.

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Fig. 8

X-shaped tensegrity sculpture: (a) planar configuration without external load and (b) chiral configuration under an external load exceeding the critical force

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Fig. 9

Variations of the uniaxial force f¯ versus relative elongation λ¯ for the tensegrity in Fig. 8(a) with different vertical springs: (a) ks1=0.116 N/mm and Ls1=158 mm and (b) ks1=0.122 N/mm and Ls1=148 mm. The symbols are the experimental results under four loading–unloading processes, and the lines are the theoretical results calculated from Eqs. (17)(20).

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Fig. 10

Strip structure made of five X-shaped tensegrity cells with different critical forces: (a) curves of uniaxial force f̂ and total twist angle A with respect to relative elongation λ̂ and (b) configuration evolution of the structure under uniaxial tensile force

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