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Research Papers

A Kirigami-Inspired 8R Linkage and Its Evolved Overconstrained 6R Linkages With the Rotational Symmetry of Order Two

[+] Author and Article Information
Ketao Zhang

Research Associate
Center for Robotics Research,
King's College London,
University of London,
Strand, London WC2R 2LS, UK;
Department of Mechanical Engineering,
Beijing Jiaotong University,
Beijing 100044, China
e-mail: ketao.zhang@kcl.ac.uk

Jian S. Dai

Chair of Mechanisms and Robotics,
MoE Key Laboratory for Mechanism Theory and
Equipment Design,
Tianjin University,
Tianjin 300072, China;
Center for Robotics Research,
King's College London,
University of London,
Strand, London WC2R 2LS, UK
e-mail: jian.dai@kcl.ac.uk

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 27, 2012; final manuscript received December 10, 2013; published online March 6, 2014. Assoc. Editor: Xianmin Zhang.

J. Mechanisms Robotics 6(2), 021007 (Mar 06, 2014) (12 pages) Paper No: JMR-12-1152; doi: 10.1115/1.4026337 History: Received September 27, 2012; Revised December 10, 2013

This paper presents a novel metamorphic 8R linkage extracted from a kirigami-fold with pregrooved creases and two overconstrained 6R linkages evolved from the 8R linkage by taking the concept of metamorphosis in the sense of structural evolution. The geometric characteristics and the parametric constraints of the evolved 6R linkages are identified following the structural evolution of the 8R linkage. The paper reveals that the evolved 6R linkages are special line-symmetric Bricard 6R loops characterized by the rotational symmetry of order two. The joint space of the overconstrained 6R linkages is analyzed and the relationship between motion parameters of the evolved 6R linkages and reconfiguration parameters of the metamorphic 8R linkage are derived. The motion characteristics of the overconstrained 6R linkages are further verified in terms of screw theory. The bifurcation and trifurcation associated with various transitory positions of the evolved 6R linkages having distinct parametric constraints are consequently identified based on constraint analysis.

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Topics: Linkages
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Figures

Grahic Jump Location
Fig. 1

A partially erected closed-loop kirigami-fold

Grahic Jump Location
Fig. 2

An 8R linkage extracted from the closed-loop Kirigami-fold: (a) the schematic diagram and (b) prototype of the 8R linkage

Grahic Jump Location
Fig. 3

The distance between axes of two nonsuccessive joints: (a) the distance between axes of R1 and R3 and (b) the distance between axes of R2 and R4

Grahic Jump Location
Fig. 4

The evolved double-parallel 6R linkage with two pairs of parallel axes: (a) sketch of the 6Rp linkage and (b) evolved 6Rp linkage (N point view)

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Fig. 5

The evolved double-orthogonal 6R linkage with two pairs of perpendicular axes: (a) sketch of the 6Ro linkage and (b) evolved 6Ro linkage (N point view)

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Fig. 6

The overconstrained 6Rp linkage corresponding to δ1 = 0: (a) sketch of the special 6Rp linkage and (b) evolved special 6Rp linkage (N point view)

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Fig. 7

The overconstrained 6Rp linkage corresponding to δ1 = π: (a) sketch of the double-centered 6Rp linkage and (b) evolved double-centered 6Rp linkage (N point view)

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Fig. 8

The overconstrained 6Ro linkage corresponding to δ2 = π/2: (a) sketch of the special 6Ro linkage and (b) evolved special 6Ro linkage (N point view)

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Fig. 9

Motion screws of the overconstrained 6Rp linkage

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Fig. 10

Transitory position of the 6Rp in Fig. 6

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Fig. 11

Two planar motion branches from transitory position: (a) a parallelogram 4R linkage and (b) an antiparallelogram 4R linkage

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Fig. 12

Transitory position and bifurcated motion branch of the 6Rp in Fig. 7: (a) the transitory position and (b) the simplified RR chain motion branch

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Fig. 13

Singular positions of the 6Ro in Fig. 8

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