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Research Papers

A Spatial Eight-Bar Linkage and Its Association With the Deployable Platonic Mechanisms

[+] Author and Article Information
Guowu Wei

Research Associate
Centre for Robotics Research,
School of Natural and Mathematical Sciences,
King's College London,
University of London,
London WC2R 2LS, UK
e-mail: guowu.wei@kcl.ac.uk

Jian S. Dai

Chair of Mechanisms and Robotics
International Centre for
Mechanisms and Robotics,
MoE Key Laboratory for Mechanism Theory and
Equipment Design,
Tianjin University,
Tianjin 300072, China
Centre for Robotics Research,
School of Natural and Mathematical Sciences,
King's College London,
University of London,
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 April 12, 2013; final manuscript received September 2, 2013; published online March 12, 2014. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 6(2), 021010 (Mar 12, 2014) (9 pages) Paper No: JMR-13-1071; doi: 10.1115/1.4025472 History: Received April 12, 2013; Revised September 02, 2013

This paper presents for the first time a novel two degrees of freedom (2-DOF) single-looped dual-plane-symmetric spatial eight-bar linkage with exact straight-line motion. Geometry and kinematics of the eight-bar linkage are investigated and closed-form equations are presented revealing the exact straight-line motion feature of the linkage on the condition that two symmetric inputs are given. In order to secure two symmetric inputs, a geared eight-bar linkage is then proposed converting the linkage into a 1-DOF linkage of exact straight-line motion. The direction of the straight-line motion produced by the proposed eight-bar linkage is changeable and is only dependent on the structure parameters of the two pairs of V-shaped R-R dyads of the linkage. Further, the proposed eight-bar linkage is applied to the synthesis and construction of a group of deployable Platonic mechanisms with radially reciprocating motion. The virtual-center-based (VCB) method is presented for the synthesis and prototypes of the deployable Platonic mechanisms are fabricated verifying the mobility and motion of the proposed mechanisms.

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Figures

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Fig. 1

A dual-plane-symmetric spatial eight-bar linkage

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Fig. 2

Geometric parameters of the eight-bar linkage

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Fig. 3

Exact straight-line motion traced by point P

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Fig. 4

The eight-bar linkage with various angles ϕ1 and ϕ2

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Fig. 5

Angle β relative to angles ϕ1 and ϕ2

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Fig. 6

The eight-bar linkage with ϕ1 = ϕ2 = 90 deg

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Fig. 7

A geared eight-bar linkage of exact straight-line motion

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Fig. 9

Synthesis of a deployable hexahedral mechanism

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Fig. 10

Prototype of a deployable hexahedral mechanism

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Fig. 11

Prototypes of deployable Platonic mechanisms

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