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Research Papers: Design of Mechanisms and Robotic Systems

Screw-System-Variation Enabled Reconfiguration of the Bennett Plano-Spherical Hybrid Linkage and Its Evolved Parallel Mechanism

[+] Author and Article Information
Ketao Zhang

Centre for Robotics Research,
Faculty of Natural and Mathematical Sciences,
King's College London,
University of London,
Strand, London WC2R 2LS, UK
e-mail: ketao.zhang@kcl.ac.uk

Jian S. Dai

Centre for Robotics Research,
Faculty of Natural and Mathematical Sciences,
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 MECHANICAL DESIGN. Manuscript received September 9, 2014; final manuscript received March 6, 2015; published online April 15, 2015. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 137(6), 062303 (Jun 01, 2015) (10 pages) Paper No: MD-14-1555; doi: 10.1115/1.4030015 History: Received September 09, 2014; Revised March 06, 2015; Online April 15, 2015

This paper presents the Bennett plano-spherical hybrid linkage and proposes a novel metamorphic parallel mechanism consisting of this plano-spherical linkage as part of limbs. In light of geometrical modeling of the Bennett plano-spherical linkage, and with the investigation of the motion-screw system, the paper reveals for the first time the reconfigurability property of this plano-spherical linkage and identifies the design parameters that lead to change of constraint equations, and subsequently to variation of the order of the motion-screw system. Arranging this linkage as part of limbs, the paper further investigates the reconfiguration property of the plano-spherical linkage evolved parallel mechanism. The analysis reveals that the platform constraint-screw system varies following both bifurcation and trifurcation with motion branch variation in the 6R linkage integrated limb structure. Consequently, this variation of the platform constraint-screw system leads to reconfiguration of the proposed metamorphic parallel mechanism. The paper presents a way of analyzing reconfigurability of kinematic structures based on the screw-system approach.

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Figures

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Fig. 1

The plane-symmetric Bennett plano-spherical hybrid linkage and its geometrical model (a) kinematic model and (b) geometric model

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Fig. 2

The singular configurations of the Bennett plano-spherical hybrid linkage (a) case (i): r  >  ldg, (b) case (ii): r  <  ldg, and (c) case (iii): r = ldg

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Fig. 3

The metamorphic parallel mechanism composed of Bennett plano-spherical hybrid linkages

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Fig. 6

The hybrid limb with closed loop subchain in planar 4R motion branch (a) kinematic model of the hybrid limb and (b) the equivalent RvPvRR kinematic chain

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Fig. 5

The hybrid limb with closed loop subchain in spherical 4R motion branch (a) kinematic model of the hybrid limb, (b) the equivalent RvRvRR kinematic chain

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Fig. 4

The hybrid limb with closed loop subchain working in overconstrained 6R linkage motion branch (a) kinematic model of the hybrid limb, (b) the equivalent RvRvRvRR kinematic chain

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Fig. 7

The motion branch of the parallel mechanism implementing 3DOF spherical motion

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Fig. 8

The motion branch of the parallel mechanism implementing 1DOF pure translation

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