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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

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 3

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

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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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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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