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Research Papers

Geometry and Constraint Analysis of the Three-Spherical Kinematic Chain Based Parallel Mechanism

[+] Author and Article Information
Ketao Zhang

Department of Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, P.R. China; Department of Mechanical Engineering, King’s College London, University of London, Strand, London WC2R 2LS, UKketao.zhang@kcl.ac.uk

Yuefa Fang

Department of Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, P.R. Chinayffang@bjtu.edu.cn

Hairong Fang

Department of Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, P.R. Chinahrfang@bjtu.edu.cn

Jian S. Dai

Department of Mechanical Engineering, King’s College London, University of London, Strand, London WC2R 2LS, UKjian.dai@kcl.ac.uk

J. Mechanisms Robotics 2(3), 031014 (Jul 23, 2010) (7 pages) doi:10.1115/1.4001783 History: Received December 08, 2009; Revised April 21, 2010; Published July 23, 2010; Online July 23, 2010

This paper presents a three-spherical kinematic chain based parallel mechanism that evolved from an origami fold. The new parallel mechanism with symmetrical structure consists of a base, a platform, and three-spherical six-bar chains as chain-legs connecting to both base and platform via revolute joints. This paper investigates the constraint of the mechanism by constructing a virtual symmetric plane that is based on the three virtual centers of the spherical chains. Revealing the geometric characteristics and constraint disposition of the constraint screw system, singularity is identified related to the constraint configuration based on Grassmann line geometry and dependency of the constraint screw system, leading to selection of the design parameters that avoid the platform singularity.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

The spherical six-bar kinematic chain from an origami fold: (a) the cardboard with pregrooved creases; (b) mapping to the equivalent kinematic chain

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Figure 3

The parallel mechanism constructed by three-spherical chains: (a) the schematic diagram; (b) the physical device

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Figure 4

Geometric parameters of the six-bar spherical kinematic chain CL1

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Figure 5

Trajectory of the virtual centers Ai

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Figure 6

Geometric parameters of the parallel mechanism

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Figure 7

The spherical six-bar kinematic chain of chain leg CL1

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Figure 8

The equivalent serial chain of the chain leg: (a) original chain-leg; (b) equivalent serial kinematic chain

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Figure 9

Disposition of the constraints in general configuration: (a) constraint illustrations with the platform; (b) three constraints on the symmetric plane

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Figure 10

Singular position of case (ii) of the platform

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