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Research Papers

Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms

[+] Author and Article Information
Lei Cui

 Postdoctoral Fellow King’s College London, University of London, Carnegie Mellon University e-mail: leicui@cmu.edu

Jian S. Dai

Chair of Mechanisms and Robotics King’s College London,  University of London, Strand, London WC2R 2LS UK; Tianjin University, Tianjin 300072, PR China e-mail: jian.dai@kcl.ac.uk

J. Mechanisms Robotics 3(3), 031004 (Jul 19, 2011) (9 pages) doi:10.1115/1.4004225 History: Received December 05, 2010; Revised April 23, 2011; Published July 19, 2011; Online July 19, 2011

This paper investigates the 6R overconstrained mechanisms by looking at an arrangement that axes intersect at two centers with arbitrary intersection-angles. From the close-loop matrix equation of the mechanism, the paper develops a set of geometric constraint equations of the 6R double-centered overconstrained mechanisms. This leads to the axis constraint equation after applying the Sylvester’s dialytic elimination method. The equation reveals the geometric constraint of link and axis parameters and identifies three categories of the 6R double-centered overconstrained mechanisms with arbitrary axis intersection-angles. The first two categories present two 6R double-centered overconstrained mechanisms and a 6R spherical mechanism. The last category evolves into the 6R double-spherical overconstrained mechanism with arbitrary axis intersection-angles at each spherical center. This further evolves into Baker’s double-Hooke mechanism and his derivative double-spherical mechanism with orthogonal axis intersection. The paper further develops the joint-space solution of the 6R double-centered overconstrained mechanisms based on the geometric constraint equation and verifies the result with a numerical example.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A general 6R mechanism

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Figure 2

The 6R double-centered overconstrained mechanism with arbitrary axis intersection angle

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Figure 3

A Hooke-spherical joint mechanism

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Figure 4

A co-axial double-spherical mechanism

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Figure 5

A 6R spherical mechanism

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Figure 6

A symmetric double-spherical mechanism

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Figure 7

Baker’s double-spherical mechanism with two orthogonal corners

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Figure 8

The joint-space curves of θ1 and θ3 to θ6 in terms of θ2

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Figure 9

(a) Fully-folded; (b) half-spread

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