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Research Papers

Synthesis of RCCC Linkages to Visit Four Given Poses

[+] Author and Article Information
Shaoping Bai

Department of Mechanical and
Manufacturing Engineering,
Aalborg University,
Denmark
e-mail: shb@m-tech.aau.dk

Jorge Angeles

Department of Mechanical Engineering,
McGill University,
Montreal, Canada
e-mail: angeles@cim.mcgill.ca

Upon adding one dimension to a line, namely, a point outside of the line, a plane is obtained, which is capable of attaining a full pose.

That is, if abstraction is made of the translation of the coupler link when formulating the problem stated in Section 2, then points Rj, for j = 1, …,m, coincide with point R0, and the problem at hand becomes one of spherical-linkage synthesis.

Angles αj, for j = 1, 2, 3, 4, are associated with a spherical linkage, which does not admit values.

Should the jth displacement be a pure translation, pj would tend to ∞; in this case, rather than the pitch, the translation dj would be used, as the authors suggested for the planar case [16].

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 21, 2013; final manuscript received September 10, 2014; published online December 4, 2014. Assoc. Editor: Qiaode Jeffrey Ge.

J. Mechanisms Robotics 7(3), 031004 (Aug 01, 2015) (9 pages) Paper No: JMR-13-1118; doi: 10.1115/1.4028637 History: Received June 21, 2013; Revised September 10, 2014; Online December 04, 2014

This paper focuses on the problem of synthesis of spatial four-bar linkages of the RCCC type for rigid-body guidance with four given poses, R denoting a revolute, C a cylindrical kinematic pair. While synthesis equations for CC and RC dyads are available in the literature, the synthesis of spatial RCCC four-bar linkages requires special attention, due to its asymmetric topology. We revisit the problem to cope robustly with the asymmetry, namely, the approximate nature of the RC dyad and the infinity of exact solutions of the CC dyad for the number of given poses. Our approach includes a robust formulation of the synthesis of CC dyads, for the determination of axis-congruences. Moreover, we formulate a uniform synthesis equation, which enables us to treat both RC and CC dyads, with properly selected constraints for both cases. Two design examples are included.

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Copyright © 2015 by ASME
Topics: Linkages
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References

Figures

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Fig. 1

The RCCC linkage, where all four links are indexed with numbers

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Fig. 2

The spherical 4R linkage, where all four bodies are indexed with numbers

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Fig. 3

A CC dyad, which becomes a RC dyad if the sliding sj vanishes

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Fig. 4

Geometric relations in the RC dyad

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Fig. 5

RC dyad generated from synthesis results: (a) in the reference configuration, where links are numbered with respect to Fig. 1; (b) in all four poses; and (c) zoom-in of the revolute joint

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Fig. 6

Cubics on the unit sphere: (a) the spherical centerpoint curve, (b) the spherical circlepoint curve

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Fig. 7

Congruences of the CC dyad: (a) the fixed axis (Z1 or Z2) and (b) the moving axis (Z3 or Z4)

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