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Research Papers

The Synthesis of the Axodes of RCCC Linkages

[+] Author and Article Information
Giorgio Figliolini

DICeM,
University of Cassino & Southern Lazio,
G. Di Biasio 43,
Cassino, Frosinone 03043, Italy
e-mail: figliolini@unicas.it

Pierluigi Rea

DICeM,
University of Cassino & Southern Lazio,
G. Di Biasio 43,
Cassino, Frosinone 03043, Italy
e-mail: rea@unicas.it

Jorge Angeles

Department of Mechanical Engineering & CIM,
McGill University,
817 Sherbrooke Street West,
Montreal, QC H3A 2K6, Canada
e-mail: angeles@cim.mcgill.ca

1Corresponding author.

Manuscript received February 27, 2015; final manuscript received October 15, 2015; published online November 24, 2015. Assoc. Editor: Federico Thomas.

J. Mechanisms Robotics 8(2), 021011 (Nov 24, 2015) (9 pages) Paper No: JMR-15-1047; doi: 10.1115/1.4031950 History: Received February 27, 2015; Revised October 15, 2015; Accepted October 20, 2015

As the coupler link of an RCCC linkage moves, its instant screw axis (ISA) sweeps a ruled surface on the fixed link; by the same token, the ISA describes on the coupler link itself a corresponding ruled surface. These two surfaces are the axodes of the linkage, which roll while sliding and maintaining line contact. The axodes not only help to visualize the motion undergone by the coupler link but also can be machined as spatial cams and replace the four-bar linkage, if the need arises. Reported in this paper is a procedure that allows the synthesis of the axodes of an RCCC linkage. The synthesis of this linkage, in turn, is based on dual algebra and the principle of transference, as applied to a spherical four-bar linkage with the same input–output function as the angular variables of the RCCC linkage. Examples of RCCC linkages are included. Moreover, to illustrate the generality of the synthesis procedure, it is also applied to a spherical linkage, namely, the Hooke joint, and to the Bennett linkage.

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Copyright © 2016 by ASME
Topics: Rotation , Linkages , Algebra
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References

Figures

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Fig. 1

Spatial four-bar linkage: Euclidean space

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Fig. 2

Spherical four-bar linkage: dual space

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Fig. 11

Oldham's arrangement by Willis [49]

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Fig. 3

Original drawings of the Poinsot cones [44]

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Fig. 4

RCCC four-bar parallelogram for a1 = a3 = 50 mm, a2 = a4 = 10 mm, α1 = α3 = 70 deg, and α2 = α4 = 30 deg

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Fig. 5

RCCC four-bar antiparallelogram for a1 = a3 = 50 mm, a2 = a4 = 10 mm, α1 = α3 = 70 deg, and α2 = α4 = 30 deg

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Fig. 6

Spherical four-bar antiparallelogram for α1 = α3 = 99 deg, α2 = α4 = 130 deg

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Fig. 7

Hooke joint for α1 = α2 = α3 = 0 deg, α4 = 135 deg

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Fig. 8

Bennett mechanism for a1 = a3 = 30 mm, α1 = α3 = 99 deg, and α2 = α4 = 130 deg

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Fig. 9

Original sketches: (a) gimbals from Cardan's book [48] and (b) Cardan joint from De Subtilitate, Book I, 1550

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Fig. 12

RCCC four-bar linkage with double-crank for a1 = 30 mm, a2 = 25 mm, a3 = 17 mm, a4 = 10 mm, α1 = 85 deg, α1 = 74 deg, α3 = 97 deg, α4 = 153 deg, and s1 = −30

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