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Technical Briefs

The Dimensional Synthesis of Spatial Cable-Driven Parallel Mechanisms

[+] Author and Article Information
K. Azizian

e-mail: kaveh.azizian.1@ulaval.ca

P. Cardou

e-mail: pcardou@gmc.ulaval.ca
Département de génie mécanique,
Université Laval,
Québec, PQ G1V 0A6, Canada

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 18, 2012; final manuscript received July 15, 2013; published online September 11, 2013. Assoc. Editor: Vijay Kumar.

J. Mechanisms Robotics 5(4), 044502 (Sep 11, 2013) (8 pages) Paper No: JMR-12-1075; doi: 10.1115/1.4025173 History: Received June 18, 2012; Revised July 15, 2013

This paper presents a method for the dimensional synthesis of fully constrained spatial cable-driven parallel mechanisms (CDPMs), namely, the problem of finding a geometry whose wrench-closure workspace (WCW) contains a prescribed workspace. The proposed method is an extension to spatial CDPMs of a synthesis method previously published by the authors for planar CDPMs. The WCW of CDPMs is the set of poses for which any wrench can be produced at the end-effector by non-negative cable tensions. A sufficient condition is introduced in order to verify whether a given six-dimensional box, i.e., a box covering point-positions and orientations, is fully inside the WCW of a given spatial CDPM. Then, a nonlinear program is formulated, whose optima represent CDPMs that can reach any point in a set of boxes prescribed by the designer. The objective value of this nonlinear program indicates how well the WCW of the resulting CDPM covers the prescribed box, a null value indicating that none of the WCW is covered and a value greater or equal to one indicating that the full prescribed workspace is covered.

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Figures

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Fig. 1

Notation used for the kinetostatic analysis of spatial cable-driven parallel mechanisms

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Fig. 2

A spatial CDPM with eight cables

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Fig. 3

The contracted WCW and the true COWCW of the CDPM appearing in Fig. 2 for ZYZ Euler angles of φ = θ = 0.03 rad, = 0.03 rad, and ψ = 0.03 rad

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Fig. 4

The six-dimensional prescribed box as the Cartesian product of two three-dimensional boxes: (a) one in the space of point positions, (b) the other in the space of orientations

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Fig. 5

3D view of the resulting CDPM with seven cables for φ = 0,θ = 0,ψ = 0 all in rad

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Fig. 6

Workspace visualizations of CDPM of example II: (a) the COWCW corresponding to the orientation φ = θ = ψ = 0  rad and (b) the regions of cable-cable interferences for the same orientation

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