Research Papers

The Dimensional Synthesis of Planar Parallel Cable-Driven Mechanisms Through Convex Relaxations

[+] Author and Article Information
K. Azizian

 Département de Génie Mécanique, Université Laval, Québec, QC, G1V 0A6, Canadakaveh.azizian.1@ulaval.ca

P. Cardou

 Département de Génie Mécanique, Université Laval, Québec, QC, G1V 0A6, Canadapcardou@gmc.ulaval.ca

J. Mechanisms Robotics 4(3), 031011 (Jul 06, 2012) (13 pages) doi:10.1115/1.4006952 History: Received October 14, 2011; Revised May 11, 2012; Published June 29, 2012; Online July 06, 2012

The wrench-closure workspace (WCW) of parallel cable-driven mechanisms is the set of poses for which any wrench can be produced at the end-effector by a set of positive cable tensions. In this paper, we tackle the dimensional synthesis problem, namely, that of finding a geometry for a planar parallel cable-driven mechanism (PPCDM) whose WCW contains a prescribed workspace. To this end, we first recall a linear program to determine whether a given pose is inside or outside the WCW of a given PPCDM. The relaxation of this linear program over a box leads to a nonlinear feasibility problem that can only be satisfied when this box is completely inside the WCW. We extend this feasibility problem to find a PPCDM geometry whose WCW includes a given set of boxes. These boxes represent the prescribed workspace or an estimate thereof, which may be obtained through interval analysis. Finally, we introduce a nonlinear program through which the PPCDM geometry is changed while maximizing the scaling factor of the prescribed set of boxes. When the optimum scaling factor is greater or equal to one, the WCW of the resulting PPCDM contains the set of boxes.

Copyright © 2012 by American Society of Mechanical Engineers
Topics: Cables , Geometry , Mechanisms
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Figure 1

A prototype of planar parallel cable-driven mechanism with four cables at Robotics Laboratory of Université Laval [6]

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Figure 2

Sketch of an m-cable PPCDM

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Figure 3

A PPCDM with four cables

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Figure 4

Contracted WCW and cross sections of the exact WCW of the PPCDM geometry found in Ref. [12]

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Figure 5

An scaled-up box and its corresponding parameters

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Figure 6

Distribution of the randomly generated initial points with the obtained scaling factors

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Figure 7

One of the obtained PPCDMs

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Figure 8

Scaled boxes and COWCWs for the orientations φ = − π/3, − π/9, π/9, π/3

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Figure 9

Evolution of scaling factor

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Figure 10

Approximated desired workspace with multiple boxes

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Figure 11

The obtained PPCDM and its corresponding COWCW



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