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Technical Briefs

Classifying the Boundaries of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms by Visual Inspection

[+] 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

B. Moore

Département de Génie Mécanique,  Université Laval, Québec, QC, G1V 0A6, Canadabrianmoore222@gmail.com

Lemma 5 is not proved in the paper due to space limitations.

J. Mechanisms Robotics 4(2), 024503 (Apr 25, 2012) (5 pages) doi:10.1115/1.4006520 History: Received December 23, 2010; Revised February 21, 2012; Published April 25, 2012; Online April 25, 2012

The wrench-closure workspace 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 non-negative cable tensions. It is already known that the boundary of the constant-orientation wrench-closure workspace of a planar parallel cable-driven mechanism is composed of segments of conic sections. However, the relationship between the geometry of the mechanism and the types of these conic sections is unknown. This technical report proposes a graphical method for determining the types of these conic sections from the mechanism geometry. It is also shown that the proposed method can be applied to find the constant-orientation singularities of a 3-RP R planar parallel robot, since these conic sections correspond to the boundary segment of the analogous three-cable driven planar parallel mechanism.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Sketch of a planar cable-driven mechanism with m cables

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Figure 2

A 3-RP R planar parallel mechanism

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Figure 3

Two triangles of a selected set of base and moving-platform points, with their corresponding parabola

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Figure 4

A line segment between the focus point and the directrix of a parabola equally divided by a perpendicular tangent line

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Figure 5

A planar parallel cable-driven robot with four cable

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Figure 6

Graphical algorithm applied to determine the type of conic section of two triangles depicted in Fig. 3

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