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Research Papers

Geometric Determination of the Interference-Free Constant-Orientation Workspace of Parallel Cable-Driven Mechanisms

[+] Author and Article Information
Simon Perreault

Département de Génie Mécanique, Université Laval, Québec, QC, G1V 0A6, Canadasimon.perreault.2@ulaval.ca

Philippe Cardou1

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

Clément M. Gosselin

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

Martin J.-D. Otis

Département de Génie Mécanique, Université Laval, Québec, QC, G1V 0A6, Canadamartin.otis.2@ulaval.ca

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1

Corresponding author.

J. Mechanisms Robotics 2(3), 031016 (Jul 27, 2010) (9 pages) doi:10.1115/1.4001780 History: Received September 29, 2009; Revised January 08, 2010; Published July 27, 2010; Online July 27, 2010

The increasing use of parallel cable-driven mechanisms calls for a better understanding of their behavior and highly efficient algorithms to attenuate their drawbacks at the design stage. One of these drawbacks is the high probability of mechanical interferences between the moving parts of the mechanism. In this paper, the phenomenon is described under the assumption that a cable is a line segment in space. When a mechanical contact occurs between two cables or between a cable and an edge of the end effector, these entities necessarily lie in the same plane, and then the three-dimensional problem becomes two-dimensional. This fact is used to simplify the equations, and leads to exhaustive descriptions of the associated interference loci in the constant-orientation workspace of a cable-driven mechanism. These results provide a fast method to graphically represent all interference regions in the manipulator workspace, given its geometry and the orientation of its end effector.

Copyright © 2010 by American Society of Mechanical Engineers
Topics: Cables , End effectors
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References

Figures

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Figure 1

Kinematic modeling

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Figure 2

The moving platform and a pair of cables that are attached to it

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Figure 3

Interference between cables i and j

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Figure 4

Conditions for the interference between cables

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Figure 5

Regions of Pij for which di∊[0,1]

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Figure 6

Regions of Pij for which dj∊[0,1]

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Figure 7

Regions Cij+ and Cij−, which include interferences between cables i and j

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Figure 8

Kinematic modeling of an end-effector edge

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Figure 9

A combination of a cable and an edge

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Figure 10

Interference between a cable and an edge

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Figure 11

Conditions for the interference between a cable and an edge

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Figure 12

Regions of Pij for which di∊]0,1]

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Figure 13

Regions of Pij for which dj∊[0,1]

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Figure 14

Region Eij which includes interferences between cable i and edge j

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Figure 15

Cable/cable and cable/edge interference regions for a generic PCDM with reference orientation (ϕ=0 deg, θ=0 deg, and ψ=0 deg)

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Figure 16

Comparison of the experimental measures and theoretical results

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