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Research Papers

Wrench-Closure Workspace Generation for Cable Driven Parallel Manipulators Using a Hybrid Analytical-Numerical Approach

[+] Author and Article Information
Darwin Lau

Department of Mechanical Engineering,  The University of Melbourne, Victoria, 3010, Australiadtlau@student.unimelb.edu.au

Denny Oetomo

Department of Mechanical Engineering,  The University of Melbourne, Victoria, 3010, Australiadoetomo@unimelb.edu.au

Saman K. Halgamuge

Department of Mechanical Engineering,  The University of Melbourne, Victoria, 3010, Australiasaman@unimelb.edu.au

J. Mech. Des 133(7), 071004 (Jul 08, 2011) (10 pages) doi:10.1115/1.4004222 History: Received August 13, 2010; Revised May 03, 2011; Published July 07, 2011; Online July 08, 2011

In this paper, a technique to generate the wrench-closure workspace for general case completely restrained cable driven parallel mechanisms is proposed. Existing methods can be classified as either numerically or analytically based approaches. Numerical techniques exhaustively sample the task space, which can be inaccurate due to discretisation and is computationally expensive. In comparison, analytical formulations have higher accuracy, but often provides only qualitative workspace information. The proposed hybrid approach combines the high accuracy of the analytical approach and the algorithmic versatility of the numerical approach. Additionally, this is achieved with significantly lower computational costs compared to numerical methods. It is shown that the wrench-closure workspace can be reduced to a set of univariate polynomial inequalities with respect to a single variable of the end-effector motion. In this form, the workspace can then be efficiently determined and quantitatively evaluated. The proposed technique is described for a 3 degrees of freedom (3-DOF) and a 6-DOF cable driven parallel manipulator. A detailed example in workspace determination using the proposed approach and comparison against the conventional numerical approach is presented.

FIGURES IN THIS ARTICLE
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Copyright © 2011 by American Society of Mechanical Engineers
Topics: Cables , Manipulators
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References

Figures

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Figure 3

6-DOF manipulator model

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Figure 4

α-β cross-section of the 3-DOF manipulator’s WCW at γ≈π/6 rad with Δα = Δβ = Δγ = π/60 rad for α,β∈[−π2,π2] rad

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Figure 5

3D Visualization of the 3-DOF manipulator’s workspace for α,γ∈[0,π2] rad and β∈[−π2,0] rad

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Figure 6

α-β cross-section of the 3-DOF manipulator’s workspace at γ≈3π8 rad with Δα = Δβ = Δγ = π/60 rad

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Figure 7

α-β cross-section of the 3-DOF manipulator’s workspace at γ≈7π16 rad with Δα = Δβ = Δγ = π/60 rad

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Figure 8

α-β cross-section of the 3-DOF manipulator’s workspace at γ≈3π8 rad with Δα=Δβ=Δγ=π200 rad

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Figure 9

α-β cross-section of the 3-DOF manipulator’s workspace at γ≈7π/16 rad with Δα = Δβ = Δγ = π/200 rad

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Figure 10

x-y cross-section of 6-DOF manipulator’s WCW at α = β = γ = 0∘ with Δy=0.01m for x,y∈[0,1]m

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Figure 11

x-y cross-section of 6-DOF manipulator’s WCW at α = β = 0∘, γ = 5∘, with Δy=0.01m for x,y∈[0,1]m

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Figure 1

General model for cable manipulator

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Figure 2

3-DOF ball joint manipulator model

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