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Research Papers

Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform

[+] Author and Article Information
Qimi Jiang

Department of Mechanical Engineering, Laval University, Quebec, QC, G1V 0A6, Canadaqimi_j@yahoo.com

Clément M. Gosselin

Department of Mechanical Engineering, Laval University, Quebec, QC, G1V 0A6, Canadagosselin@gmc.ulaval.ca

J. Mechanisms Robotics 1(2), 021004 (Jan 06, 2009) (9 pages) doi:10.1115/1.3046137 History: Received April 01, 2008; Revised September 30, 2008; Published January 06, 2009

The evaluation and representation of the orientation workspace of robotic manipulators is a challenging task. This work focuses on the determination of the theoretical orientation workspace of the Gough–Stewart platform with given leg length ranges [ρimin,ρimax]. By use of the roll-pitch-yaw angles (ϕ,θ,ψ), the theoretical orientation workspace at a prescribed position P0 can be defined by up to 12 workspace surfaces. The defined orientation workspace is a closed region in the 3D orientation Cartesian space Oϕθψ. As all rotations R(x,ϕ), R(y,θ), and R(z,ψ) take place with respect to the fixed frame, any point of the defined orientation workspace provides a clear measure for the platform to, respectively, rotate in order around the (x,y,z) axes of the fixed frame. An algorithm is presented to compute the size (volume) of the theoretical orientation workspace and intersectional curves of the workspace surfaces. The defined theoretical orientation workspace can be applied to determine a singularity-free orientation workspace.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

The MSSM architecture (top view)

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Figure 2

Orientation workspace surfaces

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Figure 3

The orientation workspace at P0(0,234/3,5/4) with ρimax=1.8 and ρimin=1.2. (a) 3D representation and (b) top view.

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Figure 4

Geometric limitation of leg length

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Figure 5

The workspace section on the plane: θ=θi

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Figure 6

The orientation workspace at P0(0,234/3,5/4) with ρimax=1.75 and ρimin=1.30

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Figure 7

The orientation workspace at P0(12,1,54) with ρimax=1.8 and ρimin=1.2

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Figure 8

The maximal singularity-free orientation workspace at P0(0,234/3,5/4) (Vmax=2.967244, ρimax=1.828782, and ρimin=1.102122). (a) 3D representation and (b) top view.

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Figure 9

Procedure for computing the volume V1 of the orientation workspace with θ≤0

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