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Research Papers

Geometric Optimization of the MSSM Gough–Stewart Platform

[+] Author and Article Information
Qimi Jiang

Department of Mechanical Engineering, Laval University, Québec City, QC, G1V 0A6 Canada

Clément M. Gosselin1

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

1

Corresponding author.

J. Mechanisms Robotics 1(3), 031006 (Jul 14, 2009) (8 pages) doi:10.1115/1.3147202 History: Received April 18, 2008; Revised November 21, 2008; Published July 14, 2009

Abstract

This work focuses on analyzing the effects of the geometric parameters on the singularity-free workspace in order to determine the optimal architecture for the minimal simplified symmetric manipulator Gough–Stewart platform. To this end, the reference orientation is taken as the considered orientation because it is an impartial orientation. In this orientation, the singularity surface becomes a plane coinciding with the base plane. Accordingly, an analytic algorithm is developed to determine the singularity-free workspace. The analysis shows that: (1) for similar isosceles triangle base and platform, the optimal architecture is one for which both the base and the platform are equilateral triangles, and the size ratio between the platform and the base is $12$; and (2) if the base and the platform are not similar triangles, the global optimal architecture is difficult to determine. Only an approximate optimal architecture is available.

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Topics: Optimization

Figures

Figure 1

The MSSM architecture (top view)

Figure 2

The singularity surfaces for different architectures in the orientation with ϕ=−0.527351 and θ=ψ=−1.054701

Figure 3

The singularity-free workspaces for different architectures in the reference orientation

Figure 4

Determination of the contact point(s)

Figure 5

The singularity-free workspace with t1=1, t2=2, and k=35

Figure 6

The maximal singularity-free workspace of the 2D optimization (t1=1/34, t2=34, and k=12)

Figure 7

Volume V as a function of t1 and k

Figure 8

Volume V as a function of t1(k=0.6)

Figure 9

Volume V as a function of k for given t1

Figure 10

The six centers of the workspace spheres with t1=1/34 and k=0.3,12,0.7

Figure 11

The singularity-free workspace with different size ratios

Figure 12

Distribution of the initial values for the 2D optimization

Figure 13

Distribution of the initial values for the 3D optimization

Figure 14

The local Vmax as a function of the initial nodes

Figure 15

The approximate global maximal singularity-free workspace of the 3D optimization

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