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Research Papers

# Effects of Orientation Angles on the Singularity-Free Workspace and Orientation Optimization of the Gough–Stewart Platform

[+] Author and Article Information
Qimi Jiang

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

Clément M. Gosselin1

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

1

Corresponding author.

J. Mechanisms Robotics 2(1), 011001 (Nov 12, 2009) (10 pages) doi:10.1115/1.4000518 History: Received September 04, 2008; Revised August 08, 2009; Published November 12, 2009

## Abstract

The singularity-free workspace of parallel mechanisms is highly desirable in a context of robot design. This work focuses on analyzing the effects of the orientation angles on the singularity-free workspace of the Gough–Stewart platform in order to determine the optimal orientation. In any orientation with $ϕ=θ=0 deg$ and $ψ≠±90 deg$, the singularity surface becomes a plane coinciding with the base plane. Hence, an analytic algorithm is presented in this work to determine the singularity-free workspace. The results show that the singularity-free workspace in some orientations can be larger than that in the reference orientation with $ϕ=θ=ψ=0 deg$. However, the global optimal orientation is difficult to determine. Only an approximate optimal orientation is available. The results obtained can be applied to the design or parameter setup of the Gough–Stewart platform.

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## Figures

Figure 9

V as a function of θ(ϕ=ψ=0 deg)

Figure 10

The six centers of the workspace spheres for three different ψ values with ϕ=θ=0 deg

Figure 11

Determination of the contact point(s)

Figure 12

The singularity-free workspace in the orientation with ψ=7.639 deg and ϕ=θ=0 deg

Figure 13

The singularity-free workspace in the orientation with ψ=28.69 deg and ϕ=θ=0 deg

Figure 14

The singularity-free workspace in the orientation with ψ=60 deg and ϕ=θ=0 deg

Figure 15

V as a function of ψ(ϕ=θ=0 deg)

Figure 16

The singularity-free workspace (a) and singularity surface (b) in the orientation with ϕ=25.084 deg, θ=3.042 deg, and ψ=7.639 deg

Figure 17

The distribution of initial orientations

Figure 18

The approximate maximal singularity-free workspace (a) and singularity surface (b) in the orientation with ϕ=−14.046 deg, θ=19.954 deg, and ψ=−6.845 deg

Figure 19

The singularity-free workspace (a) and singularity surface (b) in the orientation with ϕ=0.063 deg, θ=−0.089 deg, and ψ=−89.687 deg

Figure 1

The MSSM architecture (top view)

Figure 2

The singularity surface with t1=1/34, t2=34, and k=3/5; and ϕ=45 deg, θ=60 deg, and ψ=15 deg

Figure 3

The singularity-free workspace in the reference orientation (ϕ=θ=ψ=0 deg)

Figure 4

Flight simulator (courtesy of CAE Electronics Ltd., Canada)

Figure 5

The singularity surface (a) and singularity-free workspace (b) in the orientation with ϕ=25.084 deg and θ=ψ=0 deg

Figure 6

V as a function of ϕ(θ=ψ=0 deg)

Figure 7

The singularity surface in the orientation with θ=81.442 deg and ϕ=ψ=0 deg

Figure 8

The singularity-free workspace (a) and singularity surface (b) in the orientation with θ=3.042 deg and ϕ=ψ=0 deg

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