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RESEARCH PAPERS

# Analytic Form of the Six-Dimensional Singularity Locus of the General Gough-Stewart Platform

[+] Author and Article Information
Haidong Li

Département de Génie Mécanique, Université Laval, Québec, Canada, G1K 7P4lhaidong@gmc.ulaval.ca

Clément M. Gosselin1

Département de Génie Mécanique, Université Laval, Québec, Canada, G1K 7P4gosselin@gmc.ulaval.ca

Marc J. Richard

Département de Génie Mécanique, Université Laval, Québec, Canada, G1K 7P4mrichard@gmc.ulaval.ca

Boris Mayer St-Onge

Département de Génie Mécanique, Université Laval, Québec, Canada, G1K 7P4borris@gmc.ulaval.ca

1

Corresponding author.

J. Mech. Des 128(1), 279-287 (Apr 27, 2005) (9 pages) doi:10.1115/1.2118733 History: Received June 08, 2004; Revised April 27, 2005

## Abstract

The determination of the 6D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables $(x,y,z,ϕ,θ,ψ)$, using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.

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## Figures

Figure 1

General architecture of the Gough-Stewart platform. (a) Gough-Stewart platform; (b) notation used.

Figure 2

Singularity loci in 3D Cartesian space with constant orientations. (a) With ϕ=−2°, θ=30°, ψ=−87°; (b) with ϕ=30°, θ=30°, ψ=30°.

Figure 3

Singularity loci in 3D Cartesian space with constant positions (all lengths are given in mm). (a) With x=0, y=0, z=0; (b) with x=100, y=100, z=100.

Figure 4

Singularity locus in 3D Cartesian space with z=100, θ=30°, ψ=−87° (all lengths are given in mm)

Figure 5

Singularity locus in 3D Cartesian space with x=y=0, ϕ=30° (all lengths are given in mm)

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