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A Vector Expression of the Constant-Orientation Singularity Locus of the Gough–Stewart Platform

[+] Author and Article Information
Clément Gosselin

e-mail: gosselin@gmc.ulaval.ca

Philippe Cardou

Département de Génie Mécanique,
Université Laval,
1065 Avenue de la Médecine Québec,
QC G1V 0A6, Canada

This condition is a special case which corresponds also to a type I singularity.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received October 17, 2012; final manuscript received April 11, 2013; published online June 10, 2013. Assoc. Editor: J. M. Selig.

J. Mechanisms Robotics 5(3), 034502 (Jun 24, 2013) (4 pages) Paper No: JMR-12-1168; doi: 10.1115/1.4024295 History: Received October 17, 2012; Revised April 11, 2013

This paper presents a vector expression of the constant-orientation singularity locus of the general Gough–Stewart platform. The third-degree vector expression obtained does not contain a constant term, which allows the factorization of an instance of the position vector, thereby leading to a very compact form. Additionally, an expression of the vector orthogonal to the singularity locus is obtained as a byproduct. An alternative expression that reduces the number of times that the position vector appears in the expression is also presented. It is shown that a simplified architecture such as that of the Minimal Simplified Symmetric Manipulator (MSSM) can significantly reduce the complexity of the coefficients appearing in the expression.

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References

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Figures

Grahic Jump Location
Fig. 1

A generic Gough–Stewart platform

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