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.
A Vector Expression of the Constant-Orientation Singularity Locus of the Gough–Stewart Platform
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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.
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Doyon, K., Gosselin, C., and Cardou, P. (June 24, 2013). "A Vector Expression of the Constant-Orientation Singularity Locus of the Gough–Stewart Platform." ASME. J. Mechanisms Robotics. August 2013; 5(3): 034502. https://doi.org/10.1115/1.4024295
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