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Rationality of the locus of singularities of the general Gough-Stewart platform

Abstract : We prove that the set of singular configurations of a general Gough Stewart platform has a rational parametrization. We introduce a reciprocal twist mapping which, for a general orientation of the platform, realizes the cubic surface of singularities as the blowing up of a quadric surface in five points.
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Submitted on : Tuesday, April 2, 2019 - 10:27:42 AM
Last modification on : Monday, January 18, 2021 - 10:38:01 AM
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Michel Coste, Seydou Moussa. Rationality of the locus of singularities of the general Gough-Stewart platform. SIAM Journal on Applied Algebra and Geometry, Society for Industrial and Applied Mathematics 2020, 4 (3), pp.401-421. ⟨10.1137/19M1253277⟩. ⟨hal-02083002⟩

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