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

Michel Coste (1) , Seydou Moussa (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Département de Mathématiques - Université de Maradi

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.

Keywords: parallel robot; cubic surface; singularities

Domains: Mathematics [math]; Algebraic Geometry [math.AG]

Michel Coste, Seydou Moussa. Rationality of the locus of singularities of the general Gough-Stewart platform. SIAM Journal on Applied Algebra and Geometry, 2020, 4 (3), pp.401-421. ⟨10.1137/19M1253277⟩. ⟨hal-02083002⟩