Liaison Linkages

Matteo Gallet (1) , Georg Nawratil (2) , Josef Schicho (3)

1 RICAM - Johann Radon Institute for Computational and Applied Mathematics
2 TU Wien - Institute of Discrete Mathematics and Geometry [Vienne]
3 RISC - Research Institute for Symbolic Computation

The complete classification of hexapods - also known as Stewart Gough platforms - of mobility one is still open. To tackle this problem, we can associate to each hexapod of mobility one an algebraic curve, called the configuration curve. In this paper we establish an upper bound for the degree of this curve, assuming the hexapod is general enough. Moreover, we provide a construction of hexapods with curves of maximal degree, which is based on liaison, a technique used in the theory of algebraic curves.

Domains: Algebraic Geometry [math.AG]

Matteo Gallet, Georg Nawratil, Josef Schicho. Liaison Linkages. MEGA'2015 (Special Issue), Jun 2015, Trento, Italy. ⟨hal-01350773⟩