On the rationality of the singularity locus of a Gough–Stewart platform — Biplanar case

•Singularity locus of Gough–Stewart platform as surface over the field of rational functions of SO(3)•Simple rational parametrization of this surface•Family of parallel plane sections consisting of the conics of a linear pencil

We propose to study the singularity locus of a Gough–Stewart platform as a surface defined over the field of rational functions on the group of rotations. From the geometric properties of this surface we deduce, in the generic biplanar case, a rational parametrization and a family of parallel planes cutting the surface in the conics of a linear pencil, which are uniform for all generic orientations.