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.