On the rationality of the singularity locus of a Gough-Stewart platform - biplanar case

摘要

We propose to study the singularity locus of a Gough-Stewart platform as a surface defined over the field of rational functions on the 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.