Stewart Gough platforms with non-cubic singularity surface

In the general case the singularity locus of a parallel manipulator of Stewart Gough type is a cubic surface in the space of translations. In this article we determine all Stewart Gough platforms which possess only a linear or quadratic singularity surface. These manipulators have the advantage, that their singularity surface can easily be visualized because it is a plane or a quadric for any orientation of the platform. Moreover we also give a geometric interpretation of these manipulators.