A remarkable set of Schönflies-singular planar Stewart Gough platforms

We present a set of planar parallel manipulators of Stewart Gough type which are singular with respect to the Schönflies group X(a) without being architecturally singular. This set of so-called Schönflies-singular planar parallel manipulators is characterized by the property that the carrier plane of the platform or of the base anchor points is orthogonal to the rotational axis a of the Schönflies group X(a). By giving the necessary and sufficient conditions we provide a complete classification of this set. Beside this algebraic characterization we also present a geometric one. Moreover we discuss the self-motional behavior of these manipulators and prove that they possess a quadratic singularity surface.