Self-motions of Stewart--Gough platforms
Computer Aided Geometric Design
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We present a set of planar parallel manipulators of Stewart Gough type which are singular with respect to the Schonflies group X(a) without being architecturally singular. This set of so-called Schonflies-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 Schonflies 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.