Singularity analysis of a class of kinematically redundant parallel Schönflies motion generators

This paper provides an analysis of the singularities of a class of kinematically redundant parallel manipulators. The studied mechanisms are capable of spatial translations in addition to rotation around an axis with constant orientation. Such motion is classified as Schönflies motion and is of high importance for industrial applications. The studied mechanisms include a manipulated platform composed of two platform sections, which are connected by a passive joint. The mechanisms include five actuated kinematic chains of a specific type, where three kinematic chains are connected to one platform section and two to the other section. Several novel mechanisms in this class are introduced and the singularities of all introduced variants are analyzed utilizing screw theory. In particular, all configurations leading to a redundant passive motion (RPM) singularity are determined. In such configurations, at least one of the passive joints in the mechanism may have a non-zero velocity while the velocity of the tool and all actuated joints are zero. For the studied mechanisms, such configurations correspond to the system of wrenches acting on the platform section including the tool has full rank while the wrench system acting on the other platform section is rank deficient.