Singularity analysis of a general class of planar parallel manipulators

With regard to planar parallel manipulators, a general classification of singularities into three groups is introduced. The classification scheme relies on the properties of the Jacobian matrices of the manipulator at hand. The Jacobian matrices of a general class of planar parallel manipulators are derived and the three types of singularities are identified for them. This class contains 20 manipulators constructed with three different combinations of legs of the PRR, PPR, RRR and RPR types, P and R representing prismatic and revolute pairs, respectively