A geometrical method for the singularity analysis of 3-RRR planar parallel robots with different actuation schemes

A parallel robot, due to its closed-loop structure, normally has two Jacobian matrices: the inverse and forward Jacobian matrices. Conventional methods for singularity analysis of planar parallel robots are based on analysis of the ranks of the two Jacobian matrices. The inverse singularity has been well studied as the inverse Jacobian matrix always has a simple diagonal form. However, the forward singularity analysis is somehow complicated, partially because some essential geometric relations may be occulted in the formulation of the forward Jacobian matrix. This paper focuses on the forward singularity analysis of a class of 3-RRR planar parallel robots with various actuation schemes. A simple geometric approach based on the concept of instantaneous center is proposed. By analyzing the instantaneous mobility of the moving platform when all the active joints are locked, the necessary and sufficient geometrical conditions for the forward singularity configurations are readily identified. It has been shown that this simple geometrical approach can be employed for singularity analysis of various planar parallel robots and mechanisms.