Singularity loci of planar parallel manipulators with revolute actuators

The determination of the singularity loci of planar parallel manipulators is addressed in this paper. The inverse kinematics of two kinds of planar parallel manipulators (a two-degree-of-freedom manipulator and a three-degree-of-freedom manipulator) are first computed and their velocity equations are then derived. At the same time, the branches of the manipulators are distinguished by the introduction of a branch index K_i. Using the velocity equations, the singularity analysis of the manipulators is completed and expressions which represent the singularity of the manipulators are obtained. A polynomial form of the singularity loci is also derived. For the first type of singularity of parallel manipulators, the singularity locus is obtained by finding the workspace limits of the manipulators. For the second type of singularity, the loci are obtained through the solution of nonlinear algebraic equations obtained from the velocity analysis. Finally, the graphical representation of the complete singularity loci of the manipulators is illustrated with examples. The algorithm introduced in this paper allows the determination of the singularity loci of planar parallel manipulators with revolute actuators, which has been elusive to previous approaches.