Architecture singularity analysis for a class of parallel manipulators

The present investigates the architecture singularity of a class of parallel manipulators. In general, singularity of parallel manipulators can be categorized into inverse and forward kinematic singularities. Based on the kinematics, the inverse Jacobian matrix of the parallel manipulator is factorized into three parts as: limb length diagonal matrix, structure parameter matrix and the motion parameter matrix so that the singularity analysis becomes convenient. Because each limb length is not zero, there does not exist inverse singularity. Only forward kinematic singularity exists in the parallel manipulators. The forward kinematic singularity is divided into architecture singularity and motion singularity. Architecture singularity is global and results in no solutions for forward kinematics. It should be avoided at the design stage. The class of parallel manipulators becomes architecture singularity as long as their six vertices of the platform are placed in a quadratic curve. Since the architecture singularity can be algebraically expressed, the constraints to avoid the undesired effects of the architecture singularity can be straightforwardly implemented for the design of the parallel manipulators and the planning of workspace and trajectory.