Singularity Analysis and Singularity Crossing Control of a Five-Bar Parallel Manipulator

This paper presents singularity analysis and singularity of type 2 crossing control of a two-degrees-of-freedom five-bar parallel manipulator. Firstly, the kinematics constraint equations of the manipulator is established, the velocity Jacobian matrix is obtained by differentiating the equation with respect to time. Based on jacobian matrices the forward and inverse singular loci are presented in the workspace. Secondly, the dynamic model of the closed loop systems is established in matrix form by applying the Lagrangian equation with multipliers. The trajectory tracking controller is designed based on the inverse dynamics and simple PD in operational space. Numerical simulations are carried out to verify the efficiencies of the proposed method.