Aiming at maximizing the workspace of the parallel robot,a parallel robot mechanism model with four degrees of freedom was proposed.The parallel robot has the advantages of geometric symmetry,simple kinematics,and infinite expansion of the translational workspace along the direction of the linear guide.The projection method was used to simplify the displacement analysis,and the closed-loop vector method was used to analyze the instantaneous kinematics characteristics of the parallel robot mechanism.Through the rank analysis of the Jacobian matrix,the forward singular configuration,reverse singular configuration,combined singular configuration and local singular configuration of the Jacobian matrix were determined,and the local singular characteristics of the distal parallelogram with offset angle were studied.Based on the analysis of workspace,an optimization model with the objective function of the maximum area occupied by the mechanism was established,and the design parameters were optimized by genetic algorithm.The results show that when the offset angle is 15°,the reachable workspace increases by 17%.