Abstract: For the redundantly actuated parallel robot with both translational and rotational degrees of freedom (DOFs), anoptimal design method is proposed. Firstly, a parallel robot bio-inspired by human jaw is introduced, with a 6-PUS (prismaticuniversal-spherical) parallel mechanism imitating 6 main masticatory muscles and 2 passive HKPs (higher kinematic pairs) imitating mandibular joints. As characteristics of the mechanism with passive HKPs are considered, the dimensionallyhomogeneous Jacobian matrix of the robot is established by using the pose description method based on the three points onthe end-effector. Then, an optimization method of the redundantly actuated parallel robot is given, based on analyses on howthe velocity error transmission performance is effected by the structure and dimension of the robot. Finally, the performanceindex is set to perform the dimension optimization of the redundantly actuated parallel robot. The global error standarddeviation decreases by 39.83% compared with that of the robot configuration before optimization. The results show that theproposed optimal design method improves the velocity transmission performance of the parallel mechanism, and it can beextended and applied to the optimal design of other robots.