Abstract: A novel absolutely symmetrical 3-R（4r）（4r）R parallel mechanism with three translational degrees of freedom is proposed. Based on the screw theory, the mechanism principle of achieving the three-dimensional translations is analyzed, and the drive input joints are chosen and discussed, and the platform singularity and the drive singularity and the branch singularity of the parallel mechanism are analyzed. Then, the kinematics model is established, and the analytic solutions of the inverse and forward positions are obtained. By use of numerical simulation, the correctness of the inverse and forward position solutions are verified. The research results show that there is no platform singularity in the parallel mechanism, and the kinematic model is simple, and the forward position solution is unique.