For a type of prismatic-joint revolute-joint universal-joint-2 prismatic-joint revolute-joint universal-joint pc-joint（PRU-2PRUPc） parallel mechanism without parasitic motion， the kinematics analysis is performed. Firstly， the analysis of degrees and parasitic motion of PRU-2PRUPc parallel mechanism are carried out based on screw theory. Secondly， the analytical solution of the motion kinematics is deduced， and the positive solutions are obtained using particle swarm optimization algorithm， verifying the correctness of the inverse solution， and using Adams for kinematics simulation verification. Thirdly， the singularity analysis of the mechanism is performed based on screw theory， and the singularity of the input and output are obtained. Finally， the analysis of the mechanism is performed based on motion/force transmission indices， and the performance of the parallel mechanism are plotted， laying a theoretical foundation for subsequent optimization and application.