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According to the theory and method of topological design of parallel mechanism（PM） based on position and orientation characteristic （POC） equation, a three degree of freedom two translation and one rotation （2T1R）spatial parallel mechanism with zero coupling degree and one redundant branch chain was proposed. The topological analysis and kinematics analysis of the PM were carried out. Because the coupling degree of the PM was zero, it was easy to solve the symbolic forward position solution, which verified the correctness of the forward and inverse kinematics solution. Three kinds of possible singular positions of the PM were analyzed, and the singular configuration diagram of the PM was drawn; the Cartesian stiffness model of each branch chain was established by using the virtual spring method, and the stiffness distribution diagram of each branch chain and the whole mechanism was obtained by using Matlab software. At the same time, the change trend of torsional stiffness and linear stiffness in Cartesian stiffness matrix was given and analyzed, and the influence of redundant branch chain on the overall stiffness performance was discussed. The results showed that the PM had symbolic positive position solution and partial motion decoupling characteristics, and its passive redundant branch chain can avoid singular position; improve the kinematic performance of the PM; increase the stiffness of the PM; and make the mechanism more flexible. The construction had a wider application. At the same time, it was verified that the overall stiffness performance of the PM can be increased by 22% by using the redundant branch chain. The research result provided a theoretical basis for the PM based pipe bender prototype design.