According to the theory and method of topological structure design of parallel mechanism (PM) based on position and orientation characteristic (POC) equation, firstly, a low coupling parallel mechanism of three translation and one rotation (3T1R) was designed, and its topological structures were analyzed, including POC, degrees of freedom and coupling degree. It was shown that the PM had partial motion decoupling, but the coupling degree of the PM was one (k=1). That meant only the numerical solutions of direct position solution can be obtained, which was not conducive to the subsequent scale optimization, error analysis and dynamic analysis. Therefore, the topology decoupling optimization design was carried out, that was, the coupling degree k=0 and the symbolic direct position solution can be obtained under the condition that the basic functions (DOF, POC) and partial motion decoupling remained unchanged. Secondly, using the kinematics modeling principle based on topology characteristics, the symbolic direct position solution of the optimal mechanism was solved. Furthermore, based on the derived Jacobian, the conditions for singularity of the mechanism were analyzed. Finally, based on the inverse position solution and the direct position solution, the workspace of the mechanism was solved. It showed that the workspace analysis based on the direct position solution had the advantages of simple calculation process and less calculation amount. The work can lay a foundation for the subsequent scale optimization, error analysis and dynamic analysis of the mechanism.