The work aims to design a new closed loop parallel mechanism with ball joints, and analyze its position solution and working space, in view of the excellent motion performance of the 4S closed-loop structure. The mechanism model was firstly established for the designed closed-loop parallel mechanism. Then, the constraint screw was used to calculate its degree of freedom. Secondly, the forward and inverse position solution was solved based on the numerical method and its correctness was verified by the corresponding motion example. Finally, the numerical search method was used to solve the working space and for the analysis. The moving platform could realize 3 degrees of freedom around the y-axis rotation, and of the movement along y and z directions. The working space of the closed-loop parallel mechanism was continuously stable and had no holes within the range of constraint parameters. The three-branch and 4S closed-loop parallel structure reduces the over-constrained and singular-position type, has excellent motion performance and large motion space, and considerable application prospects in the field of parallel machine tools and industrial robots.