The work aims to propose a low coupling degree three translation spatial parallel mechanism to solve the complicated kinematics analysis, dynamics analysis and error analysis caused by the complex structure and high coupling degree of the three translation parallel mechanism. Topological parameters such as DOF, coupling degree and azimuth feature set of the mechanism were analyzed. The analytic expressions of forward and inverse solutions of the kinematic position equations were established and verified by an example. At the same time, according to the calculation of Jacobian matrix, the existence conditions of the singularity of positive position solution and the singularity of inverse position solution were derived. Furthermore, the operating space of the mechanism was studied and a three-dimensional shape map of the operating space was obtained. In addition, the mathematical model with the goal of motion dexterity and operation space volume was established. The objective function expression was given. The NSGA-Ⅱ algorithm was selected to complete multi-objective parameter optimization with Pareto solutions. The analysis showed that the outer boundary of the workspace was smooth and there was a cavity inside, which was a hemispherical structure. The optimal value of both volume and global dexterity can be taken into account when selecting parameters in a relatively balanced and gentle area, so as to provide reference for this type of mechanism in sorting, packaging and other application fields.