A two translation one rotation (2T1R) parallel robot mechanism with zero coupling degree and symbolic position forward solution was designed by using the parallel mechanism topology design theory and method based on position and orientation characteristics (POC) equation.The POC,degree of freedom and coupling degree of the mechanism were analyzed and calculated and so on.Based on the characteristics of the kinematic pair arrangement of the mechanism,the kinematic equation was established,and the position analytical expressions of forward kinematics and inverse kinematics were calculated.The reliability of the calculation results was verified by a group of examples.The singularity of the mechanism was studied and the conditions for the singularity of the positive solution and the inverse solution were given.The workspace of the mechanism was analyzed.Taking the given workspace as the constraint condition,the optimization objective of the actual workspace minimization was established,and the optimal solution of the design structure parameter size satisfying the given workspace and minimizing the actual workspace was obtained by beetle swarm optimization algorithm.The results show that the mechanism has symbolic positional positive solution,regular workspace shape,symmetrical distribution and smooth boundary.