Abstract: The positioning accuracy of precision positioning device in the plane is taken as the task-based requirement, a planar 2PR-R compliant parallel mechanism with two degrees-of-freedom was designed as the ontology configuration, its Jacobian matrix was built based on vector mapping relationship, so that its kinematic characteristics of multi-inputs and multi-outputs could be verified. Furthermore, a multi-objective function of the optimization problem was established by two sub-objectives of the static stiffness and first-order natural frequency as optimization objective, which was based on the kinematic characteristics of 2PR-R compliant parallel mechanism. Taking the Jacobian matrix of planar 2PR-R compliant parallel mechanism as motion constant and its material volume fraction as inequality constraint to build the numerical model for the optimization problem, and the optimization solution was solved by level-set algorithm. Finally, the boundary curve of optimization result is fitted by SolidWorks technology, and the static problem of the optimal configuration was analyzed based on OptiStruct. Results shown that the differential kinetic characteristics of planar 2PR-R compliant parallel mechanism optimal configuration is consistent with its parallel prototype mechanism, the positional accuracy is achieved at the micron level.