Geometric errors have an important effect on the pose accuracy of the parallel mechanism (PM). In order to reveal the influences of geometric error sources on the pose accuracy of the parallel mechanism and determine its optimal intervals, a 2UPR-RPS parallel mechanism was taken as an example to demonstrate the accuracy design of overconstrained PMs. An error mapping model of the parallel mechanism was established by using the firstorder perturbation method, based on which the geometric error sources that affected pose accuracy of the endeffector were obtained. The set of sensitivity index of the geometric error sources was formulated with the interval analysis theory and the sensitivity analysis was carried out to reveal the influence of the geometric error sources on the pose accuracy of the endeffector. Based upon the proposed sensitivity index, a accuracy synthesis model of the geometric error sources was established, in which the uniform design method was used to provide appropriate pose points within the workspace of the parallel mechanism. The optimal intervals of the geometric error sources of the parallel mechanism were derived and the accuracy class and the fitting tolerances of key components of the parallel mechanism were determined. The Pseudo Monte Carlo method of Sobol sequence was used to estimate the pose accuracy of the endeffector of the parallel mechanism. The simulation results showed that the optimal intervals of the geometric error sources obtained by accuracy synthesis met the accuracy requirements of the endeffector, confirming the feasibility of the accuracy design and providing a reference for the development of physical prototype.