To meet the increasing requirements for precision hybrid machine tools, this paper presents a geometric error propagation model-based accuracy synthesis method for parallel manipulators (PMs) with one translational and two rotational (1T2R) motion abilities. A unified geometric error propagation model of a family of 1T2R PMs is established with the first-order kinematic perturbation method. A set of geometric error propagation intensity indexes is formulated to describe the geometric error propagation characteristics in a quantitative manner. The equivalent effects of specified terminal accuracy are derived to directly determine the allowable values of all geometric source errors. Based on these, a computation algorithm is summarized for designating a tolerance allocation scheme to meet the specified terminal accuracy of a 1T2R PM. To demonstrate the accuracy synthesis method, a novel 1T2R PM with a 2UPR-1RPS (“R,” revolute joint; “U,” universal joint; “S,” spherical joint; “P,” prismatic actuated joint) topology is taken as an example to allocate geometric tolerances under the specified terminal accuracy. Following the tolerance allocation scheme, a laboratory prototype of the exemplary PM is fabricated and further experimentally measured. The measured kinematic results indicate that the prototype possesses an acceptable position error smaller than 0.15 mm, verifying the feasibility of the proposed accuracy synthesis method. Hence, the proposed method can be applied as a forward tolerance design tool to reduce the design iterations and development risks of low-mobility parallel robots.