Reduced-degree-of-freedom parallel mechanisms have advantages such as simple structure, low manufacturing cost, high motion accuracy, and high output strength. Among these, the 2R1T parallel mechanism is a typical example, finding applications in many fields. This paper proposes a configuration synthesis method for the 2R1T parallel mechanism based on the Atlas method. Building on the Atlas method theory, the principle of equivalent degrees of freedom, and Blanding’s rule, it reveals the relationship between the degrees of freedom diagram and the constraint diagram and presents a synthesis process. The configuration synthesis of the 2R1T parallel mechanism is carried out, using the 3UPU and 6UPU parallel mechanisms as examples. The quantity and properties of the degrees of freedom are analyzed based on screw theory and the modified G-K formula, verifying the correctness of the proposed method. The content of this paper offers valuable reference for the configuration synthesis of 2R1T parallel mechanisms and other parallel mechanisms.