Since parallel mechanisms (PMs) have good stiffness, accuracy, and dynamic characteristics, a large number of PMs have been invented recently. A few kinds of them are found to have excellent performances, and one kind is two-rotational and one-translational (2R1T) PM. The existing research on 2R1T PMs shows that this kind of mechanism has outstanding rotational properties and a well-translational workspace. Many 2R1T mechanisms with good performances have been proposed, among which the typical ones are 3PRS, 2UPR-SPR, and 3UPS-UP. Based upon the existing 2R1T mechanisms, a new 2R1T mechanism, 2UPR-PRS, is proposed and analyzed in this paper, which combines PRS and UPR chains, respectively, from 3PRS and 2UPR-SPR together. In this way, the high stiffness provided by the PRS chain and the variable rotational characteristics from two symmetric UPR chains are integrated into the proposed 2UPR-PRS mechanism. First, the conceptual design of this mechanism is carried out. Second, its inverse kinematics is solved. Finally, the mobility of the mechanism is analyzed by a newly developed method through a parameterizing twist in a continuous motion manner, and its kinematic model is thus formulated, revealing the rotational characteristics of the mechanism with the variable axis.