Parallel mechanisms (PMs) with two rotational and one translational (2R1T) degrees of freedom (DOFs) have attracted much attention these years. The 2R1T PMs can be divided into various categories due to different motion patterns, such as the UP equivalent PMs, the RPR equivalent PMs, the PU equivalent PMs and the 3-PPS equivalent PMs. In this paper, the 2R1T PMs have the same motion characteristics with the 3-RSR PM are studied and synthesized. This kind of PMs can be called as 3-RSR equivalent 2R1T PMs. The 3-RSR equivalent 2R1T PMs can realize both continuous rotations about fixed axes and continuous translation along fixed directions. The constraint and motion characteristics of the 3-RSR equivalent 2R1T PMs are analyzed. The design of the branches for the 3-RSR equivalent 2R1T PMs is dealt with using the screw theory and the subchains. A group of novel 3-RSR equivalent 2R1T PMs are obtained.

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