Based on the single-opened-chain (SOC) unit theory, a new parallel mechanism with two translational and one rotational（2T1R）degrees of freedom was put forward. First, the degrees of freedom and the motion output characteristic were analyzed, and then both the forward and the inverse analytical solutions of the moving platform’s position were obtained. The singular configurations of the mechanism were also discussed; the change of the position with respect to the pose angle in singular configuration was obtained through programming with Matlab software. All the above analysis provides foundation for the further research on properties and dynamics of the mechanism. 