In order to address the problem of high manual dependence and difficulty in meeting the demands of rapid sorting and transporting when sorting and transporting various products in the logistics packaging production line, a RRU/(rR)PS/UPS (R: revolute joint, U: universal joint, rR: reconfigurable revolute joint, P: prismatic joint, S: spherical joint) reconfigurable parallel mechanism was proposed. Based on the screw theory, the degree of freedom and the rotation axis of the mechanism were analyzed. The inverse solution model of the mechanism position was established, and the parasitic motion of the mechanism in different modes was derived according to the geometric constraint conditions. The workspace and motion/force transmission performance of the mechanism in two modes were analyzed, and its singularity was analyzed based on the input and output characteristics of the mechanism. Finally, taking the workspace index and global transmission index of the mechanism under two motion modes as the optimization function, the particle swarm algorithm was used to optimize the size parameters of the mechanism. The results show that the mechanism can be switched between one-translation and two rotation (1T2R) and two-translation and one rotation (2T1R) motion modes through the rR joint. In both motion modes, it is a full-cycle degree of freedom mechanism with continuous rotation axis. In the two motion modes, the overall workspace of the mechanism is large, and the motion/force transmission performance is good, which can meet the requirements of various operation modes of the production line.