The multi-mode robot has the characteristics of intelligent reconfigurable and variable structure, and can actively or passively adapt to the changing environment. The work aims to design a multi-motion mode parallel mechanism that can be applied in the field of packaging engineering. Based on the screw theory, by studying the correlation between the line vector and the couple in different geometric spaces, it was concluded that the constraint force could be transformed into the normal constraint couple under certain conditions, which provided theoretical support for the parallel mechanism to realize multi-mode motion. Through the deformation of the 3-(RRR)E(RR)S parallel mechanism, it was concluded that the mechanism had three motion modes of 3R, 2T1R and 2R1T, and the degree of freedom was 3 in each motion mode, with full-cycle mobility. Based on the 3-(RRR)E(RR)S parallel mechanism, the constraint conditions of the mechanism are changed by changing the spatial position relationship of the branch constraint force line vector, so that the parallel mechanism can realize 3R, 2T1R and 2R1T multi-mode motion. It meets the needs of logistics sorting, grasping and positioning, product space attitude adjustment, etc.