The work aims to propose a 2-UPS/UPR/(rT)PS reconfigurable parallel mechanism with dual configuration for the printing and packing links on the product processing and packaging assembly line. Based on the screw theory, the number and properties of degrees of freedom of the mechanism in two configurations were analyzed. The degree of freedom calculation results were verified according to the modified Kutzbach-Grübler formula. The closed vector method was used to calculate the inverse kinematics of the mechanism under the two modes. The reachable workspace of the mechanism in two modes was solved. Through the analysis of application examples, the displacement change of the driving branch line of the mechanism during the two links of printing and packing was studied, and it was concluded that the mechanism could meet the requirements of printing and packing. The 2-UPS/UPR/(rT)PS parallel mechanism had two motion modes of 2R1T and 2R2T, and the workspace was continuous. The 2-UPS/UPR/(rT)PS reconfigurable parallel mechanism can be switched between 2R1T and 2R2T motion modes by changing the axis of the kinematic pair, which can be applied to the printing and packing of products.