The work aims to propose a novel three-translation pad printing machine based on 2-CPR/UPS parallel mechanism, so as to expand the application filed of parallel mechanism and improve the pad printing quality. The degree of freedom of mechanism was solved by screw theory, and verified with modified Kutzbach-Grübler formula. The Jacobian matrix mathematical model of the mechanism was established. The limit coordinate search method was used to solve the workspace. The singularity of mechanism was analyzed based on Jacobian matrix. The distribution of dexterity index in the workspace was obtained. The mechanism could realize three-translation motions. The shape of the workspace was cuboid, and the interior was continuous without cavity and singular position. The dexterity index was uniformly distributed in the workspace. The novel three-translation pad printing machine can satisfy the requirements of the movement and working range during pad printing. The research results show that the mechanism has no singular position in the workspace and has good dexterity performance.