The work aims to propose a 2-SPR/RUPR parallel mechanism for engraving and painting on arbitrary surfaces. The screw matrix of 2-SPR/RUPR parallel mechanism was established based on screw theory. The degree of freedom of the mechanism was calculated by modified G-K formula. The position inverse of the parallel mechanism was solved by geometrical method and D-H method. The 3D dynamic method was used to search the workspace of the mechanism and then the data points were imported into MATLAB for drawing the workspace. The inverse solution of the 2-SPR/RUPR parallel mechanism was obtained, and the working space was a solid mushroom cloud. An example of engraving and inkjet printing pattern on a surface was given. The mechanism can be applied for engraving and painting on curved surface, so that the cutter is perpendicular to the curved surface, thereby improving the effect of engraving and painting, and can realize engraving and painting on any curved surface.