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A novel computer graphics and computer aided geometric approach is used for machining a complicated shape workpiece and lettering on a 3D free surface or a plane by adopting a novel 3-DOF(Degree of Freedom) parallel robot. Based on the geometry constraint and dimension-driving technique, a 3-UPRR parallel simulation mechanism and its workspace are created. Then a 3D free surface and a guiding plane of tool path are constituted, and combined with the 3-UPRR parallel robot. Finally a novel 3-UPRR simulation parallel machine tool for machining a 3D free surface is created. By real-time controlling two driving dimension on the guiding plane, the process of machining complete. The simulation results are verified by the analytic results. The computer aided geometric variation approach has the advantages of simple and straightforward, without any need of compiling program.