For introducing a weakened line into a component 10, which is rigid per se and does not conform to a supporting mold or a receiving means in correspondence with the true shape, especially into an injection-molded part such as an instrument panel of an automobile, a device is provided comprising a multi-axis machine tool with a CNC-control suited for processing base-oriented programs, and a receiving means 11 for the component 10 to be processed, distance sensors 13 for the CNC-control being assigned to the receiving means to detect the actual three-dimensional position of the component.