The use of free form bevel gear generators was limited by the processes currently available to cut bevel and hypoid gears with face cutter heads. Since a free form cutting or grinding machine has three rotational and three linear freedoms it is possible to perform all possible relative movements between the cutter and the work during the generation process. The universal motion concept is applied to axes of the basic gear generation model only. It allows each of them to change the setting during the generation process according a higher order function. This approach enables a free form gear machine to produce an entire variety of modifications to the flank surfaces.