Gear shaped cutter – a profiling method developed in graphical form
The classical methods for the study of enveloping surfaces are known as basic methods, such as Olivier theorems, Gohman method or Willis theorem. Other methods are known as specific methods, as, for example, the Nikolaev method for profiling tools which generate helical surfaces, or complementary methods for the study of enveloping surfaces. This paper presents an alternative method – the method of relative trajectories – for profiling tools which generate by enveloping ordered curls of profiles associated with a pair of rolling centrodes. An analytical argument is presented, for the study of generation using gear shaped cutter as well as a graphical method developed in CATIA design environment, using capabilities of this software. Numerical applications are also presented, including a comparison between the results obtained with an analytical method and the results obtained with the graphical method, in order to prove the quality of the proposed method.