Alternative formulation of the theory of gearing

In this paper the theory of gearing is presented by means of a new approach that does not need reference systems. All equations are written in terms of vectors and therefore are valid regardless of the reference system actually employed. The overall formulation becomes more compact and clearer. As an example, the proposed approach is applied to the generation of spiral bevel gears. To actually perform all calculations, only one reference system is required, thus avoiding the chain of reference systems typical of the traditional approach.