Comparison of different methods in gear curvature analysis using a new approach

In the literature, some methods for curvature analysis of gears can be found, apparently very different from one another. This article presents a comparison of three approaches to stress their similarities or differences and field of application: the classic one by Litvin, its development by Chen and another one proposed by Wu and Luo and revisited by the present authors. All these methods are re-examined and expressed in a new form by means of a new approach to the theory of gearing that employs vectors and tensors. An extension of the relative motion is also considered, assuming translating axes of the gear pair and modified roll