Differential Contact Path and Conjugate Properties of Planar Gearing Transmission

Abstract

This paper presents a general conjugation model based on the intrinsic kinematical properties of the contact path. The model is truly general for any planar transmission through contact curves, such as gearing. The effectiveness of the method is not affected by the type of centrodes or motion and path of contact. With the method, for any given centrodes and any chosen path of contact, the corresponding conjugate curves can be identified and the geometric properties of the conjugation can be determined even before the conjugate curves are found. The method is demonstrated with straight, circular, and polynomial paths of contact in both circular and noncircular gears. The versatility of the theory and the outstanding features of the method become obvious with treating arbitrary centrodes or any planar motion transmission. The freedom of selecting contact path suggests the possibility of optimal conjugation design.