Some geometrical aspects of skew polyangular involute gearing

Abstract

This paper deals with certain ongoing investigations that are part of a larger work. The larger work is not yet complete. An overall descriptive form of words, general spatial involute gearing, appears to be appropriate. This is intended to encompass all that gearing which (a) transmits between shafts that are skew, (b) employs paths for the points of contact (for drive and for coast) that are both straight and both located in space remote from the centre distance line, and (c) appeals to pure spatial involute geometry, namely the geometry of mating involute helicoids, for its kinematic synthesis and practical mechanical design. Methods to achieve nominated requirements such as centre distance, shaft angle, radial offset and tooth ratio naturally become available, and methods for machining the teeth based upon the known concept of phantom rack are seen to be possible. The field of polyangular architecture is a sub-set of the wider field, equiangular architecture is another, and ordinary planar involute gearing is a special case of the latter. Hypoid gearing, which is non-involute, is excluded.