The Bressesque Surface: Distribution of Screw Pitch

Abstract

Presented is an overview of the T-N interpretation of the famous planar Euler–Savary formula. The T-N spatial analog interpretation consists of two components: the established axial component along with a new transverse component. The axial component entails the spatial Euler–Savary relation involving the Disteli axis and motion parallel to the instantaneous screw axis (ISA). The transverse component emulates the classical planar Euler–Savary relation involving motion perpendicular to the ISA. Within the T-N interpretation is an inflection surface together with a family of Bressesque surfaces. Traditionally, a Bresse circle is a planar motion concept defined by points with zero tangential acceleration. Here, the Bressesque surfaces do not consider accelerations akin to the planar scenario. Instead, the Bressesque surfaces are defined as a linear combination of two axes of the inflection surface. These two axes are used to establish a skew axis gear set where the axodes are tangent along a generator of the Bressesque surface. This tangency is the ISA for the gear set. What is new is the screw pitch for each generator of the hyperboloidal Bressesque surface. Two graphs are shown: the first graph is the variation in screw pitch in terms of the ray angle and the second graph is the variation in speed ratio of the skew axes gear set in terms of the ray angle.