Investigations of Gears Geometry Using the Surface Constructor Kinematical Modelling System

Abstract

In the area of production of machines there is a need for high quality gears that work with improved efficiency. The goal of the machine designers is to improve the characteristics of existing types of gearings or invent new ones. The paper introduces a powerful new theory, the „Reaching Model”, for generating enveloped kinematical surfaces that connect in spatial curves or to develop surface pairs connecting in a point-like manner because of the applied theoretical intermediary generating surface. The model and the software application based on it proved its suitability for gear surface development many times. The application implementing the theory provides advanced 3D visualization capabilities for displaying and animating kinematical surfaces, co-ordinate systems and other space attributes. This application has the Surface Constructor (SC) name and sets the goal of providing maximum freedom in modelling different kinematical surfaces and arrangements. For the entering of surfaces and motions, expressions can be used and symbolic algebraic computations carried out automatically behind the scenes. This complex application models the kinematical modelling process itself and can handle practically limitless types of gearings.