Development of the Manufacturing Geometry of Conical and Cylindrical Worms by Analysing of Their Axoids

Abstract

In this paper an examination has been outlined a possibility of further generalization respecting the DudĂĄs?s kinematic-mathematical model, which is suitable for the production geometric development of elements of helicoid drive pairs. The positioning of the rolling surfaces of the cylindrical and conical surfaces, as axoids of worms, in the extended model to the projective space under the right conditions, based on the surfaces invariant to projective transformations can be a right extension of the model, as the projective space model includes the Euclidean space model in full. The machining of the conical worm surfaces modelled in this method involves the clarification of the kinematic-geometric relations of production geometry in the Euclidean space model, which shows the possibility of further development of production geometry. The goal of generalization of the mathematical description is the systematization by creating central collinear projective connection between axoids (rolling cones and rolling cylinders). Managing the production geometry of the worms in a system is also a further improvement in manufacturing precision.