Еквидистанти на сферични циклоиди

Abstract

Plane cycloids can be obtained from two rolling in cylinders with parallel axes. If these cylinders are transformed to tangential cones with coincident vertexes the plane cycloids become space cycloids. The mathematical description of the movement of a rolling cone over a static cone can be presented by matrix calculations or by transformations of an initial coordinate system, which is connected with the static cone. The obtained curve is a spherical cycloid. The application of the spherical cycloids is closely connected with the description of their equidistants. In this paper the mathematical models of spherical cycloids and their equidistants is derived by transformations of the initial coordinate system. Examples for equidistants of different types of space cycloids are obtained and shown.