Algorithms of generating cuspidal edges of developable surfaces

Ruled surfaces (torses) are widely used when designing surfaces of machine parts, architectural projects, building structures, plow-bottom surfaces, etc. A ruled surface is generated by moving a straight line continuously in a straight line space in predetermined manner. Otherwise, a ruled surface is a one-parameter set of lines. Ruled surfaces are handy for practical application, since they can be manufactured from rectilinear elements widely provided by modern industry. All ruled surfaces are in divided into two types: developable and nondevelopable. Torses can be superposed on a plane by means of flexural deformation without strain and compression. This property of developable surfaces makes possible to easily produce them from flat materials. It is common knowledge that a torse is a surface which represents a set of lines being in contact with a given spatial line. A line which is tangent to all generatrices is called a cuspidal edge of the given developable surface. Thus, creation of spatial lines is a main point in designing developable surfaces. The article deals with algorithms of generating spatial lines by means of rolling machines for cylinders, cones and generalized torses that can be used hereafter as cuspidal edges when designing developable surfaces.