Profiling of the Generating Rack of an Ordered Curl Known in Discrete Form by the Virtual Pole Method

Situations encountered in “reverse engineering” are relatively common in which, to address a problem of profiling generating tools for processing an orderly curl of surfaces (cylindrical or helical teeth), data known by measuring the existing product are used. The surface numerical representation can be done in the form of a points cloud. The profiling algorithm proposed in the paper is based on the possibility of measuring surfaces and their representation through an ordered cloud of points. The algorithm uses the complementary theorem of the virtual pole, for profiling the rack tool generating a piece that has an ordered curl of profiles. The methodology is not limited to the profiling of the rack tool but can be extended to the problem of profiling the primary peripheral surface of some screw-type tools, generating the ordered curl of surfaces. The paper also presents a numerical application developed based on a specific software product.