The works of Prof. B. A. Perepelitsa from Kharkov Polytechnic Institute and his disciples to develop an applied methodology of multiparameter mappings in relation to the profiling and functioning of complex curvilinear objects and transmission mechanisms in mechanical engineering, mainly with examples of gears, are presented. The completed review is gratefully devoted to the 10th anniversary of Fiability & Durability Journal, which has repeatedly provided its platform to the authors to highlight this development of the wide Romanian, European and world scientific community.
