Abstract: In this paper, the background for formation of the theory, its main missions and main features, and its main scopes of applications are concisely narrated. General problems of the theory are abstractly presented. Some fundamentals of the theory, such as finite rotation of vector about fix-oriented axis, engineering differential geometry, conjugate motions, conjugate geometrical configurations, problem of contact-drive, and tooth form of PK conjugation, are concisely presented. Two illustrative examples of application of the theory are cited.