Nowadays, the main method of machining the gears with a module in the range 1–25 mm, which are integral parts of modern machines, remains hobbing. Operations of the toothed crown processing determine the efficiency of the entire technological process of manufacturing gears. Thus, the time expenses and performance, the cost of the gears, and their final quality depend to a large extent on these indicators in operations of hobbing. Considering the importance of this process for mechanical engineering, considerable attention of scientists is devoted to its modelling. Chip parameters are the key source of information required for comprehensive and complete analysis of the hobbing process. Despite the large number of publications devoted to this problem, there is still no methodology for adequate reproduction of these parameters. Known methods and models are characterized by significant simplifications and do not reproduce completely the kinematics of this complex process. This article presents a new approach to graphical modelling of the chip parameters in the hobbing process, which is based on the analysis and synthesis of elementary kinematic motions, related to unit motions and displacements of the hob cutting elements in the process of removing the metal in the gap between the teeth of the processed gear. The algorithm for forming the instantaneous transitional surface between the gear teeth and the three-dimensional (3D) space geometry of the chips on all active teeth of the tool is implemented in the graphic system AutoCAD. The article presents the results of computer modelling of chips in the climb and up-cut hobbing with Archimedean and convoluted hobs. Complete information on the geometric structure of the cut layers provides the basis for complex and system modelling of this process at the level of separate racks, teeth and edge of a hob. In combination with the data on the intensity of plastic deformation, stresses and temperature obtained for the corresponding conditions of hobbing in the Deform system, data on the parameters of the cut layers create opportunities for predicting the heating and wear of cutting elements of a hob, their loading, strength of protective coatings, transient processes of the cutting force and temperature, designing of optimal technological processes of hobbing and management of these processes.
 G. Sulzer, “Leistungssteigerung bei der Zylinderradherstellung durch genaue Erfassung der Zerspankinematik” [“Increased performance in cylinder wheel production through accurate detection of the cutting edge kinematics”], PhD dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, North Rhine-Westphalia, Germany, 1974. [in German].
 P. Gutman, “Zerspankraftberechnung beim Wälzfräsen” [“Cutting force calculation during hobbing”], PhD dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, North Rhine-Westphalia, Germany, 1988. [in German].
 G. Venohr, “Beitrag zum Einsatz von hartmetall Werkzeugen beim Waelzfraesen” [“Contribution to the use of carbide tools during rolling”], PhD dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, North Rhine-Westphalia, Germany, 1985. [in German].
 K. Joppa, “Leistungssteigerung beim Waelzfraesen mit Schnellarbeitsstahl durch Analyse, Beurteilung und Beeinflussung des Zerspanprozesses” [“Increasing the performance of rolling with high-speed steel by analyzing, assessing and influencing the cutting process”], PhD dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, North Rhine-Westphalia, Germany, 1977. [in German].
 J. Tondorf, “Erhoehung der Fertigungsgenauigkeit beim Waelzfraesen durch systematische Vermeidung von Aufbauschneiden” [“Increasing the manufacturing accuracy of the rolling process by systematically avoiding built-up edges”], PhD dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, North Rhine-Westphalia, Germany, 1978. [in German].
 A. Antoniadis, “Determination of the impact tool stresses during gear hobbing and determination of cutting forces during hobbing of hardened gears”, PhD dissertation, Aristoteles University of Thessaloniki, Thessaloniki, Greece, 1988.
 A. Antoniadis, N. Vidakis, and N. Bilalis, "Fatigue Fracture Investigation of Cemented Carbide Tools in Gear Hobbing, Part 1: FEM Modeling of Fly Hobbing and Computational Interpretation of Experimental Results", Journal of Manufacturing Science and Engineering, vol. 124, issue 4, pp. 784-791, 2002.
 A. Antoniadis, N. Vidakis, and N. Bilalis, "Fatigue Fracture Investigation of Cemented Carbide Tools in Gear Hobbing, Part 2: The Effect of Cutting Parameters on the Level of Tool Stresses – A Quantitative Parametric Analysis", Journal of Manufacturing Science and Engineering, vol. 124, issue 4, pp. 792-798, 2002.
 V. Sinkevicius, "Simulation of gear hobbing geometrical size", Mechanika, vol. 5, no. 50, pp. 34-39, 1999.
 V. Sinkevicius, "Simulation of Gear Hobbing Forces", Mechanika, vol. 3, no. 28, pp. 58-63, 2001.
 M. Komori, M. Sumi, and A. Kubo, "Method of preventing cutting edge failure of hob due to chip crush", JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing, vol. 47, issue 4, pp. 1140-1148, 2004.
 M. Komori, M. Sumi, and A. Kubo, "Simulation of hobbing for analysis of cutting edge failure due to chip crush", Gear Technology, pp. 64-69, September/October 2004.
 V. Dimitriou, N. Vidakis, and A Antoniadis, "Advanced Computer Aided Design Simulation of Gear Hobbing by Means of Three-Dimensional Kinematics Modeling", Journal of Manufacturing Science and Engineering, vol. 129, pp. 911-918, October 2007.
 K.-D. Bouzakis, S. Kombogiannis, A. Antoniadis, and N. Vidakis, "Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models", Journal of Manufacturing Science and Engineering, vol. 124, pp. 42-51, February 2002.
 I. Ye. Hrytsay, “Modeliuvannia parametriv zriziv, syl ta momentiv pid chas narizannia zubchastykh kolis cherviachnymy frezamy” [“Simulation of the parameters of sections, forces and moments during the cutting of gear wheels with worm cutters”], Mashynoznavstvo [Mechanical Engineering], no. 7, pp. 19-23, 1998. [in Ukrainian].
 I. Ye. Hrytsay, V. V. Sytnik, “Sylove pole shnekovoi zuboriznoi frezy ta yoho kilkisna otsinka” [“Power field of a screw cutter mill and its quantitative estimation”], Visnyk Natsionalnoho universytetu "Lvivska politekhnika" [Bulletin of Lviv Polytechnic National University], no. 371, pp. 3-13, 1999. [in Ukrainian].
 V. Stupnytskyy, “Features of Functionally-Oriented Engineering Technologies in Concurrent Environment”, International Journal of Engineering Research & Technology, vol. 2, issue 9, pp. 1181-1186, September 2013.
 V. Stupnytskyy, “Thermodynamic pattern of the workpiece machining by the rheological imitation modelling in DEFORM-3D system”, Visnyk Natsionalnoho universytetu "Lvivska politekhnika" [Bulletin of Lviv Polytechnic National University], no. 772, pp. 102-114, 2013.
 V. Stupnytskyy, “Computer Aided Machine-Building Technological Process Planning by the Methods of Concurrent Engineering”, Europaische Fachhochschule [European Applied Sciences], vol. 2, no. 3, section 1, pp. 50-53, 2013. [in Ukrainian].