Abstract
In the paper there are considered procedures for designing a transition curved tooth leg of helical cylindrical gears. A significant parameter of a transition curve is a diameter of boundary points. The boundary point diameter belongs to a bottom point of the involute profile of the teeth side surface of a gear ring. The boundary point position must be lower of the design end point of the involute profile defined by the designer of gearing. A diameter value depends upon a great number of production factors: a profile and wear of a grinding disk, setting up parameters, teeth machining modes of a gear ring, but it is impossible to ensure the specified values of the diameter of boundary points without a correct design solution in the course of the form choice of milling cutter protuberance. The solution on protuberance acceptable parameters of a gear-cutting tool is made by the designer of a cutter during graphic run-in fulfillment. In the paper there are revealed conditions under which arise mistakes in the course of graphic run-in fulfillment within the limits of one teeth pitch of a milling cutter. There are shown recommendations for the fulfillment ensuring the diameter dimension of boundary points of the transition curve specified by the designer of gearing. The data on the design parameter impact of the hob protuberance upon the continuance of cutting edge interaction are shown. There are recommendations given to prevent undercut arising caused by the fulfillment of graphic two-dimensional run-ins of cylindrical helical gears. 
 The work purpose: the elimination of tooth leg excessive undercut in helical cylindrical gears with the protuberance of a worm milling cutter at the expense of the fulfillment of graphic run-in conditions. 
 The investigation methods: the graphical modeling of a run-in process. 
 The investigation results and novelty: there are defined conditions of arising an excessive undercut in the tooth leg of helical cylindrical gears during the fulfillment of graphic run-ins of a tool rack. 
 The conclusions: for mistake prevention in the calculations of the protuberance geometrical parameters of the helical milling cutter the graphic run-in must be carried out not less than on the 1.5 pitch of the milling cutter.
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