Abstract: In machine, using the modified gear can raise the strength of tooth drastically but do not add to the manufacture cost. However, owing to the trigonometric and involute function have to be used frequently when calculating the engagement equation and a transcendental character can not be avoid in the equation when driving with the intersecting axl, the geometric calculation of gear is too inconvelent to apply the modified gear widly. Author converts the engagement equation into Maclaur in Seriesn to result. in a set of simplified equation. By means of it can calculate the engega went equation rapidly and accurately Besides, it still trues of the case, in which the original tooth profile is equal to the arbitrary value. Hence, the simplified equation offers appropriate sense in theory and application.