Abstract: A profile-shift-modification method for the involute gears is worked out, in which the modification coefficient varies with the position of the pitch-lines of gears, and is applied to design non-circular gear transmission. The model of the generating rack with a modification shift amount, and the pure-rolling model are set up separately, and then joined together by using the so-called equation of mesh, to obtain the mathematical model of tooth profile in the coordinate system of the gear. According to the feature that the curvature radius of the pitch-lines of the non-circular gears varies with the rolling points of the pitch-lines, it is put forward that the coefficients of profile-shifted-modification are determined by the pitch-lines. In the end, for the high-order elliptical gears, fabricating a modification coefficient with cosine function of the pitch-line position, their teeth profiles described to verify the correctness of the model.

Key words: Conjugate rack, Graphic simulation, High-order elliptical gears, Non-circular gear, Profile-shift-modification