Abstract: In order to supply a reasonable design method for involute gear pair with variable shaft angle, this kind of gear pair is studied based on the gear meshing theory of two degrees of freedom. The formulae of calculating the position of the swing axle of the two gear stands and the working width of the mated gear are derived according to what there is no undercut on the face of the mated gear within the range of shaft angle, the permissible minimum and maximum value of the distance between the swing axle and the axle of the involute gear are obtained; the formula to calculate the contact ratio different shaft angle is obtained; the parameters of instanta-neous contact ellipse of the meshing point are deduced. The results indicate the working width of the mated gear reach the maximum value when the distance between the swing axle and the axle of the involute gear is closed to the permissible maximum value; the maximum contact ratio is obtained when the absolute value of the maximum shaft angle is chosen and the minimum one is gained when the shaft angle is zero; the parameters of instantaneous contact ellipse of the meshing point on the reference circle of the middle section of the mated gear are very close to the average value of other points, therefore, the contact quality can be evaluated according to this point, which can greatly simplify the calculation. A set of exhaustive methods of the geometric design of this kind of transmission is supplied.

Key words: Involute gear, Transmission with variable shaft angle, Two degrees of freedom