A kinematics parametric method to generate new tooth profiles of gear sets with skew axes

The geometric characteristic of tooth profiles of gear sets with skew axes can be studied by using the parametric polar angular (pressure angle) function, the meshing equation, and the constraints of continuity conditions. In this paper, the general mathematical model of skew gear sets, their numerical solution methods and special analytic solutions are presented. These can be used to investigate the inherent characteristics of skew gears and architect special gears such as bevel gears when the small pinion offset above or below the center of the gear is made equal to zero, helical gears or spur gears if the shaft twisting angle is equal to zero. Two examples are presented to demonstrate the application of the mathematical model developed in this paper. The first example is proposed to synthesize new skew gear sets when the special twisting angle for crossed axes and rotation speed ratio are given. The second example is deduced to demonstrate the special case for the spherical crown gears with skew axes.