Synthesizing an Internal Bevel Gear

A method of synthesis of an internal bevel gear by coefficients of profile shift and shaft angle is presented. Formulas for calculating qualitative rates are derived: slip ratio, specific pressure ratio and overlap ratio. It is noted that such gear in comparison with the external bevel gear is characterized by better qualitative rates. These calculated dependencies are the basis for the work of the Internal bevel gears x64 program to generate macros for modeling such gear. The internal toothed wheel can be manufactured on a three-, four-, or five-axis CNC milling machines, as well as on a 3D printer.