Mathematical model and undercutting of cylindrical gears with curvilinear shaped teeth

A rack cutter with a curved-tooth is considered the generating tool for the generation of the proposed gear, and a mathematical model of cylindrical gears with curvilinear shaped teeth is developed according to the gearing theory. The developed computer program can develop profiles of the curvilinear-tooth gear with point contacts. The developed gear tooth mathematical model is used to investigate the tooth undercutting of curvilinear-tooth gears via differential geometry and the numerical method.