Kinematic Modeling for the Nutation Drive Based on Screw Theory

The paper describes a study of a relative screw motion of a pair of internal and external spiral bevel gears with double circular-arc tooth profile in a nutation drive by screw theory and focuses on the kinematic modeling for the nutation drive. According to the instantaneous screw motion theory, the meshing function of the nutation drive for the kinematic modeling is developed based on the gear meshing theory and the coordinate system transformation between a crown gear and an internal or an external spiral bevel gear. The equations for the tooth profile of the crown gear, internal and external spiral bevel gears are further obtained based on the standard double circular-arc tooth profile and equal strength principles. Finally, the controllable precision three dimension modeling method for the tooth profile of the external and internal spiral bevel gears is further proposed.