The kinematics of the rotary into helical gear transmission

A higher kinematic pair that converts rotary motion into helical motion is presented as an alternative to the screw joint (a lower kinematic pair). First, the existence of a rolling transmission pair for a rotary-to-helical motion conversion is proven. Then, the corresponding pair of rolling surfaces (pitch surfaces) and their relative position is defined for any set of kinematic transmission parameters. Some calculated examples are presented. A method for gear-tooth forming from the pitch surfaces using Boolean operations with a computer-aided design (CAD) program is proposed. Finally, applying this methodology, a pair of gears for rotary into helical transmission has been obtained using a 3D printer. The prototype presents negligible clearances and backlash, high reversibility, as well as continuous gearing without interference. The meshing equation for a simple generating surface is also provided.