Computerized design and mathematical modeling of spherical pivoting gears for variable shaft angles

Abstract

The development of gear drives that enable variable shaft angles or that are insensitive to large shaft angle variations has been a topic of interest across various industries for decades. Traditional approaches to developing such geometries present issues such as severe undercutting on tooth surfaces. This work introduces spherical pivoting gears as a type of gear drive that allows for shaft angles ranging from parallel to asymptotically approaching 90°. The computerized design and mathematical modeling of this type of gear geometry are presented and defined for unitary transmission ratios. To validate the obtained geometry, unloaded Tooth Contact Analysis (TCA) is conducted for several pivoting angles, revealing very low transmission errors that increase as the pivoting angle increases. Additionally, the geometry is evaluated under alignment errors and through Finite Element Analysis (FEA). Results indicate that the proposed design is feasible for applications requiring variable shaft angles, provided the transmitted torque remains low.