Principal Planes and Principal Reference Systems Associated with a Gear Pair

For a gear pair with a specified set of the design parameters, a corresponding vector diagram for the rotation vectors can be constructed. Use of the principal directions allows for construction of a set of principal planes and principal reference systems associated with a gear pair. By means of the principal planes and principal reference systems, the analysis of gearings of all types can be significantly simplified. Multiple reference systems are commonly applied when investigating a gear pair. For the analytical description and investigation of the kinematics of gear pairs and the geometry of the interacting tooth flanks of the gear and a mating pinion, corresponding reference systems are used. To investigate the kinematics and the geometry of a gear pair, all the components need to be analytically described in a common reference system. Coordinate system transformations are necessary to represent the entire gearing in a common coordinate system.