A Method of Local Synthesis of Gears Grounded on the Connections Between the Principal and Geodetic Curvatures of Surfaces

A spatial gear-mechanism with double curvature tooth surfaces is discussed. The following results are obtained: a) the relationship between the principal curvatures of the surfaces, b) the conditions under which the path of the contact point on the surface is a geodetic line in the local sense. A method of synthesis of mismatched gearing proposed here permits determination of optimal conditions of meshing in the vicinity of the main contact point.