Geometry design of an elementary planetary gear train with cylindrical tooth-profiles

This work presents a concept of elementary gear trains such that the tooth-profiles of the pinion are cylindrical. The pitch radius is replaced by the distance between the gear center and the tooth center as the radius of gears. Based on coordinate transformation, triple vector product of differential geometry, and theory of conjugate surfaces, equation of meshing is derived. A program is developed to solve the conjugate surface equations, and to show the solid modeling of the proposed elementary planetary gear trains.