The Synthesis of the Pitch Surfaces of Internal and External Skew-Gears and Their Racks

Abstract

The synthesis of the pitch surfaces of any pair of external and internal skew gears, using dual algebra and the principle of transference, is the subject of this paper. The spatial motion of the Euclidean space is transferred to the dual space in order to obtain a simplified dual spherical motion, thus emulating the motion of bevel gears. The relative screw motion is hence analyzed by determining the position of the instant screw axis and the angular and sliding velocities. Moreover, the hyperboloid pitch surfaces of the driving and driven gears are synthesized, along with the helicoid pitch surface of their rack. Several numerical results are reported.