This article presents an efficient and direct method for the synthesis of compound planetary differential gear trains for the generation of specified multiple speed ratios. It is a train-value method that utilizes the train values of the integrated train components of the systems to form design equations which are solved for the tooth numbers of the gears, the number of mating gear sets and the number of external contacts in the system. Application examples, including vehicle differential transmission units, rear-end differentials with unit and fractional speed ratios, multi-input functions generators and robot wrist joints are given.

March 19-22, 1989. First International Applied Mechanical Systems Design Conference. Convention Center, Nashville, TN. April 25-27, 1989. ASME 5th Annual Power Transmission & Gearing Conference, Chicago, IL

Involute spur gears are very sensitive to gear misalignment. Misalignment will cause the shift of the bearing contact toward the edge of the gear tooth surfaces and transmission errors that increase gear noise. Many efforts have been made to improve the bearing contact of misaligned spur gears by crowning the pinion tooth surface. Wildhaber(1) had proposed various methods of crowning that can be achieved in the process of gear generation. Maag engineers have used crowning for making longitudinal corrections (Fig. 1a); modifying involute tooth profile uniformly across the face width (Fig. 1b); combining these two functions in Fig. 1c and performing topological modification (Fig. 1d) that can provide any deviation of the crowned tooth surface from a regular involute surface. (2)