Redesign of a spatial gear pair using configuration spaces

This paper presents an industrial case study in which a spatial higher pair is redesigned using our configuration space method of kinematic analysis. The task is to remove occasional blocking in an asynchronous reverse gear pair from a car transmission. A systematic kinematic analysis is required because the blocking configurations are unknown and because very few initial configurations cause blocking. We use our configuration space method of kinematic analysis to solve the problem. We determine why the gears block by constructing a series of twodimensional configuration spaces that model the engagement kinematics. Blocking occurs when two consecutive pairs of teeth make contact during engagement. The gear angles at the contact determine whether or not the gears will block. Our analysis determines that blocking occurs in 4% of the angle space. Fine tuning the gear parameters reduces the range to 0.5%, but cannot eliminate the blocking. Removing every second gear tooth eliminates the blocking. The analysis results are consistent with the experimental data. The case study demonstrates that the configuration space method helps solve industrial problems that are outside the scope of prior work.