Kinematics of transmissions consisting of an outboard ball joint and an inboard generalized tripod joint

Abstract

This paper presents the kinematics of transmissions consisting of an outboard ball joint close to the wheel and a tripod joint close to the gearbox. Emphasis is placed on the intrinsic properties of the tripod joint owing to the orthogonality between the tripod legs and the intermediate shaft. In particular, it is shown that the roller-tripod centre distances are available analytically with a mere dependence on the intermediate shaft rotation angle and the joint angle. For the whole transmission, the kinematics reduces to two non-linear equations with the upper two angles as unknowns. Following numerical simulations, an approximate solution is proposed for evaluating the departure from constant velocity behaviour. A generalized joint derived by bending the tripod legs and the tulip ramps is introduced, and the influence of these geometrical modifications on the roller-to-tripod centre distances is shown. Optimization techniques based on evolutionary algorithms have been introduced for minimizing the generation of vibrations caused by roller-to-tripod movements. In many of the examples shown, geometric approaches have been used both for illustration and calculation.