Geometry of Homokinematic Spatial Cardan Shafts by Dual Methods

Abstract

The structure of a Hooke or Cardan universal joint is a spherical four bar linkage. This linkage has in general a varying velocity transmission ratio. To get a homokinematic transmission, it is necessary to use at least two Hooke joints in a track of three shafts, the input shaft, the intermediate shaft and the output shaft. During a constant angular velocity of the input of the first Hooke joint the second Hooke joint has to compensate the variable angular velocity of the intermediate shaft driving the output shaft. In general the input and the output axis do not lie in one line. Even they must not intersect each other. It will be shown that not only two but also more than two Hooke joints can be provided in order to minimise the deflection angles between the axes. In this paper the geometrical computation of Cardan shafts with two Hooke joints and particularly with three Hooke joints in spatial arrangements will be treated by the dual method with ε ² = 0. The planar arrangements and the several cases of given dates for spatial Cardan shafts with two Hooke joints without the dual method are left to the revised and now reprinted Richtlinie VDI 2722 (Guide Line of the Society of German Engineers). The chapters 1 and 2 are abridged parts and used figures of it are signified.