Vector analysis of the kinematic characteristics of two-joint cardan shaft

Using the example of a two-joint cardan shaft, a method is presented for analytically describing its kinematic characteristics based on the use of vector analysis, which the author has been successfully using for a long time in designing various lever mechanisms. The proposed vector analysis method is based on the spatial coordinate transformation method. In this method, to get a vector rotated in space, you must specify the source vector, the vector around which the rotation will be performed, the angle of rotation itself and if a new vector length is required. In the proposed vector analysis method for describing the kinematics of a two-joint cardan shaft, the coordinates of the points of the axes of the cardan shafts and the radius of the cross are the basic geometric data. The adequacy of the results of kinematic analysis by the vector method was tested in two ways. In the first case, the values obtained by the vector method for the coordinates of all the characteristic points of the two-joint cardan shaft were compared with the corresponding coordinates of the characteristic points of the identical parametric model built in the three-dimensional CAD package. In the second case, the angular velocities and accelerations of the shafts of the two-joint cardan shaft obtained by the vector method were compared with the analytical dependencies given in the well-known literature sources. As a result of all the checks, it was concluded that the proposed method of vector analysis of two-joint cardan shaft is absolutely adequate. The developed method of vector analysis of the kinematic characteristics of two-joint cardan shaft can be further used to find the vector-loads (forces and moments) acting in the cardan transmission elements in order to conduct subsequent strength calculations. The proposed vector analysis method of two-joint cardan shaft is universal and can be successfully applied to describe the kinematics not only of two-joint cardan shaft, but also for polycardan transmission of any complexity.

vector analysis, coordinate transformation method, cardan shaft, polycardan shaft, irregularity of rotation