A deformation model of a parallel kinematic machine tool

The computation of the static stiffness of a parallel kinematic machine tool (PKM) can generally be performed in different ways, e.g. by using the kinematic Jacobian matrices or the finite element method. The use of the Jacobian matrices represents a relatively simple and thus fast computation method to determine the static stiffness of PKM. However, this method usually assumes that deformations do only lie in the direction of the guiding chains. In contrast, a FE model can be built more detailed but this implies a higher computation time. For the purpose to correct the static deformation of PKM by the control system, the computation time is an important criterion beside the accuracy of the computed results. In this article, it will be shown that deformations not lying in the direction of the guiding chains do also have to be considered in the case of the selected demonstrator. In order to obtain sufficiently accurate results within a short computation time, a method based on computing the inverse and forward kinematics is employed here. The computation results are compared with a model based on the kinematic Jacobian matrices and a finite element model. Finally, some outlooks will be given.