General planar dynamics of a sliding flexible link

A finite element dynamic model of a sliding link through a prismatic joint where the prismatic joint hub is executing general planar motion is formulated. In contrast to previously reported formulations, a finite element mesh with a fixed number of elements is used, where the element length is constant. The time-dependent boundary conditions manifested by the prismatic joint constraints are considered. A transition element with variable stiffness is introduced at the interface with the joint hub. In this finite element formulation, all the inertia coupling terms between the beam reference motions and the local elastic deformations are considered. In addition, the model accounts for the dynamics of the end mass as well as the associated coupling effects. Numerical simulations and comparisons with results obtained by other methods are presented to demonstrate the validity and accuracy of the model.