The Development of a Sliding Joint for Very Flexible Multibody Dynamics

In this paper, a formulation for a spatial sliding joint, which a general muItibody can move along a very flexible cable, is derived using absolute nodal coordinates and non-generalized coordinate. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the non-generalized coordinate, which is neither related to the inertia forces nor external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. In the constraint equation for the sliding joint, since three constraint equations are imposed and one non-generalized coordinate is introduced, one constraint equation is systematically eliminated. Therefore, there are two independent Lagrange multipliers in the fInal system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph/catenary systems for high speed-trains.