ALE formulation for dynamic modeling and simulation of cable-driven mechanisms considering stick–slip frictions

This paper proposes an arbitrary Lagrange Euler (ALE) method for dynamic modeling and simulation of cable-driven mechanisms considering stick–slip frictions. The dynamic equations of the cables are presented based on the ALE formulation. The frictional forces acting at the Eulerian nodes are derived from the Coulomb dry friction model. The detections for stick–slip motions of different contact points between the cables and the holes are carried out independently through a trial-and-error method. The stiff problems yielded by the high stiffness of the cables are released by using a model smoothing method. The dynamic equations of the system are integrated by an explicit solver, avoiding the calculation of Jacobian matrix of the dynamic equations with respect to state variables, which is nonexistent in the stick–slip transition points. The effectiveness and correctness of the proposed method are verified by comparison with previous studies and with experiments. The proposed method not only can capture stick–slip motions, which are consistent well with experiments, but also has a high calculation efficiency.