Hybrid modeling for dynamic analysis of cable-pulley systems with time-varying length cable and its application

The dynamic analysis of cable-pulley systems is investigated in this paper, where the time-varying length characteristic of the cable as well as the coupling motion between the cable and the pulleys are considered. The dynamic model for cable-pulley systems are presented based on the principle of virtual power. Firstly, the cubic spline interpolation is adopted for modeling the flexible cable elements and the virtual 1powers of tensile strain, inertia and gravity forces on the cable are formulated. Then, the coupled motions between the cable and the movable or fixed pulley are described by the input and output contact points, based on the no-slip assumption and the spatial description. The virtual powers of inertia, gravity and applied forces on the contact segment of the cable, the movable and fixed pulleys are formulated. In particular, the internal node degrees of freedom of spline cable elements are reduced, which results in that only the independent description parameters of the nodes connected to the pulleys are included in the final governing dynamic equations. At last, two cable-pulley lifting mechanisms are considered as demonstrative application examples where the vibration of the lifting process is investigated. The comparison with ADAMS models is given to prove the validity of the proposed method.