Efficient and Accurate Simulation of the Cable – Pulley Interaction in Weight – Lifting Machines

This paper presents different approaches that can be used fo r modeling cables in weight–lifting machines. It is shown that modeling the cable as a linear spring, althou g very simple and efficient, is energetically inconsistent and produces spurious terms in the equations o f motion if the cable deformation along the segment in contact with the pulley is not considered. In orde r to overcome this problem and obtain an efficient yet accurate method for the simulation of such syst em , a semi–analytical method is derived by introducing an analytical model of the cable–pulley intera ction [10] in the system, and the obtained results are compared to a finite–element numerical model. The semi–a nalytical model is based on a continuum mechanics approach of the cable; it assumes Coulomb frictio n between the pulley and the cable and neglects the inertia of the segment of cable in contact with the pulley . The numerical model is based on the Absolute Nodal Coordinate Formulation (ANCF) [ 13], and accounts for both the inertia forces and the bending an d axial deformation of the cables.