An Improved Assumed Modes Method for Dynamic Analysis of Cable-Pulley Systems

Cable-Driven Mechanisms are broadly used in various fields owing to the wide workspace and high load capacity. However, the dynamic modeling of the mechanisms faces two main challenges: the cables’ time-varying length vibration characteristics and the stress discontinuity conditions that are induced by the cable-pulley coupling. Previous studies often approximate the cable vibration field using smooth, differentiable test functions. Although these methods can theoretically provide accurate solutions, they require high-order discretization to maintain precision when dealing with stress discontinuity conditions at the cable-pulley contact point. This not only increases computational costs but also leads to deviations in the calculated cable strain field due to the Gibbs effect at stress discontinuities. To address the issue, an extended dynamic model based on the modal acceleration method is proposed in this paper. By introducing piecewise linear test functions to expand the modal function set, the proposed extended model can explicitly embed the stress discontinuity effect into the dynamic equations, thus independently describing the stress characteristics imposed by the pulley on the cable. Numerical simulations demonstrate that the extended model can achieve high-precision results at low discretization orders and effectively avoid the Gibbs effect. The extended model can achieve precision comparable to traditional sine test function methods at a discretization order that is 1 to 2 orders lower.