Modeling Dynamic of the Cable-Pulley System Considering the Contact Geometry Based on 2D-SDF

The contact dynamics between the cable and the pulley is a typical multiscale problem, where the potential contact range is large, but the actual contact area is small. Traditional finite element methods for describing these local frictional contact details face a trade-off between computational efficiency and accuracy. To address the multiscale frictional contact problem in the cable-pulley system, this paper proposes the novel modeling method cable-pulley system considering the detail contact geometry based on two-dimensional Signed Distance Field (2D-SDF). A flexible cable model is established using an ALE (Arbitrary Lagrangian-Eulerian) description, and a length-variable, topologically consistent driving cable model is constructed through proportional constraints of ALE material coordinates. The dynamically constrained ALE cable nodes serve as fixed contact detection points. The geometric profile of the pulley is accurately described by a discrete 2D-SDF, which is precomputed offline to reduce the discrete search data. Online, bilinear interpolation is applied for efficient calculation of contact parameters, forming a non-search-based contact detection strategy for the cable-pulley system. The accuracy of the proposed method is verified through simulation.