Element-free rope pulley calculations: Advancing deployable skeleton performance optimization

• Reverse establish rope's elastic-plastic model via test data. • Calculate tension distribution using friction Eulerian equation. • Meshless pulley rope method avoids contact detection, aiding co-simulation with multi-body dynamics software. • Enhance lower frame's joint stiffness and pre-torque to control top plate unfolding trajectory. Objects in rope-driven multibody systems are controlled via embedded pulleys and ropes, and these systems are widely utilized in large deployable structures, aircraft interception systems, robots, cranes, and other mechanical systems. However, the proposed calculation methods are time-consuming, complex, and the neglect of plasticity. To address these issues, we propose a meshless rope-pulley method that eliminates rope elements. The basic idea involves reverse-establishing the elastic-plastic model of the rope based on test data and calculating the tension distribution in conjunction with the friction Eulerian equation. The macroscopic model, which lacks complex integration and matrix operations, can be readily integrated with multi-body dynamics analysis software for collaborative simulation. The accuracy and efficiency of the proposed method have been confirmed through numerical and experimental examples. Subsequently, the method has been employed to evaluate, compare, and design the dynamic synchronization performance of a deployable skeleton. The results obtained can directly guide the actual design of deployable skeletons, and the proposed method is applicable to similar mechanical systems.