Numerical Algorithm for Simulation of Hybrid-Degrees of Freedom Belt-Pulley Systems: Application to X-Y Positioning Mechanism

This paper presents a comprehensive investigation into the modeling and dynamic analysis of a XY mechanism, considering the potential occurrence of motor pulley slipping. The research commenced with the establishment of kinematic relationships among system components and the definition of virtual pulleys. By characterizing static and kinetic frictions for individual system elements, various rolling and slipping states were explored. The study unveiled that the system, excluding motor pulleys, experiences a stick-slip phenomenon due to friction between actuator components and the ground, resulting in deadzones during motion initiation. To address this, a novel friction model encompassing deadzones was introduced, and equations accounting for the stick-slip phenomenon were derived. Moreover, recognizing that each actuator motor can be in either a rolling or slipping state, it was established that the mechanism represents a hybrid-DOF dynamic system. The equations of motion switch between four modes, denoted as RR, SR, RS, and SS, contingent on input voltages, kinematic and dynamic variables, and friction coefficients between motor pulleys and belts. Calculating the required friction to maintain rolling was essential; insufficient friction between motor pulleys and belts leads to motor slipping. The determination of the system's subsequent dynamics considered different motor states, varying DOF, and the interplay of stick-slip phenomena with deadzones. Ultimately, dynamic analyses of the mechanism were conducted through simulations in three distinct scenarios. This study effectively highlights the nonlinear effects and complexities inherent in this mechanism, offering valuable insights into its behavior under different conditions.