Dynamic response and chaos in planar multi-link mechanism considering revolute clearances

Abstract

During actual motion, there are inevitably clearances between the motion pairs of the mechanism, and the clearances will have a large impact on stability of the mechanism. Previous studies mainly focused on the dynamic response of simple mechanisms with single clearance and less on chaos. Even if chaos is studied, it mainly focused on the chaos of mechanisms and less on the chaos of clearance joints; however, it is well known that the analysis of chaotic characteristics of clearance is the key to fault diagnosis of kinematic pairs. In order to give a computational methodology for dynamic analysis of planar multi-link mechanism considering multi-clearances and master the dynamic response of planar multi-link mechanism, the dynamic response and chaos of a planar six-bar mechanism are researched. A multiple clearances dynamic model of planar six-bar mechanism is built by Lagrange multiplier method, and the dynamic model is solved by Runge–Kutta method. The influence of different clearance positions, clearance numbers and clearance sizes on dynamic response of mechanism is analyzed. The nonlinear characteristic analysis of six-bar mechanism is conducted, and chaotic phenomena of the clearance joint are explained by Poincare maps and phase diagrams. The bifurcation diagram at clearance of the revolute joint changes with different clearance values, friction coefficients and driving speeds is given. Those above results provide an important theoretical basis for the study of influence of multi-clearance on dynamic responses and chaotic phenomena of planar multi-link mechanism.