一种含转动副间隙多连杆机构非线性动力学行为分析方法

摘要

给出一种通过对欠驱动机构的分析来预测含转动副间隙多连杆机构动态特性的方法,利用该方法对含转动副间隙平面多连杆机构的非线性动态特性进行分析.以含转动副间隙的二自由度九连杆机构为研究对象,首先通过将转动副间隙看作虚拟无质量连杆,据此可把合转动副间隙九连杆机构变为欠驱动的十连杆机构;然后利用拉格朗日方程建立欠驱动十连杆机构的非线性动力学模型,采用龙格-库塔法对动力学模型进行数值求解,分析机构中滑块的位置、速度和加速度等运动输出、曲柄的驱动力矩等动力学响应,通过相图和庞加莱映射图对含转动副间隙的二自由度九连杆机构中存在混沌现象进行辨识;最后研究不同间隙值和不同驱动速度对九连杆机构混沌的影响,并绘制分岔图.该研究对于进一步研究含多间隙复杂连杆机构的非线性动力学研究具有重要价值.%A method of forecasting the dynamic behavior of the multi linkage mechanism with clearance by analyzing the underactuated mechanism was proposed,and the nonlinear dynamic behavior of the planar multi-linkage mechanism with clearance was studied with this method.The 2 degree of freedoms (DOFs) nine-bar mechanism with revolute clearance was taken as the research object.Firstly,by regarding the clearance of the revolute joint as a virtual massless link,the nine-bar mechanism with clearance was transformed into an underactuated ten-bar mechanism.A nonlinear dynamic model of the underactuated mechanism was established by using Lagrange equation.The RungeKutta method was used to solve the dynamic equations of the mechanism.The dynamic responses such as kinematics of slider,motion output of speed and acceleration speed,and driving torque of crank were analyzed.The chaos phe nomenon existing in the mechanism was identified by phase diagrams and Poincaré portraits.The effects of different clearance values and different driving speeds on chaos were studied and the bifurcation diagrams were drawn.The research has an important value for the further nonlinear dynamics research of the multi-linkage mechanism with clearance.