基于3R伪刚体模型的柔顺杆动力学建模及分析

Dynamics Modeling and Analysis of Compliant Bar based on 3R Pseudo-rigid-body Model

介绍了柔顺机构中的3R伪刚体模型。利用Matlab软件的符号运算推导出了该模型柔顺杆的动能和变形能方程。应用拉格朗日方程建立了柔顺杆末端载荷作用下的动力学模型。特征半径系数和刚度系数代入方程组获得向心力、惯性力矩、科氏惯性力矩等系数,并分析了其相互耦合对伪刚体角变量的影响。通过数值求解二阶变系数微分方程组获得动态响应曲线和位形图,曲线反映出伪刚体杆从1杆到3杆振幅逐渐增大、杆件的耦合降低的振荡情况,较2R伪刚体模型的动力学方程模拟柔顺杆动力特性更具实用性和通用性。

The 3R pseudo - rigid - body model of compliant mechanism is introduced. The kinetic energy equation and deformation energy equation of compliant bar is deduced by Matlab software symbolic operation. The dynamics model of the compliant bar under the action of end load by applying Lagrange equation. The centripetal force factor, the moment of inertia factor, and the Carioles force factor are obtained through characteristic radius factor and stiffness factor substituted into equations group, and mutual coupling effect of the angle variable are analyzed. The dynamic response curves and its configuration charts are obtained through the numerical solution of two order variable coefficient linear differential equations. It shows that the pseudo - rigid - body amplitude from 1 - bar to 3 - bar increases gradu- ally and rod coupling reduces. The result shows that the dynamics equations of 3R pseudo - rigid body model are more practical and versatile for simulating the dynamics characteristics of compliant bar than 2R pseudo - rigid body model.