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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 in compliant structure is introduced. The kinetic energy and deformation energy equations of this model are deduced by the symbolic operation of Matlab software. The dynamic model of soft rod under the end load was established by using Lagrange equation. The characteristic radius coefficient and stiffness coefficient are substituted into the equation to obtain the coefficients of centripetal force, moment of inertia and Coriolis moment, and the influence of their mutual coupling on the pseudo-rigid body angular variation is analyzed. The dynamic response curve and the bitmap are obtained by numerical solution of the second order differential coefficient differential equations. The curves show that the amplitude of the pseudo-rigid rod gradually increases from 1 to 3 and the coupling of the rod decreases. Compared with the 2R pseudo-rigid model The kinetic equation simulation soft rod dynamic characteristics more practical and versatility.