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为了研究柔性机械臂的弹性运动稳定性,分析末端附加质量和关节惯量对弹性运动稳定性的影响,并计算柔性机械臂的动态最大许用载荷,建立了单连杆柔性机械臂的物理模型,用时空分离法和拉普拉斯变换法求解了柔性机械臂的弹性运动微分方程,用拉格朗日法建立了末端有集中质量的柔性机械臂的动力学模型并对其简化和截断。在指定状态变量、控制作用和输出变量后,建立了状态空间表达式和传递函数,并且用劳斯判据建立了稳定性判据并对其进行了简化。用得到的稳定性判据分析了末端附加集中质量和关节惯量对柔性机械臂弹性运动稳定性的影响,并从保证弹性运动稳定的角度计算了柔性机械臂的最大许用载荷。
In order to study the elastic stability of the flexible manipulator, the influence of the additional mass and the inertia of the joint on the stability of the elastic motion was analyzed, and the maximum allowable dynamic load of the flexible manipulator was calculated. The physical model of the single-link flexible manipulator was established, The time-space separation method and Laplace transform method are used to solve the elastic differential equation of flexible manipulator. The dynamic model of flexible manipulator with concentrated mass at the end is established by Lagrange method, and the simplified and truncated flexible manipulator model is established. After assigning state variables, controlling functions and output variables, state space expressions and transfer functions are established, and stability criterion is established and simplified by Claus criterion. The stability criterion of the flexible manipulator is used to analyze the influence of the concentrated mass and the inertia of the tip on the stability of the flexible manipulator. The maximum allowable load of the flexible manipulator is calculated from the viewpoint of ensuring the stability of the elastic manipulator.