基于劳斯判据的柔性机械臂弹性运动稳定性分析  

Analysis of Elastic Motion Stability of Flexible Manipulator Arm based on Roth Criterion

作　　者：韩莉莉[1] 刘广瑞[2] 宁祎[3] 

机构地区：[1]河南工业大学机电工程学院,河南郑州450007 [2]郑州大学机械工程学院,河南郑州450007 [3]河南工业大学机器人研究所,河南郑州450007

出　　处：《机械传动》2014年第8期115-120,共6页Journal of Mechanical Transmission

基　　金：国家"863"计划项目(2012AA2082);国家自然科学基金(61075083)

摘　　要：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 motion stability of flexible manipulator arm,to analyze the effect of the end position addition mass and rotary inertia on the elastic motion stability,and to compute the maximum dynamic allowable payload,the physics model of a flexible manipulator arm is established,the differential equation of elastic motion of the flexible manipulator arm is solved by using the method of the separation of time and space and the method of Laplace transformation,the dynamics model of flexible manipulator arm carried addition mass on its end position is established,simplified and truncated by using Lagrange equation.The state space expression and transfer function are established with the state variable and control input and output variable designated,the elastic motion stability rule is built upon and simplified by using Roth criterion.The influence of the end position addition mass and articulation rotational inertia of flexible manipulator arm on its elastic motion stability is analyzed by using the stability rule,and the dynamic maximum allowable payload of flexible manipulator arm on its end position is computed in order to guarantee its elastic motion stability.

关 键 词：劳斯判据 柔性机械臂 弹性运动稳定性 动态最大许用载荷 驱动关节转动惯量 

分 类 号：TP241[自动化与计算机技术—检测技术与自动化装置]