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工业机械手末端执行器以预定轨迹执行任务是工业生产中常见的运动形式。由于预定轨迹而产生的约束关系,使工业机械手的动力学特性表现出高度的非线性和耦合性,因此,利用传统的拉格朗日方程建立其动力学模型显得困难重重。针对受约束的工业机械手的动力学建模问题,基于分析力学界著名的Udwadia-Kalaba方程,获得了工业机械手在预定轨迹约束下各关节所需附加力矩的解析表达式及系统的动力学方程,克服了传统拉格朗日方程需借助拉格朗日乘子获得动力学方程的缺点。工业机械手的关节角变化规律和末端机械手运动轨迹的数值仿真结果证明所建立动力学方程符合实际情况。
Industrial Robotic End Effectors Performing tasks on a predetermined trajectory is a common form of motion in industrial production. Due to the restrained relationship of the scheduled trajectory, the dynamics of industrial robot show a high degree of nonlinearity and coupling. Therefore, it is difficult to establish its dynamic model by using the traditional Lagrange equation. Aiming at the problem of constrained industrial manipulator dynamics modeling, based on the well-known Udwadia-Kalaba equation of analytical mechanics, the analytical expressions of the additional torques required by industrial manipulators and the dynamic equations of the system under the predetermined trajectory constraints are obtained. Overcomes the shortcomings that the traditional Lagrange equation needs the Lagrange multiplier to obtain the kinetic equation. The change rule of the joint angle of the industrial manipulator and the numerical simulation of the trajectory of the end manipulator proves that the dynamic equation is in accordance with the actual situation.