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由于某种既定任务而产生的约束关系的存在,使得双臂协调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。针对平面双臂协调搬运机械手的动力学建模问题,基于传统的拉格朗日方程给出并证明了平面多杆机械手动力学方程的一般表达式。然后利用上述表达式,并基于分析力学界著名的Udwadia-Kalaba方程的建模思想,获得双臂协调机械手在预定轨迹下各杆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。双臂协调机械手的关节角变化规律和被搬运物体轨迹的数值仿真结果证明所建立的动力学方程符合实际情况。
Owing to the existence of the constraint relationship due to a given task, the dynamic characteristics of the two-arm coordinated manipulator exhibit a high degree of nonlinearity and coupling. Therefore, it is very difficult to establish its dynamic model by using the traditional Lagrange equation. Aiming at the problem of dynamic modeling of manipulator with planar arms and arms, the general expression of the mechanical equation of planar multi-rod manipulator is given and proved based on the traditional Lagrange equation. Then, based on the above expression and based on the well-known modeling theory of Udwadia-Kalaba equation in analytical mechanics, the analytic expression of the additional torque required by each arm of the two-arm coordinated manipulator and the kinetic equation of the system are overcome, The traditional Lagrange equation needs the Lagrange multiplier to get the shortcoming of the kinetic equation. The results show that the established dynamic equation accords with the actual situation by adjusting the joint angle of the two arms and the trajectory of the object being transported.