双臂协调机械手动力学建模的新方法

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。

New approach for dynamics modeling of dual-arm cooperating manipulators

High nonlinearity and coupling were shown from the dynamic characteristics of dual-arm cooperating manipulators because of the constrained relationship brought by desired task. Therefore, it was difficult to establish dynamical equation with traditional Lagrange equation. Aimed at the dynamics modeling of dual-arm cooperating planar manipulators, a generalized dynamical equation of multi-link planar manipulators was established and proved with traditional Lagrange equation. Then the additional torque and dynamical equation of dual-arm cooperating planar manipulators subject to some desired trajectory were acquired based on the famous Udwadia-Kalaba equation in analytical mechanics field and the above-mentioned generalized dynamical equation of multi-link planar manipulators. The new approach overcomes the disadvantage of obtaining dynamical equation from traditional Lagrange equation by Lagrange multiplier. The stimulation results of the varying law of the joint angles and the motion path of the bar prove that the dynamical equation established by this method conforms to the matter of fact.