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为了对柔性机械臂力学特性问题进行深入研究,通过运用机械臂低振动逆动力学和时变模态展开方法,建立单连杆柔性机械臂的动力学模型,将机械臂自激弹性振动模型引入计算模型中,提出最优输入力矩与扰动最优力矩计算方法,并针对关节处不同工作状态进行动力学响应分析,最后根据计算数据建立相关模型进行数值验证。研究结果表明,柔性机械臂在建模过程中包含非线性项,消除模型线性化误差,给定机械臂结构和运动要求时,可首先算出最优输入力矩,从而对机械臂实现开环控制;通过采用扰动模型,了解柔性作用,算法的收敛性和速度较普通模型有显著提高,结果具有良好的鲁棒性;当关节转动固定后,机械臂端点作谐振动,若振动频率接近机械臂固有频率时,扰动响应发散,反之则为稳态振动;当关节移动固定后,匀速转动,转速小于临界转速时,扰动响应衰减或稳定,反之则发散。
In order to further study the mechanical characteristics of flexible manipulator, a dynamic model of single-link flexible manipulator is established by using low-vibration inverse kinematics and time-varying modal expansion. The self-oscillating vibration model of manipulator is introduced In the calculation model, the calculation method of the optimal input torque and the optimal moment of disturbance is proposed, and the dynamic response analysis is carried out according to the different working conditions at the joints. Finally, the relevant models are established according to the calculation data for numerical verification. The results show that the flexible manipulator includes the nonlinear term in the modeling process and eliminates the linearity error of the model. When the manipulator structure and motion requirements are given, the optimal input torque can be calculated first, so that the manipulator can be open - loop controlled. By using the perturbation model, we can know the effect of flexibility. The convergence and speed of the algorithm are significantly improved compared with the ordinary model. The results show that the algorithm has good robustness. When the joint is fixed, the end of the manipulator resonates. If the vibration frequency is close to the inherent Frequency, the disturbance response diverges, otherwise the steady state vibration; when the joint moves fixed, uniform rotation, speed is less than the critical speed, the disturbance response decay or stability, otherwise it diverges.