柔性机械臂的非线性振动分析

建立了由两个柔性杆和一个柔性饺链组成的柔性机械臂的动力学方程,利用非线性振动的平均法进行了摄动分析,求得了系统在主共振和多重共振下的定常解,发现系统在第二阶主共振和1∶2 内共振的情况下有内共振阈值和双拟饱和现象存在,增大低阶模态阻尼是抑制内共振、防止产生大幅低频振动的有效手段。

Nonlinear Dynamical Analysis of Flexible Robotic Manipulator

An analysis is presented for the nonlinear planer response of a flexible robotic manipulator with two flexible links and one flexible joint. The manipulator is idealized into three degree of freedom dynamic system which represents the first three vibration modes:the flexural vibration of beam 1, the flexural vibration of beam 2, and the flexible rotating of the joint. The steady state solutions are derived in the cases of primary resonance of the second mode with the presence or lack of the internal resonance via asymptotic analytical method. For all these solutions, appropriate stability analysis is also performed. It is shown that in the internal resonance the vibration amplitude of the first mode (beam 1)will be larger than that of the second mode(beam 2) under excitation. There is a threshold of excitation for the internal resonance and we call it critical excitation to internal resonance (CEIR). Increasing the damping coefficient of the first mode (beam l) may increase the CEIR, and then the manipulator can work more safely.