中文摘要：

研究了欠驱动机械臂的多稳态行为与驱动频率之间的关系.机械臂被抽象为三根铰接质量杆的三连杆系统,并在基础端承受弱简谐振动驱动.通过拉格朗日方程建立质量三连杆动力学方程,利用多尺度法对建立的模型进行理论分析,得出三连杆多稳态响应的分岔图.通过数值仿真,得出不同频率下三连杆的多稳态.通过建立实验装置,观察了理论预测.实验结果验证了理论分析的正确性.实验和理论结果都表明,随着振动驱动频率的变化,系统会出现单稳态、双稳态、三稳态和四稳态运动.

英文摘要：

The relations between the driven frequency and the multi-steady-state response for an underactuated manipulator were performed. The manipulator was modeled to be three mass rods linked in hinges. The three-linking rod was subjected to a harmonic and weak driving at the based end. The Lagrange principle was employ to propose and analyze dynamical equations of the system, respectively. The bifurcation diagram of the multistable responses was shown for the three-linking rod. The experimental device was installed to observe the analytical predictions. It was seen that the experimental results were in good agreement with those from the analysis. Both experimental and analytical results show that the vibration can induce the single, two, three and four stable responses with the driving frequency varying.