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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.
The relationship between multi-steady state behavior and driving frequency of underactuated manipulator is studied.The manipulator is abstracted as a three-link system with three articulated mass rods and is subjected to a weak harmonic vibration drive at the base.According to Lagrangian The equation establishes the mass three-link kinetic equation, and uses the multi-scale method to make a theoretical analysis of the established model to obtain the bifurcation diagram of the multi-steady state response of the three-link.Furthermore, numerical simulation shows that the three- Steady state.According to the experimental setup, the theoretical prediction is observed.The experimental results verify the correctness of the theoretical analysis.The experimental and theoretical results show that the monostable, bistable, Steady-state and steady-state movement.