The dipteran flight mechanism of the insects is commonly used to design the nonlinear flight robot system. However, the dynamic response of the click mechanism of the nonlinear robot system with multiple stability still unclear. In this paper, a novel dipteran robot model with click mechanism proposed based on the multiple stability of snap-through buckling. The motion of equation of the nonlinear flight robot system is obtained by using the Euler-Lagrange equation. The nonlinear potential energy, the elastic force, equilibrium bifurcation, as well as equilibrium stability are investigated to show the multiple stability characteristics. The transient sets of bifurcation and persistent set of regions in the system parameter plane and the corresponding phase portraits are obtained with multiple stability of single and double well behaviors. Then, the periodic free vibration response are defined by the analytical solution of three kinds of elliptical functions, as well as the amplitude frequency responses are investigated by numerical integration. Based on the topological equivalent method, the chaotic thresholds of the homo-clinic orbits for the chaotic vibration of harmonic forced robot system are derived to show the chaotic parametric condition. Finally, the prototype of nonlinear flapping robot is manufactured and the experimental system is setup. The nonlinear static moment of force curves, periodic response and dynamic flight vibration of dipteran robot system are carried out. It is shown that the test results are agree well with the theoretical analysis and numerical simulation. Those result have the potential application for the structure design of the efficient flight robot.

翻译：昆虫的双翅目飞行机制常用于设计非线性飞行机器人系统。然而，具有多稳定性的非线性机器人系统中咔嗒机制的动态响应仍不清楚。本文基于突跳屈曲的多稳定性提出了一种具有咔嗒机制的新型双翅目机器人模型。通过欧拉-拉格朗日方程推导出非线性飞行机器人系统的运动方程。研究了非线性势能、弹性力、平衡分岔及平衡稳定性以揭示多稳定性特征。系统参数平面中的瞬态分岔集和持续区域集以及相应的相图展示了单阱和双阱行为的多稳定性。然后，通过三种椭圆函数的解析解定义了周期自由振动响应，并通过数值积分研究了幅频响应。基于拓扑等价方法，推导了谐波强迫机器人系统同宿轨道混沌振动的混沌阈值，以揭示混沌参数条件。最后，制造了非线性扑翼机器人样机并搭建了实验系统。完成了双翅目机器人系统的非线性静力矩曲线、周期响应及动态飞行振动实验。结果表明，测试结果与理论分析和数值模拟吻合良好。这些结果对高效飞行机器人的结构设计具有潜在应用价值。