带弹性元件扑翼机构的动力学分析及实验

为研究扑翼飞行器传动机构的能量特性，以特拉华大学机械系统实验室所研制样机为原型进行了建模。引入气动项和拉力弹簧建立了完整的动力学模型。分析发现，气动项的力矩峰值为惯性项的4.8倍，对电机的转矩峰值的影响起主要作用。运用正交法进行仿真发现，引入拉力弹簧可以使电机转矩峰值最大降低77.5%，与理论分析相符合。进一步的物理实验验证了理论分析和仿真结果的正确性，并得到了当弹簧的连接点位置为185 mm、原长为200 mm及刚度为0.1 N/mm时实验结果取得最优值，可为扑翼机传动机构的优化设计提供依据。此外，引入弹性元件也可有效降低电机的转速波动，进而为仿生扑翼飞行器的生产和实践应用提供理论指导。

Flapping mechanism with elastic components: dynamic analysis and experiment

To investigate the energy characteristics of flapping-wing transmission mechanisms, this study establishes a complete dynamic model based on the prototype of the Mechanical Systems Laboratory of Delaware University, taking into account the aerodynamic term and a tension spring. Analyses reveal that the peak torque of the aerodynamic term contributes a value of 4.8 times that of the inertia term, dominantly influencing the peak torque of the motor. Orthogonal simulations show that, consistent with the theoretical analyses, the introduction of the tension spring can reduce the peak torque of the motor up to 77.5%. Meanwhile, experimental results exhibit good agreement with theoretical and simulation results. Furthermore, the optimal solution (the position of joint point 185 mm, the original length of the spring 200 mm and the stiffness 0.1 N/mm) is obtained, providing reference for the optimization design of the transmission mechanism. In addition, elastic elements can also effectively reduce the speed fluctuation of the motor, thus providing theoretical guidance for the production and practical application of bionic flapping-wing air vehicles.