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Abstract In this paper, we presented the design, integration, and experimental verification of a flapping wing apparatus. The purpose for this apparatus is to provide a framework to study the applicability of various types of sensors on flapping wings in the presence of forward speed. This work is inspired by the discoveries of mechanosensory hairs on insect wings that perform like strain-gauge sensors. To design the apparatus, we started by kinematic analysis of a crank-slider mechanism to actuate the wings. After that, we constructed the equations of motion of the entire system to find the proper gear ratio, motor properties, and other geometric dimensions. For the aerodynamic modeling, we used a quasi-steady formulation and presented a closed-form solution for the aerodynamic torque. Then, we explained the integration process and manufacturing of the main parts and presented two prototypes for the apparatus. At the end, we showed the final constructed versions of the apparatus and presented the experimental response and compared them with the simulation. 

Abstract In this paper, we first presented a four-bar linkage mechanism for actuating the wings in a flapping wing flying robot. After that, given the additional constraints imposed by the four-bar linkage, we parameterized the wing kinematics to provide sufficient control authority for stabilizing the system during 3D hovering. The four-bar linkage allows the motors to spin continuously in one direction while generating flapping motion on the wings. However, this mechanism constrains the flapping angle range which is a common control parameter in controlling such systems. To address this problem, we divided each wingbeat cycle into four variable-time segments which is an extension to previous work on split-cycle modulation using wing bias but allows the use of a constant flapping amplitude constraint for the wing kinematic. Finally, we developed an optimization framework to control the system for fast recovery while guaranteeing the stability. The results showed that the proposed control parameters are capable of creating symmetric and asymmetric motions between the two wings and, therefore can stabilize the hovering system with minimal actuation and flapping angle amplitude constraint.