# Resonance-Driven Passive Folding/Unfolding Flapping Wing Actuator
## 1 Introduction  
In recent years, bioinspired flapping-wing micro aerial vehicles (FWMAVs) have attracted considerable attention owing to their wide application fields, such as for use in rescue missions, inspection of building structures, and remote sensing. In addition, their flight performance has also gained interest because it could be inherent to the flying ability of natural birds and insects. One of the concerns of the FWMAVs compared to the prevalent multirotor systems is the robustness of their wings. As the wing is lighter and a larger structure than a rotor, it is liable to be fragile. Although natural birds and insects should also face the same problem, their wings are foldable, and thus the breakage risk by collision is decreased.  
Bioinspired foldable wings have been reportedly developed by several research groups. [PERSON] et al. [1] and [PERSON] et al. [2] researched on beetle-inspired foldable wings driven by a shape memory alloy actuator. [PERSON] et al. [3] reported on a bat-like wing with a motorized folding/unfolding system. In the case of a fixed but not a flapping wing, [PERSON] et al. [4] and [PERSON] et al. [5] presented foldable wings actuated by motorized systems. [PERSON] et al. [6] reported on the use of a passive folding/unfolding system in a motor-driven foldable wing, and demonstrated the actuation of the folding/unfolding motion mainly by the centrifugal force, associated with the flapping motion of the wing. Because this passive folding/unfolding system does not require additional actuation devices, it is considered to have advantages of being lightweight and consuming less power. We consider these advantages to be suitable for MAV applications, and thus employed the passive folding/unfolding wing system in the current study.  
[PERSON] and [PERSON] [6] proposed a bat-scaled wing system. Whether this concept is applicable to insect-scaled FWMAVs still needs to be ascertained. In their report, the wing-flapping motion wasforcibly defined by a motorized system. However, in an insect-scaled FWMAV, the wing motion is generally actuated by resonance [7; 8; 9; 10]; the stroke amplitude of the wing is amplified by matching the resonant frequency of the system with the actuation force. We expect the passive folding/unfolding wing system and resonant flapping actuation system to interact with each other, and this could play an important role in the folding/unfolding characteristics. To the best of the authors' knowledge, this possible interaction phenomenon has not yet been studied.  
In this paper, we report on the theoretical modelling and experimental demonstration of the passive folding/unfolding wing system with a resonant-driven actuator. The contributions of this study are summarized as follows:  
* We provide a simplified system model with experimental validation.
* The system is observed to show bistability, and the stable region shifts because of the actuation frequency and voltage (torque).
* We propose a method to enlarge the stable region, in which the frequency and voltage are simultaneously modulated. This contributes to the extension of the variable range of the lift force.  
In Section 2, we describe the structure of the actuator and the experimental method. Section 3 is devoted to the simplified theoretical modelling. The experimental results and discussion based on a comparison between the experiment and theory are reported in Section 4. Finally, the conclusions of this study are drawn in Section 5.