Building upon prior work, the development of a scalable high frequency flapping wing robotic test platform is presented. Weighing 4.0 grams and operating at frequencies in excess of 90Hz, the platform is capable of generating a lift-to-weight ratio of approximately 1.3 and demonstrated lift-off tethered to an external power supply. From a previous electromagnetic actuator design, the coil cross-section profile was reshaped and “virtual spring” magnets were relocated to reduce mass and improve overall efficiency. Conducting experiments on a set of reconfigured actuators paired back-to-back, a magnetic interaction torque was discovered coupling the response of the combine system. Investigations into this interaction revealed a wing-to-wing synchronization effect accounting for asymmetries in the individual actuators and resulted in a system equilibria bifurcation with decreases to their separation distance. The coupling of the combined system bears a striking resemblance to the biomechanical linkage system in Dipteran flies which has also been shown to result in the synchronization of asymmetric wings. With the current embodiment of the robotic platform serving as a proof-of-concept for later iterations, a scaling of the system to the order of insects is predicted to have lift-to-weight ratios near two and will be the target for future work.

A design principle for selecting the stiffness of a wing rotational flexure hinge on bio-inspired flapping wing robots is presented. In this work, a systematic approach of selecting rotational stiffness values such that the primary mode of resonance occurs at harmonics of the wing stroke frequency is proposed. Using the quasi-steady aerodynamic model as a basis, simulations were performed to assess the effects of wing hinge stiffness on the rotational dynamics, while also evaluating effects on the mean lift coefficient. Based on the results from simulation, an operating mode for the optimal wing hinge stiffness is proposed. As verification, test wings incorporating a flexible rotational hinge were fabricated from laser machined composites and tested at a range of flapping frequencies. Wing kinematics were then extracted from high speed video and the resulting lift generation was evaluated. Experimental data from wing-hinge stiffnesses designed such that the primary mode of rotational resonance occurs near twice the flapping frequency showed near optimal cycle-averaged lift at targeted frequencies and low sensitivity to wing parameter variation. As a result, for a given set of vehicle parameters, the proposed principle serves as design guideline from which an initial rotational hinge stiffness can be selected and iterated to achieve optimal lift.

An electromagnetic actuator weighing 2.6 g and operated up to resonant frequencies in excess of 70 Hz is presented with the intended application to flapping-wing MAVs. Comprised of a single electromagnetic coil, a permanent magnet rotor, and a “virtual spring” magnet pair, system resonance is achieved using a periodic excitation voltage applied to the coil, resulting in harmonic wing motion. Analytical models describing the electrodynamic interactions of system components and flapping-wing aerodynamic mechanisms are used to develop the equations governing the system's dynamics. Preliminary analysis based on simulation is used to build a working prototype from which further validation is conducted. Wing kinematics and mean lift measurements from the prototype demonstrated a lift-to-weight ratio of over one at 24 V. Based on a simplified equation of motion, approximate solutions for primary resonance mode and peak-to-peak (pk-pk) stroke amplitude were determined using the method of multiple time scales. Validated from frequency response experiments conducted on bioinspired test wings, these approximate solutions are used as a basis for an optimization framework. Finally, the developed framework is used to investigate the performance of the proposed actuator at different scales, predicting lift-to-weight ratios well above one for a wide range of the parameter space.

In this paper, we develop a theoretical framework for a flapping-wing actuation mechanism. Driven by oscillating magnetic torque acting on the rotor, the proposed actuator operates as a forced nonlinear oscillator. The resonance of the system is achieved by using a virtual magnetic spring without any mechanical components. Analytical models of the driving torque and the wing flapping (rotor) dynamics are derived and validated by experimental measurements from a parallel study. The flapping amplitude at primary resonance is obtained by solving the dynamic equation using the method of multiple time scale. The aerodynamic lift is then calculated based on quasi-steady aerodynamic model. Finally, the developed framework is used to investigate the feasibility and performance of the proposed actuator at different scales, while we show that a lift-to-weight ratio over one can be achieved in a large domain of design parameter space.

The design and construction of a 2.6 gram electromagnetic actuator operated at resonance is presented. This design is based on wedge-shaped electromagnetic coil generating a driving torque on a rotor embedded with permanent magnets. Additional permanent magnets are used to create a virtual spring effect, supply a restoring torque to the rotor and adding nonlinear system stiffness. Flapping wing parameters were varied systematically to generate 16 unique wing profiles, from which wings were fabricated. Independent bench tests for the coil and spring magnets were used to modify analytical models of the actuator, derived in detail in a parallel study. Based on the equations of motion, estimates for the primary mode of resonance and the peak-peak stroke amplitude were determined using an approximate solution. Frequency response tests were conducted on the flapper using the set of test wings at varying supply voltages and spring configurations to verify the predicted resonate frequencies and amplitudes. Wing kinematics and mean lift measurements were performed for the flapper operating at resonance, producing a lift-to-weight ratio for the actuator of over one at 24V.

In this study, we present a motor-driven flapping-wing actuator, designed to operate at its resonant frequency using a torsion spring. The wing is driven by a DC motor directly through gear transmission. Linear torsion springs mounted on the load shaft creates restoring torque when the wing is displaced from its mid-stroke position. The actuator dynamics is obtained using system identification. The flapping motion of the wing is achieved by closed-loop motor control, for example, tracking a sinusoidal wave with the frequency tuned to match the resonant frequency of the system. PID and LQR controllers are applied for instantaneous wing kinematics tracking: A PID controller is able to precisely track the trajectory with relatively large control input; on the other hand, a linear quadratic regulator (LQR) achieves large flapping amplitude with small input effort. We show that the mechanism is able to track sinusoidal motions with different amplitude, bias and frequencies with relatively large range by changing the springs, therefore generating roll and pitch torques that can be used for flight control. Then a Hopf oscillator based central pattern generator is also shown to be an alternative trajectory to track. The proposed wing actuation mechanism provides an at-scale wing testing platform for flapping wing micro aerial vehicles.