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The complex wing motion of insects and small birds leads to high lift production in nature. Specific lift-enhancing mechanismsarise from the combination of a horizontal stroke motion and a secondary wing pitching motion. Research around flapping wing nano air vehicles (FWNAVs) copies this wing motion to fly small drones, in an effort to benefit from the same mechanisms. A flapping wing aerodynamic model can predict the force production of the FWNAV and helps to understand the influence of the wing kinematics thereon. This work starts from a quasi-steady model expression for the aerodynamics and proposes a wind tunnel procedure to identify the force coefficients in the model empirically. The procedure is based on a test case performed by the AVT-202 research team which combines wing translation and wing rotation, imitating the aerodynamic condition of the flapping wing in a simplified set-up. Comparison of measurements and model simulations demonstrates that the procedure can be used to update the model parameters for our specific FWNAV configuration, leading to an empirical relation for the force coefficients. Simulations with the updated model using the empirical relations show good agreement with measured force production for a wide range of input variables.

This system was developed for a first FWNAV prototype at KU Leuven [13]. Another configuration uses a direct transmission from the motor to the wing motion and the motor is driven with an alternating current [12,17,18]. This system reduces the complexity of the drive-line and therefore system robustness improves. Control can be exerted by actively adapting the motor current [19].The introduction of an elastic element into the drive-line, which is designed to operate at a near resonance frequency is shown to reduce the overall power requirements of the system [12,20]. This concept is currently used in the Kulibrie FWNAV which serves as reference prototype. A third configuration uses a piezoelectric actuator [21]. This concept is particularly effective for very small designs but a DC-DC converter is needed, which poses a significant weight challenge.Improvement of overall performance is essential to increase the use of FWNAVs in practical applications. This can be done by optimizing the wing design and aerodynamics [22,23] or by optimizing the drive-line dynamics. Because the wing stroke is the most demanding motion of the system, this work focuses on the wing drive-line dynamics, driving the stroke motion to accomplish this performance gain. The study uses a model-based approach to complement the foregoing experimental work. This model-based approach starts from a lumped parameter single degree of freedom (DOF) mass-spring-damper model, which is adopted by several research groups [12,15,18,20,[24][25][26]. This model concept is used in the assumption that the influence of the wing pitch dynamics on the stroke dynamics is negligible. However the change in wing inclination is in previous research always included in the calculation of the wing aerodynamics. This work starts from the idea that 1 DOF is sufficient to model the relevant phenomena present in the drive-line dynamics and it completely removes the model terms related to the second DOF [27]. The input to the resulting second order nonlinear time-invariant model is the motor current. The model simulation provides an instantaneous stroke angle.A sensitivity analysis using the resulting model expression identifies the parameters which have the largest influence on performance. The efficiency of the drive-line system is used as the key performance indicator. This paper distinguishes between wing motion parameters and drive-line system parameters. Sensitivity analysis of the wing motion parameters gives the optimal controller input settings. Efficiency analysis of the drive-line system parameters is utilized to predict the

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