Flying insects and robots that mimic them flap and rotate (or pitch) their wings with large angular amplitudes. The reciprocating nature of flapping requires rotation of the wing at the end of each stroke. Insects or flapping-wing robots could achieve this by directly exerting moments about the axis of rotation using auxiliary muscles or actuators. However, completely passive rotational dynamics might be preferred for efficiency purposes, or, in the case of a robot, decreased mechanical complexity and reduced system mass. Herein, the detailed equations of motion are derived for wing rotational dynamics, and a blade-element model is used to supply aerodynamic force and moment estimates. Passive-rotation flapping experiments with insect-scale mechanically driven artificial wings are conducted to simultaneously measure aerodynamic forces and three-degree-of-freedom kinematics (flapping, rotation and out-of-plane deviation), allowing a detailed evaluation of the blade-element model and the derived equations of motion. Variations in flapping kinematics, wing-beat frequency, stroke amplitude and torsional compliance are made to test the generality of the model. All experiments showed strong agreement with predicted forces and kinematics, without variation or fitting of model parameters.
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