Folding in and out: passive morphing in flapping wings.

We present a new mechanism for passive wing morphing of flapping wings inspired by bat and bird wing morphology. The mechanism consists of an unactuated hand wing connected to the arm wing with a wrist joint. Flapping motion generates centrifugal accelerations in the hand wing, forcing it to unfold passively. Using a robotic model in hover, we made kinematic measurements of unfolding kinematics as functions of the non-dimensional wingspan fold ratio (2-2.5) and flapping frequency (5-17 Hz) using stereo high-speed cameras. We find that the wings unfold passively within one to two flaps and remain unfolded with only small amplitude oscillations. To better understand the passive dynamics, we constructed a computer model of the unfolding process based on rigid body dynamics, contact models, and aerodynamic correlations. This model predicts the measured passive unfolding within about one flap and shows that unfolding is driven by centrifugal acceleration induced by flapping. The simulations also predict that relative unfolding time only weakly depends on flapping frequency and can be reduced to less than half a wingbeat by increasing flapping amplitude. Subsequent dimensional analysis shows that the time required to unfold passively is of the same order of magnitude as the flapping period. This suggests that centrifugal acceleration can drive passive unfolding within approximately one wingbeat in small and large wings. Finally, we show experimentally that passive unfolding wings can withstand impact with a branch, by first folding and then unfolding passively. This mechanism enables flapping robots to squeeze through clutter without sophisticated control. Passive unfolding also provides a new avenue in morphing wing design that makes future flapping morphing wings possibly more energy efficient and light-weight. Simultaneously these results point to possible inertia driven, and therefore metabolically efficient, control strategies in bats and birds to morph or recover within a beat.