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Buzz pollination involves the release of pollen from, primarily, poricidal anthers through vibrations generated by certain bee species. Despite previous experimental and numerical studies, the intricacies of pollen dynamics within vibrating anthers remain elusive due to the challenges in observing these small-scale, opaque systems. This research employs the discrete element method to simulate the pollen expulsion process in vibrating anthers. By exploring various frequencies and displacement amplitudes, a correlation between how aggressively the anther shakes and the initial rate of pollen expulsion is observed under translating oscillations. This study highlights that while increasing both the frequency and displacement of vibration enhances pollen release, the rate of release does not grow linearly with their increase. Our findings also reveal the significant role of pollen–pollen interactions, which account for upwards of one-third of the total collisions. Comparisons between two types of anther exits suggest that pore size and shape also influence expulsion rates. This research provides a foundation for more comprehensive models that can incorporate additional factors such as cohesion, adhesion and Coulomb forces, paving the way for deeper insights into the mechanics of buzz pollination and its variability across different anther types and vibration parameters. 

Abstract Flying insects have a robust flight system that allows them to fly even when their forewings are damaged. The insect must adjust wingbeat kinematics to aerodynamically compensate for the loss of wing area. However, the mechanisms that allow insects with asynchronous flight muscle to adapt to wing damage are not well understood. Here, we investigated the phase and amplitude relationships between thorax deformation and flapping angle in tethered flying bumblebees subject to wing clipping and weighting. We used synchronized laser vibrometry and high-speed videography to measure thorax deformation and flapping angle, respectively. We found that changes in wing inertia did not affect thorax deformation amplitude but did influence wingbeat frequency. Increasing wing inertia increased flapping amplitude and caused a phase lag between thorax deformation and flapping angle, whereas decreasing wing inertia did not affect flapping amplitude and caused the flapping angle to lead thorax deformation. Our findings indicate that bumblebees adapt to wing damage by adjusting their wingbeat frequency rather than altering their wing stroke amplitude. Additionally, our results suggest that bumblebees operate near a wing-hinge-dominated resonant frequency, and that moments generated by steering muscles within the wing hinge influence the phase between thorax deformation and wing stroke nontrivially. These insights can inform the design of resilient, insect-inspired flapping-wing micro air vehicles. 

Abstract Several agriculturally valuable plants store their pollen in tube-like poricidal anthers, which release pollen through buzz pollination. In this process, bees rapidly vibrate the anther using their indirect flight muscles. The stiffness and resonant frequency of the anther are crucial for effective pollen release, yet the impact of turgor pressure on these properties is not well understood. Here, we performed three-point flexure tests and experimental modal analysis to determine anther transverse stiffness and resonant frequency, respectively. Dynamic nanoindentation was used to identify the anther storage modulus as a function of excitation frequency. We subsequently developed mathematical models to estimate how turgor pressure changes after the anther is removed from a flower, thereby emulating zero water availability. We found that anther stiffness decreased by 60% at 30 min post-ablation and anther resonant frequency decreased by 20% at 60 min post-ablation. Models indicated that turgor pressure in the fresh anther was ~0.2–0.3 MPa. Our findings suggest that natural fluctuations in turgor pressure due to environmental factors such as temperature and light intensity may require bees to adjust their foraging behaviors. Interestingly, the anther storage modulus increased with excitation frequency, underscoring the need for more sophisticated mechanical models that consider viscous fluid transport through plant tissue. 

Insects have developed diverse flight actuation mechanisms, including synchronous and asynchronous musculature. Indirect actuation, used by insects with both synchronous and asynchronous musculature, transforms thorax exoskeletal deformation into wing rotation. Though thorax deformation is often attributed exclusively to muscle tension, the inertial and aerodynamic forces generated by the flapping wings may also contribute. In this study, a tethered flight experiment was used to simultaneously measure thorax deformation and the inertial/aerodynamic forces acting on the thorax generated by the flapping wing. Compared to insects with synchronous musculature, insects with asynchronous muscle deformed their thorax 60% less relative to their thorax diameter and their wings generated 2.8 times greater forces relative to their body weight. In a second experiment, dorsalventral thorax stiffness was measured across species. Accounting for weight and size, the asynchronous thorax was on average 3.8 times stiffer than the synchronous thorax in the dorsalventral direction. Differences in thorax stiffness and forces acting at the wing hinge led us to hypothesize about differing roles of series and parallel elasticity in the thoraxes of insects with synchronous and asynchronous musculature. Specifically, wing hinge elasticity may contribute more to wing motion in insects with asynchronous musculature than in those with synchronous musculature. 

Small-scale flapping-wing micro air vehicles (FWMAVs) are an emerging robotic technology with many applications in areas including infrastructure monitoring and remote sensing. However, challenges such as inefficient energetics and decreased payload capacity preclude the useful implementation of FWMAVs. Insects serve as inspiration to FWMAV design owing to their energy efficiency, maneuverability, and capacity to hover. Still, the biomechanics of insects remain challenging to model, thereby limiting the translational design insights we can gather from their flight. In particular, it is not well-understood how wing flexibility impacts the energy requirements of flapping flight. In this work, we developed a simple model of an insect drive train consisting of a compliant thorax coupled to a flexible wing flapping with single-degree-of-freedom rotation in a fluid environment. We applied this model to quantify the energy required to actuate a flapping wing system with parameters based off a hawkmoth Manduca sexta. Despite its simplifications, the model predicts thorax displacement, wingtip deflection and peak aerodynamic force in proximity to what has been measured experimentally in flying moths. We found a flapping system with flexible wings requires 20% less energy than a flapping system with rigid wings while maintaining similar aerodynamic performance. Passive wing deformation increases the effective angle of rotation of the flexible wing, thereby reducing the maximum rotation angle at the base of the wing. We investigated the sensitivity of these results to parameter deviations and found that the energetic savings conferred by the flexible wing are robust over a wide range of parameters. 

Abstract Insect wings are heterogeneous structures, with flexural rigidity varying one to two orders of magnitude over the wing surface. This heterogeneity influences the deformation the flapping wing experiences during flight. However, it is not well understood how this flexural rigidity gradient affects wing performance. Here, we develop a simplified 2D model of a flapping wing as a pitching, plunging airfoil using the assumed mode method and unsteady vortex lattice method to model the structural and fluid dynamics, respectively. We conduct parameter studies to explore how variable flexural rigidity affects mean lift production, power consumption and the forces required to flap the wing. We find that there is an optimal flexural rigidity distribution that maximizes lift production; this distribution generally corresponds to a 3:1 ratio between the wing’s flapping and natural frequencies, though the ratio is sensitive to flapping kinematics. For hovering flight, the optimized flexible wing produces 20% more lift and requires 15% less power compared to a rigid wing but needs 20% higher forces to flap. Even when flapping kinematics deviate from those observed during hover, the flexible wing outperforms the rigid wing in terms of aerodynamic force generation and power across a wide range of flexural rigidity gradients. Peak force requirements and power consumption are inversely proportional with respect to flexural rigidity gradient, which may present a trade-off between insect muscle size and energy storage requirements. The model developed in this work can be used to efficiently investigate other spatially variant morphological or material wing features moving forward. 

Abstract Flapping insect wings collide with vegetation and other obstacles during flight. Repeated collisions may irreversibly damage the insect wing, thereby compromising the insect's ability to fly. Further, reaction torques caused by the collision may destabilize the insect and hinder its ability to maneuver. To mitigate the adverse effects of impact, some insect wings are equipped with a flexible joint called a “costal break.” The costal break buckles once it exceeds a critical angle, which is believed to improve flight stability and prevent irreversible wing damage. However, to our knowledge, there are no models to predict the dynamics of the costal break. Through this research, we develop a simple model of an insect wing with a costal break. The wing was modeled as two beams interconnected by a torsional spring, where the stiffness of the torsional spring instantaneously decreases once it has exceeded a critical angle. We conducted a series of static tests to approximate model parameters. Then, we used numerical simulation to estimate the reaction moments, angular impulse, and peak stresses experienced by the wing during a collision. When evaluated over the duration of an external load, we found that buckling could reduce reaction moments and angular impulse up to 82% and 99%, respectively, compared to a homogeneous wing. This suggests the costal break can enhance flight stability. On the other hand, buckling maximally increased peak stresses two times compared to a homogeneous wing, indicating the costal break does not reduce likelihood of damage under the simplified loading considered. 

Abstract Approximately 10% of flowering plant species conceal their pollen within tube-like poricidal anthers. Bees extract pollen from poricidal anthers via floral buzzing, a behavior during which they apply cyclic forces by biting the anther and rapidly contracting their flight muscles. The success of pollen extraction during floral buzzing relies on the direction and magnitude of the forces applied by the bees, yet these forces and forcing directions have not been previously quantified. In this work, we developed an experiment to simultaneously measure the directional forces and thorax kinematics produced by carpenter bees (Xylocopa californica)during defensive buzzing, a behavior regulated by similar physiological mechanisms as floral buzzing. We found that the buzzing frequencies averaged about 130 Hz and were highly variable within individuals. Force amplitudes were on average 170 mN, but at times reached nearly 500 mN. These forces were 30–80 times greater than the weight of the bees tested. The two largest forces occurred within a plane formed by the bees’ flight muscles. Force amplitudes were moderately correlated with thorax displacement, velocity and acceleration amplitudes but only weakly correlated with buzzing frequency. Linear models developed through this work provide a mechanism to estimate forces produced during non-flight behaviors based on thorax kinematic measurements in carpenter bees. Based on the buzzing frequencies, individual bee’s capacity to vary buzz frequency and predominant forcing directions, we hypothesize that carpenter bees leverage vibration amplification to increase the deformation of poricidal anthers, and hence the amount of pollen ejected.