skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Structural damping renders the hawkmoth exoskeleton mechanically insensitive to non-sinusoidal deformations
Muscles act through elastic and dissipative elements to mediate movement, which can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by an insect's exoskeleton, which acts as a spring with frequency-independent material properties under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a frequency-independent model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolated Manduca sexta thoraces under symmetric, asymmetric and band-limited white noise deformations. The asymmetric and white noise conditions represent two types of generalized, multi-frequency deformations that may be encountered during steady-state and perturbed flight. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, suggesting that the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of materials with frequency-independent damping to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and wing.  more » « less
Award ID(s):
2100858 1554790 1806833
PAR ID:
10438842
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of The Royal Society Interface
Volume:
20
Issue:
202
ISSN:
1742-5662
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, Journal of The Royal Society Interface)
    null (Ed.)
    Flapping-wing insects, birds and robots are thought to offset the high power cost of oscillatory wing motion by using elastic elements for energy storage and return. Insects possess highly resilient elastic regions in their flight anatomy that may enable high dynamic efficiency. However, recent experiments highlight losses due to damping in the insect thorax that could reduce the benefit of those elastic elements. We performed experiments on, and simulations of, a dynamically scaled robophysical flapping model with an elastic element and biologically relevant structural damping to elucidate the roles of body mechanics, aerodynamics and actuation in spring-wing energetics. We measured oscillatory flapping-wing dynamics and energetics subject to a range of actuation parameters, system inertia and spring elasticity. To generalize these results, we derive the non-dimensional spring-wing equation of motion and present variables that describe the resonance properties of flapping systems: N , a measure of the relative influence of inertia and aerodynamics, and K ^ , the reduced stiffness. We show that internal damping scales with N , revealing that dynamic efficiency monotonically decreases with increasing N . Based on these results, we introduce a general framework for understanding the roles of internal damping, aerodynamic and inertial forces, and elastic structures within all spring-wing systems. 
    more » « less
  2. ; ; ; ; ; (, Proceedings of the Royal Society B: Biological Sciences)
    null (Ed.)
    Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance. 
    more » « less
  3. ; ; (, Journal of Computational and Nonlinear Dynamics)
    Abstract Flapping-wing micro-air vehicles (FWMAVs) are an emerging technology inspired by flying insects that show promise in applications favoring maneuverability and vehicle compactness. However, current designs are limited by inefficient energetics, and current dynamical models of the flight system employ limiting assumptions when considering power demands. Here, we derive a system-level model of the insect flight system including the thorax, wing, and wing hinge that can inform insect-inspired FWMAV design. We applied the model to study the flight system of a hawkmoth, and used a genetic algorithm optimization to tune uncertain model parameters to minimize the power required to hover. Results show that performance is improved by utilizing multimodal excitation to produce favorable flapping kinematics. This is achieved by locating the flapping frequency of the moth between the nonlinear resonant frequencies, resulting in magnified flapping response and aerodynamically advantageous phase. The optimal flapping frequency can be predicted from the system’s underlying linear natural frequencies and is roughly 54% of the system’s mean natural frequency. Furthermore, effective solutions are configured so that the timing of the applied load and thorax responses are matched such that little effort is spent reversing the wing stroke. The optimized model parameters and corresponding kinematics show moderate agreement with those reported for the hawkmoth. To maintain hovering flight, the successful moths in the population expend approximately 58.5 W/kg. The system-level model and the governing principles identified here can inform the design of energy efficient FWMAVs moving forward. 
    more » « less
  4. ; ; (, Bioinspiration & Biomimetics)
    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. 
    more » « less
  5. ; ; ; ; (, Bioinspiration & Biomimetics)
    Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, ‘spring-wing’ flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces present possible challenges to generating stable and responsive wing motion. The energetic efficiency from resonance in insect flight is tied to the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases withN) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from 1 < N < 10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems, suggesting that mechanical resonance presents tradeoffs in insect flight control and stability. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email