{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T11:44:45Z","timestamp":1788522285900,"version":"build-2803163510"},"reference-count":32,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T00:00:00Z","timestamp":1668988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation","award":["CBET-1855383"],"award-info":[{"award-number":["CBET-1855383"]}]},{"name":"National Science Foundation","award":["CMMI-1942810"],"award-info":[{"award-number":["CMMI-1942810"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/biomimetics7040207","type":"journal-article","created":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T03:09:30Z","timestamp":1669000170000},"page":"207","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Modeling and Analysis of a Simple Flexible Wing\u2014Thorax System in Flapping-Wing Insects"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7087-3945","authenticated-orcid":false,"given":"Braden","family":"Cote","sequence":"first","affiliation":[{"name":"Mechanical & Industrial Engineering, Montana State University, 220 Roberts Hall, Bozeman, MT 59717, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1199-4576","authenticated-orcid":false,"given":"Samuel","family":"Weston","sequence":"additional","affiliation":[{"name":"Mechanical & Industrial Engineering, Montana State University, 220 Roberts Hall, Bozeman, MT 59717, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6305-0564","authenticated-orcid":false,"given":"Mark","family":"Jankauski","sequence":"additional","affiliation":[{"name":"Mechanical & Industrial Engineering, Montana State University, 220 Roberts Hall, Bozeman, MT 59717, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,21]]},"reference":[{"key":"ref_1","unstructured":"Luo, C., Espinosa, A.P., Pranantha, D., and De Gloria, A. 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