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Biomim."],"published-print":{"date-parts":[[2026,10,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    This study presents a mechanism-driven analysis of spanwise folding kinematics in bird-inspired ornithopters, in which the folding motion is generated by a planar crank\u2013rocker mechanism augmented with a folding loop. A closed-form position analysis of the linkage yields an analytical expression for the folding phase angle\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msub>\n                            <mml:mi>\u03d5<\/mml:mi>\n                            <mml:mrow>\n                              <mml:mi mathvariant=\"normal\">f<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    as a function of the flapping-loop link lengths alone, and a two-stage genetic-algorithm optimization identifies the linkage geometry that minimizes\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msub>\n                            <mml:mi>\u03d5<\/mml:mi>\n                            <mml:mrow>\n                              <mml:mi mathvariant=\"normal\">f<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    for prescribed inner-wing kinematic targets. An in-house integrated simulation framework, which couples a modified unsteady vortex-lattice method with a multi-flexible-body dynamics model, is then applied to a parametric study spanning the wing length ratio, the folding amplitude, and the mean folding angle within the resulting feasible design space. The framework is validated against wind-tunnel force measurements for flexible flapping wings and against forward-flight test data for a single-joint ornithopter. The minimum-phase configuration produces a marginally positive mean thrust at the baseline operating point, whereas the maximum-phase configuration produces negative mean thrust. Varying the wing length ratio from\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mn>1.0<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    to\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mn>2.2<\/mml:mn>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    produces an explicit lift\u2013thrust trade-off, with the lift efficiency rising by\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mn>27<\/mml:mn>\n                          <mml:mi mathvariant=\"normal\">%<\/mml:mi>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    as the outer-wing fraction grows. The mean folding angle is identified as the primary lever for tuning the lift\u2013thrust balance of the mechanism-driven folding wing, while the folding amplitude provides a secondary adjustment around each operating point. The proposed mechanism-driven framework connects linkage geometry, kinematic constraints, and aerodynamic performance within a single analytical-numerical pipeline, supporting the systematic design of bird-inspired ornithopters with spanwise folding wings.\n                  <\/jats:p>","DOI":"10.1088\/1748-3190\/ae8a9d","type":"journal-article","created":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T22:53:24Z","timestamp":1784069604000},"page":"056007","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["The effect of mechanism-driven spanwise folding kinematics on the aerodynamic performance of flapping wings"],"prefix":"10.1088","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6341-660X","authenticated-orcid":true,"given":"Hyeon-Ho","family":"Yang","sequence":"first","affiliation":[{"name":"Korea Advanced Institute of Science and Technology (KAIST)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1470-416X","authenticated-orcid":true,"given":"Sang-Gil","family":"Lee","sequence":"additional","affiliation":[{"name":"Korea Advanced Institute of Science and Technology (KAIST)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5311-9855","authenticated-orcid":true,"given":"Jae-Hung","family":"Han","sequence":"additional","affiliation":[{"name":"Korea Advanced Institute of Science and Technology (KAIST)"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,9,8]]},"reference":[{"key":"bbae8a9dbib1","doi-asserted-by":"publisher","author":"Shyy","year":"2007","DOI":"10.1017\/CBO9780511551154","type":"book"},{"key":"bbae8a9dbib2","doi-asserted-by":"publisher","DOI":"10.1115\/1.4005525","type":"journal-article","article-title":"A review of bird-inspired flapping wing miniature air vehicle designs","volume":"4","author":"Gerdes","year":"2012","journal-title":"J. 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