The Effect of Mechanism-Driven Spanwise Folding Kinematics on the Aerodynamic Performance of Flapping Wings

Abstract 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-rocker mechanism augmented with a folding loop. A closed-form position analysis of the linkage yields an analytical expression for the folding phase angle ϕ _f as a function of the flapping-loop link lengths alone, and a two-stage genetic-algorithm optimization identifies the linkage geometry that minimizes ϕ _f 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 1.0 to 2.2 produces an explicit lift–thrust trade-off, with the lift efficiency rising by 27% as the outer-wing fraction grows. The mean folding angle is identified as the primary lever for tuning the lift–thrust 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.