Design optimization and robustness analysis of rigid–link flapping mechanisms

Rigid-link mechanisms remain widely used in flapping-wing micro-aerial vehicles (MAVs) capable of untethered flight. However, MAVs with these mechanisms require significant weight reduction to achieve high agility and maneuverability. One approach involves using single-DOF planar rigid linkages, which are rarely optimized dimensionally for high lift and low power, considering their sweeping kinematics and the unsteady aerodynamic effects. We integrated a mechanism simulator based on a quasistatic nonlinear finite element method with an unsteady vortex lattice method-based aerodynamic analysis tool within an optimization routine. We optimized three different mechanism topologies from the literature. Significant power savings of up to 55% were observed in some cases, arising from larger flapping amplitudes and improvements in sweeping velocity profiles that produced higher lift coefficients. Experimental results confirmed that the optimal solutions generated higher lift at similar power for a given flapping frequency and achieved similar lift levels at lower flapping frequencies and lower power. We also conducted a robustness analysis to quantify performance sensitivity to manufacturing tolerances. It provided a trade-off between performance and reliability and revealed the need for tight manufacturing tolerances and careful material selection. Finally, the analysis can assist in comparing and selecting suitable mechanism topologies, as we observed significant variation in performance across different topologies for a given design lift value. The presented unified computational tool can find application in flapping mechanism topology optimization, as it can simulate a broad class of single-DOF planar rigid linkages by supplying only their initial configurations.