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This paper investigates the hovering efficiency of the wing-actuation parameters of a flapping microaerial vehicle with a two-degree-of-freedom (2-DOF) driving mechanism, using finite-element analysis based on the arbitrary Lagrangian-Eulerian method (ALE-FEA). A 75-mm-long wing and multilinkage mechanism that consisted of thin plates and films was employed. It generated a flapping motion that consisted of horizontal stroke of the wing and twist around its leading edge, which were activated by the rotations of two motors. The application of the ALE-FEA was successfully extended to the structural behavior of the driving mechanism. The behaviors of the linkage mechanism, the wing, and its surrounding airflow were reproduced numerically. Various parameters were obtained, some of which were difficult to measure in real experiments, such as the pressure distribution on the wing. For cases of 25 combinations of wings' twist angles and flapping periods, lift forces and energy requirements for the motors were determined. Based on these results, the most efficient flapping combination that generated 1 gf lift force was calculated. In contrast with the combination that created the strongest lift force, the combination of a larger twist angle and a faster flapping cycle was found to provide the most efficient flight.