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This paper develops a numerical simulation tool for designing passive rotation flapping wing mechanisms. The simulation tool includes a quasi-static model of the piezoelectric actuator bending, transmission kinematics, and the small Reynolds number aerodynamic forces governing wing dynamics. To validate the developed tool, two single-wing systems with distinct resonant frequencies are manufactured and characterized. Comparison to experimental results reveals that, although discrepancies exist, the simulation is able to predict general trends of wing kinematics and lift behavior as functions of frequency, thus, being useful as a design tool. Finally, the complex models, ranging from actuator deflection to wing aerodynamics presented in this paper, allow analysis of the complete system revealing insight into several wing trajectory control methodologies, and potentially serving as a design and optimization tool for future flapping wing robots.