Furthering our understanding of the physics of flapping flight has the potential to benefit the field of micro air vehicles. Advancements in micro air vehicles can benefit applications such as surveillance, reconnaissance, and search and rescue. In this research, flapping kinematics of a ladybug was explored using a direct linear transformation. A flapping mechanism design is presented that was capable of executing ladybug or other species-specific kinematics. The mechanism was based on a differential gear design, had two wings, and could flap in harsh environments. This mechanism served as a test bed for force analysis and optimization studies. The first study was based on a Box-Behnken screening design to explore wing kinematic parameter design space and manually search in the direction of flapping kinematics that optimized the objective of maximum combined lift and thrust. The second study used a Box-Behnken screening design to build a response surface. Using gradient-based techniques, this surface was optimized for maximum combined lift and thrust. Box-Behnken design coupled with response surface methodology was an efficient method for exploring the mechanism force response. Both methods for optimization were capable of successfully improving lift and thrust force outputs. The incorporation of the results of these studies will aid in the design of more efficient micro air vehicles and with the ultimate goal of leading to a better understanding of flapping wing aerodynamics and the development of aerodynamic models.