Video of ladybug during takeoff. 3,000 fps. 6,000 s^-1 shutter. F/11.
BYU's flapping wing mechanism demonstration. This mechanism uses 5 terms of a Fourier series expansion for each degree of freedom. A quintic polynomial drives the mechanism from rest to its starting kinematic position at the beginning and end of each flapping sequence.
This is the resulting "optimal" kinematics for the BYU flapping wing mechanism after one iteration of a Box-Behnken screening design. The objective of this design was to maximize both lift and thrust. A visual display of kinematics, resulting forces, and the mechanisms motion can all be visualized at once in this video.