Power extraction from wind and water streams using flapping wings is known to be an alternative method to harvest renewable energy. The vortical flow structures around and in the wake of a NACA0012 airfoil oscillating with non-sinusoidal pitching and plunging motions are investigated using digital particle image velocimetry and compared with Navier-Stokes computations to give insight into the physics that determine the performance of an oscillating-wing power generator for a plunge amplitude of 1.05 chords, reduced frequency of 0.8, pitch amplitude of 73deg, pivot points at quarter and mid-chords, phase angles of 90 and 110deg, and stroke reversal times (TR) of 0.1 (rapid reversal) to 0.5 (sinusoidal reversal) at a Reynolds number of Re=1100. As the airfoil rotation speed during pitch reversals is increased, vortex shedding occurs earlier with higher strength. As the phase angle by which the pitching motion leads the plunging motion is increased, the shed vortex convection distance is also increased. There is good agreement between the flow structures obtained using 2_D Navier-Stokes simulations and those from particle image velocimetry measurements in terms of the formation, evolution and the timing of shedding of the leading edge and trailing edge vortices. Time-averaged vorticity results reveal that power producing oscillating-airfoils generate a time-averaged wake flow whereas an inner-jet like flow is present for all the cases with negative time averaged power output. Both particle image velocimetry measurements and Navier-Stokes simulations show that the time averaged power output is primarily determined by the timing of the formation of the leading edge vortex, its convection, and its interaction with the airfoil.