Recently, significant advances in the understanding of low Reynolds number flapping wing aerodynamics have been achieved, mostly driven by the research efforts towards the development of micro and nano air vehicles. These vehicles are being designed for indoor applications that can range from reconnaissance to espionage or rescue, where flapping wings overperform rotatory and rigid wings. Due to the fact that the flapping wings provide lift, thrust and maneuvering simultaneously, further investigation into their kinematics is essential for latter design phases. A parametric study of the aerodynamic performance of flapping wings was conducted by means of bidimensional numerical simulations, at a fixed Reynolds number of 1400. Three parameters were explored in a hovering, pitching and plunging airfoil: mean angle of attack, phase lag between pitch and plunge, and flapping mode (normal or water-treading). Lift generation and aerodynamic efficiency were evaluated for each of 30 cases that were studied. It was found that changing the angle of attack is the most effective way of producing additional lift, rather than changing the phase, whilst the best flapping mode depends on the specific application: normal flapping mode is steadily efficient for a range of angles of attack; water-treading mode is very efficient in a narrow range of angles of attack, but its efficiency declines when changing to an off-design angle of attack in spite of producing extra lift. The instantaneous vorticity and pressure fields for the best cases are analyzed to identify and explain the importance of non-stationary effects such as dynamic stall and wing-wake interactions, by comparing them to the quasi-steady predictions for the same kinematics. Finally, the results are compared and validated against similar numerical and experimental studies.