A parametric investigation into flapping flight is presented. For a Reynolds number of 75, harmonically forced flapping dynamics is studied. A wing section is modeled as two rigid links connected by a hinge with a torsion spring-damper combination. This section is wrapped in a smooth aerodynamic surface for immersion in the fluid domain. An immersed boundary method is employed on a two-dimensional structured Cartesian grid to solve the incompressible form of the Navier-Stokes equations for low Reynolds numbers by using a finite difference method. Fully coupled fluid-structure interactions are considered. Performance metrics, which include cycle-averaged lift, drag, power, and their ratios, are used to characterize the effects of different parameters and kinematics. Principal components of flow-field structures are quantified, and the system's response is correlated to performance. The thesis findings can serve as a basis to understand and identify flapping frequencies that provide high performance.