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The influence that the kinematics of pitching and heaving 2D airfoils has on the aerodynamic forces is investigated using direct numerical simulations and a force decomposition algorithm. Large-amplitude motions are considered (of the order of one chord), with moderate Reynolds numbers and reduced frequencies of order 0(1), varying the mean pitch angle and the phase shift between the pitching and heaving motions. Our results show that the surface vorticity contribution (viscous effect) to the aerodynamic force is negligible compared with the contributions from the body motion (fluid inertia) and the vorticity within the flow (circulation). For the range of parameters considered here, the latter tends to be instantaneously oriented in the direction normal to the chord of the airfoil. Based on the results discussed in this paper, a reduced-order model for the instantaneous aerodynamic force is proposed, taking advantage of the force decomposition and the chord-normal orientation of the contribution from vorticity within the flow to the total aerodynamic force. The predictions of the proposed model are compared with those of a similar model from the literature, showing a noticeable improvement in the prediction of the mean thrust, and a smaller improvement in the prediction of the mean lift and the instantaneous force coefficients.