Bats, with highly articulated wings, are some of the most agile flyers in nature. A novel three-dimensional geometric decomposition framework is developed to reduce the complex kinematics of a bat wing into physical movements used to describe flapping flight: namely flapping, stroke plane deviation and pitching, together with cambering and flexion. The decomposition is combined with aerodynamic simulations to investigate the cumulative effect of each motion on force production, and their primary contribution to the unsteady vortex dynamics. For the nearly straight and level flight of Hipposideros pratti, results show that the flapping motion by itself induced a moderate drag and lift. Stroke plane deviation increased lift, and nullified the drag. With the inclusion of the pitching motion into the kinematics, lift production further increased by a factor of more than 2.5, and exhibited a positive net thrust by virtue of the favorable wing orientation during the upstroke. The primary contribution of cambering, which included a maximum chord line displacement of ≈40% standard mean chord, was the stabilization of the leading edge vortex during the downstroke. This increased mean lift by about 35% at the expense of net thrust. Flexion was perhaps the most complex motion with maximum displacements of 75% standard mean chord. This was instrumental in reducing the negative lift during the upstroke by preventing the formation of strong leading edge vortices. The aerodynamic effective angle of attack emerged as a heuristic parameter to describe lift and net thrust production across movements.