Hemoglobin transports molecular oxygen from the lungs to all human tissues for cellular respiration. Its α2β2 tetrameric assembly undergoes cooperative binding and releasing of oxygen for superior efficiency and responsiveness. Over past decades, hundreds of hemoglobin structures were determined under a wide range of conditions for investigation of molecular mechanism of cooperativity. Based on a joint analysis of hemoglobin structures in the Protein Data Bank (Ren, companion article), here I present a reverse engineering approach to elucidate how two subunits within each dimer reciprocate identical motions that achieves intradimer cooperativity, how ligand-induced structural signals from two subunits are integrated to drive quaternary rotation, and how the structural environment at the oxygen binding sites alter their binding affinity. This mechanical model reveals the intricate design that achieves the cooperative mechanism and has previously been masked by inconsistent structural fluctuations. A number of competing theories on hemoglobin cooperativity and broader protein allostery are reconciled and unified.