Fo domain of ATP synthase functions as a rotary molecular motor, coupling proton translocation with the rotation of the c-ring rotor. This process involves proton uptake at the entry half channel, rotor rotation, and proton release to the exit half channel. While the overall coupling mechanism is established, the design principle for efficient rotation remains unclear. Here, we employed hybrid molecular simulations - combining coarse-grained modeling and Monte Carlo methods - to investigate the roles of side chain flexibility at proton-binding residues and the angular mismatch between the proton uptake process and the proton release process. Our results indicate that both factors promote rotational activity, with side chain flexibility playing a more significant role. Comparable analysis of Fo structures from different species revealed that the key residue geometry is conserved, and that the asymmetric geometry of the two half channels aligns with the mechanism suggested by simulation. These findings highlight a conserved design principle that enhances rotational efficiency and offer a mechanistic basis for engineering synthetic rotary systems.