A fundamental requirement for achieving photoinduced unidirectional rotary motion about an olefinic bond in a molecular motor is that the potential energy surface of the excited state is asymmetric with respect to clockwise and counterclockwise rotations. In most available light-driven rotary molecular motors, such asymmetry is guaranteed by the presence of a stereocenter. Here, we present non-adiabatic molecular dynamics simulations based on multiconfigurational quantum chemistry to demonstrate that this chiral feature is not essential for inducing unidirectional rotary motion in molecules that incorporate a cyclohexenylidene moiety into a protonated Schiff-base framework. Rather, the simulations show that it is possible to exploit the intrinsic asymmetry of the puckered cyclohexenylidene to control the direction of photoinduced rotation.