Approaches are currently being developed for converting ocean wave energy by creating mechanical rotations within buoys. These devices benefit from the absence of mechanical stops that may destroy devices that utilize mechanical translations within buoys. In the present work, an analysis is developed that quantifies the mechanical coupling of ocean waves to rotational motions within a buoy. The analysis accounts for motions that are nonlinear with respect to the rotation angle, thus including devices in which internal bodies may spin completely around. It is assumed that the device impedance is small relative to the wave impedance, so that the device does not alter the motion induced by the incident ocean wave. In this limit, the imposed motion on the exterior of the buoy is assumed known from wave height and period. Conversion of the rotational energy to electrical energy is modeled by representing the power takeoff as an attached frequency‐dependent impedance. The analysis is coupled to an optimization process that maximizes energy conversion by varying design parameters such as eccentric mass, eccentricity, power takeoff, and buoy geometry.