In one example, a nutating fluid-mechanical energy converter to power wellbore drilling includes a fluid-mechanical device and a rotation transfer device, each positionable in a wellbore drill string. The fluid-mechanical device includes a stator including an outer cylinder having a longitudinal passage and a longitudinal guide positioned in the longitudinal passage, which, with the stator, defines an annulus. A rotor cylinder is positioned in the annulus. The rotor cylinder includes a sidewall with a guide opening to receive the longitudinal guide. The rotor cylinder rotates within the stator along the longitudinal guide in response to the wellbore drilling fluid flow through the annulus. The rotation transfer device transfers at least a portion of a rotation of the rotor cylinder to a wellbore drill bit.