A fluid-powered rotary actuator having a body with a shaft disposed therein and having a linear-to-rotary force-converting member mounted for longitudinal movement within said body in response to the selective application of pressurized fluid thereto. The actuator uses a torque member having a flange portion attached to the body or an external structure and a grooved central portion. A piston sleeve has outward grooves meshing with inward grooves on the shaft and inward grooves for meshing with outward grooves on the torque member central portion. The body sidewall is not used as a torque transmission surface during fluid-powered operation of the actuator.