Actuation mechanisms driven by rotary motors are described whereby linear movement of a mechanical component, typically a lens barrel, is effected without rotating the linear moving component. For mechanisms driven by miniature piezoelectric motors, this is accomplished by driving a rotor which in turn causes linear, and only linear, movement of a lens barrel according to structures described in different embodiments. A preferred embodiment includes a threaded rotor moving both rotationally and axially that drives a two-piece lens barrel assembly. Another embodiment includes a rotor having a grooved split ring on its outer surface that does not move axially and drives a lens barrel through a threaded interface. Another embodiment includes a two-piece rotor that does not move axially and drives a lens barrel through a threaded interface. Typically, anti-rotation pins and corresponding grooves in a fixed structure are used to prevent the lens barrel from rotating.