This invention enables high-resolution, high-precision motion control at low cost. A novel flexure-beam motion-reducing actuator is incorporated into an XYO positioning stage to enable rigidly stable positioning of any object with sub-10-nanometer linear-positioning precision and sub-0.1-microradian rotary-positioning precision. The actuator's output element moves in the same direction as its input element. A single actuator enhances the resolution and precision of any motion-control drive mechanism by a factor as much as 50 or more, and a cascaded pair of actuators provide enhancement factors greater than 1000. In one embodiment, the enhancement factor is adjustable manually. The actuator and stage are useful for optical, lithographic and scanning probe applications.