A motor that delivers high force linear motion or high torque rotary motion to a moving element. The motor may include a driving brake, a driver, a holding brake and a flexible moving element. Operation of the motor may involve activating the holding brake, activating the driver to flex the moving element, activating the holding brake to maintain the position of a portion of the moving element, releasing the driving brake, and restoring the moving element to an unflexed position. The elements are arranged to provide linear motion, belt-driven rotary motion, or directly-coupled rotary motion using brakes and drivers arranged in linear or circular fashion. Drivers may be linear or rotary actuators or motors based on electrostatic, piezoelectric, magnetic, or electrostrictive properties. The brakes may be applied through electrostatic forces, magnetic forces, or mechanical gears engaged with a linear or rotary driving mechanism.