Abstract: A vibration-damped machine and method including beam being capable of gross movements in space relative to a stationary frame, means including a motor for causing the beam's gross movements; the gross movements tending to induce vibration into the beam, sensors for providing a signal representative of the induced beam vibration, an linear-acting inertial actuator mounted to the beam, and control means for receiving the signal and generating an output signal to actively drive the linear-acting inertial actuator at the appropriate phase, frequency and magnitude to damp induced beam vibrations. Embodiments of the vibration-damped machine are illustrated for a gantry robot, a horizontal machining center, an adhesive dispenser and a pivoting robot. The linear-acting inertial actuator is preferably controlled according to an inertial damping control method where the actuator is forced to behave as a damper attached to ground.