Abstract: A CNC system for effecting a finishing treatment of a surface, including: a mechanical assembly having a mechanical arm, adapted to move within at least two controllable axes of motion; a shoe arrangement, adapted to connect to an end of the arm and having at least one flexible surface finishing pad; and a drive mechanism adapted to drive the arm; a controller; a communication arrangement adapted to deliver communication signals between the controller and the mechanical assembly; and a positioning system providing the controller with positioning information with respect to the mechanical assembly, the system configured whereby the arm is responsive to the controller, the mechanical assembly adapted to urge the working surface against a workpiece surface, whereby a pressure is delivered thereto, the mechanical assembly including a controllable spring arrangement disposed and adapted to contribute to an overall mechanical compliance, normal to the working surface, of the mechanical assembly, the spring arrangem