A method and apparatus for robotic devices that can be used to load and remove workpieces and abrasive disks for an abrading system having a floating, rotatable abrading platen that is three-point supported by annular, flat abrading-surface of the floating platen. The rotary spindles are mounted on the flat horizontal surface of a machine base and the spindle-top flat surfaces are aligned to be precisely co-planar with each other where the rotational-centers of each of the spindles fixed-position rotary flat-surfaced spindles. The flexible abrasive disks are releasably attached to the are positioned at the center of the annular radial-width of the platen abrading-surface. Flat-surfaced workpieces are attached to the spindle-top flat surfaces and the abrasive surface of the abrasive disk that is attached to the rotating floating-platen abrading surface contacts the workpieces to perform single-sided abrading on the workpieces. Workpieces can be flat-lapped to provide precision-flat and smoothly-polished surfaces.