A polishing apparatus is provided. Another aspect pertains to a self-leveling polishing apparatus for smoothing diamonds. Yet another aspect of the present system uses a ball and swivel joint in a diamond polishing machine. A further aspect employs a polishing apparatus including a diamond-holder, an elongated arm using gravity to apply downward polishing pressure of the diamond workpiece against a polishing wheel, and a sweeping transmission to cause the holder to radially move across the rotating polishing wheel.