1. A METHOD FOR SIMULTANEOUSLY FINISHING THE CONTACTING SURFACES OF INTERNAL AND EXTERNAL TEETH IN A MISALIGNMENT COUPLING OF THE TYPE COMPRISING A TUBULAR SLEEVE HAVING INTERNAL TEETH FORMED THEREON AND A SUBSTANTIALLY CO-AXIAL MATING HUB HAVING EXTERNAL TEETH FORMED THEREON, SAID METHOD COMPRISING THE STEPS OF ROTATING SAID SLEEVE AROUND ITS AXIS, TRANSMITTING THE ROTATION TO SAID HUB INDEPENDENTLY OF THE TEETH, APPLYING A CIRCUMFERENTIAL LOADING BETWEEN THE INTERNAL AND EXTERNAL TEETH INDEPENDENTLY OF THE ROTATING MOVEMENT, MOVING THE HUB AXIALLY OF THE SLEEVE IN A RECIPROCATING MOTION, SIMULTANEOUSLY OSCILLATING THE HUB IN A RANDOM MOTION AROUND A POINT LOCATED GENERALLY IN A PLANE PASSING THROUGH THE POINTS OF GEAR TEETH ENGAGEMENT, AND APPLYING A LAPPING COMPOUND BETWEEN THE TEETH DURING MOVEMENT OF THE HUB.