1. IN AN AUTOMATIC LATHE PROVIDED WITH A THREADING DEVICE, A WORKPIECE CARRYING SPINDLE, A MOVABLE TOOLHOLDER SUPPORT, A THREADCUTTING LATHE TOOL CARRIED BY SAID TOOL-HOLDER SUPPORT, AND MEANS FOR DISPLACING SAID TOOLHOLDER SUPPORT PARALLELLY TO THE AXIS OF SAID SPINDLE, THE COMBINATION OF A DEBURRING LATHE TOOL MOUNTED ON SAID TOOL-HOLDER SUPPORT IN APPROXIMATIVELY THE SAME PLANE BUT ANGULARLY DISPLACED WITH RESPECT TO SAID THREAD CUTTING TOOL, MEANS FOR DISPLACING SAID DEBURRING LATHE TOOL WITH RESPECT TO SAID THREAD CUTTING LATHE TOOL IN A PLANE PERPENDICULAR TO SAID SPINDLE AXIS, A CONTROL DEVICE CONTROLLING SAID DISPLACEMENTS OF SAID DEBURRING LATHE TOOL, A TRANSVERSE PUSHER MADE FAST WITH SAID DEBURRING LATHE TOOL, A FIXED CAM, SAID CAM BEING INDEPENDENT OF THE TOOL-HOLDER SUPPORT, MEANS FOR ADJUSTING THE POSITION OF SAID CAM PARALLELLY TO SAID SPINDLE AXIS, MEANS FOR ADJUSTING THE AXIAL POSITION OF SAID PUSHER PERPENDICULARLY TO SAID SPINDLE AXIS AND WITH RESPECT TO THE DEBURRING LATHE TOOL, SAID PUSHER AND SAID CAM CO-OPERATING ONE WITH ANOTHER TO CONSTITUTE SAID CONTROL DEVICE CONTROLLING SAID DISPLACEMENTS OF SAID DEBURRING LATHE TOOL WITH RESPECT TO SAID THREAD CUTTING LATHE TOOL, A MOVABLE SUPPORT CARRIED BY SAID TOOL-HOLDER SUPPORT, AND MEANS FOR DISPLACING SAID MOVABLE SUPPORT WITH RESPECT TO SAID TOOLHOLDER SUPPORT PERPENDICULARLY TO SAID SPINDLE AXIS, SAID MOVABLE SUPPORT CARRYING SAID THREAD CUTTING LATHE TOOL AND SAID DEBURRING LATHE TOOL, SAID DEBURRING LATHE TOOL BEING ADAPTED TO BE DISPLACED WITH RESPECT TO SAID MOVABLE SUPPORT PERPENDICULARLY TO SAID SPINDLE AXIS, SAID CONTROL DEVICE CONTROLLING THE DISPLACEMENTS OF SAID DEBURRING LATHE TOOL, WITH RESPECT TO SAID THREAD CUTTING LATHE TOOL IN TIMED RELATION TO THE DISPLACEMENTS OF SAID TOOL-HOLDER SUPPORT AND CAUSING THE SETTING INTO AND OUT OF ACTION OF SAID DEBURRING LATHE TOOL AT THE BEGINNING AND AT THE END OF EVERY THREADING CUT OF THE THREAD, CUTTING LATHE TOOL SO AS TO HAVE THE BURR REMOVED AT THE BEGINNING AND AT THE END OF SAID THREAD.