1. A DEVICE FOR WINDING A FILAMENT ON A MANDREL COMPRISING IN COMBINATION: (A) A SUPPLY OF FILAMENTARY MATERIAL; (B) A ROTATING MANDREL, SAID FILAMENTARY MATERIAL EXTENDING FROM SAID SUPPLY TO SAID MANDREL WHEREBY THE FILAMENTARY MATERIAL IS WOUND ON THE MANDREL; (C) A GUIDE BETWEEN THE SOURCE OF FILAMENTARY MATERIAL AND THE MANDREL, SAID FILAMENTARY MATERIAL PASSING THROUGH SAID GUIDE; (D) SAID GUIDE BEING MOUNTED ON A CARRIED FOR TRANSVERSE MOVEMENT PARALLEL TO THE AXIS OF ROTATION OF THE MANDREL; (E) A HOLDER LOCATED BETWEEN SAID GUIDE AND SAID MANDREL, A FIRST AXIS OF SAID HOLDER BEING AT SUBSTANTIALLY A RIGHT ANGLE TO SAID PATH OF FILAMENTARY MATERIAL EXTENDING THROUGH THE GUIDE AND SUBSTANTIALLY PARALLEL TO THE AXIS OF THE MANDREL, AND A SECOND AXIS OF SAID HOLDER NORMAL TO THE FIRST AXIS BEING AT RIGHT ANGLES TO SAID PATH OF FILAMENTARY MATERIAL AND AT SUBSTANTIALLY A RIGHT ANGLE TO THE AXIS OF SAID MANDREL; (F) AT LEAST 4 SPROCKETS MOUNTED ON SAID HOLDER AND AN ENDLESS CHAIN PASSING OVER SAID SPROCKETS OF WHICH SPROCKETS THERE IS A FIRST SPROCKET, A SECOND SPROCKET, A THIRD SPROCKET AND A FOURTH SPROCKET IN SERIES AS THE CHAIN PASSES OVER THEM; (G) A SLIDING CONNECTION BETWEEN A POINT ON SAID CHAIN AND SAID CARRIER WHEREBY SAID CARRIER IS MOVED BY ONLY TRANSVERSE COMPONENTS OF MOVEMENTS OF THE CHAIN AS SAID POINT MAKES A FULL CYCLE ABOUT SAID SPROCKETS; AND (H) DRIVING MEANS FOR ROTATING THE MANDREL AND DRIVING THE CHAIN IN SYNCHRONISM; (I) THE FOURTH SPROCKET MOUNTED IN A FOURTH PREDETERMINED POSITION WITH AT LEAST ONE POINT OF CONTACT BETWEEN SAID CHAIN AND SAID SPROCKET ON A FIRST SIDE OF SAID SECOND AXIS; (J) THE FIRST SPROCKET MOUNTED IN A FIRST PREDETERMINED POSITION WITH AT LEAST ONE POINT OF CONTACT BETWEEN SAID CHAIN AND SAID SPROCKET ON THE SECOND SIDE OF SAID SECOND AXIS; (K) THE SECOND SPROCKET MOUNTED IN A SECOND PREDETERMINED POSITION WITH AT LEAST ONE POINT OF CONTACT BETWEEN SAID CHAIN AND SAID SPROCKET ON THE FIRST SIDE OF SAID SECOND AXIS; (L) THE THIRD SPROCKET MOUNTED IN A THIRD PREDETERMINED POSITION WITH AT LEAST ONE POINT OF CONTACT BETWEEN SAID CHAIN AND SAID SPROCKET ON THE SECOND SIDE OF SAID SECOND AXIS WHEREBY A COMPLETE REVERSAL OF DIRECTION OF TRAVEL OF THE GUIDE AND CHAIN IS CARRIED OUT AT AN INTERMEDIATE POINT LOCATED WITHIN THE END LIMITS OF TRAVEL IN EITHER DIRECTION OF THE CHAIN AND THE FILAMENT IS, AS A RESULT OF THIS REVERSAL, LAID IN OVERLAPPING RELATIONSHIP UPON ITSELF AT INTERMEDIATE POINTS ON THE MANDREL.