Abstract: A machine for winding shells with convex ends on mandrels using thread such as resin-impregnated fibreglass threads comprises a mechanism for rotating the mandrel around its longitudinal axis, a thread guide installed on a traverse carriage located on a horizontal guide, and a mechanism for moving the carriage over the horizontal guide. The thread guide is mounted on the carriage with a provision for moving relative to it in the direction perpendicular to the mandrel axis. The horizontal guide is arranged parallel to the mandrel axis. The mechanism for moving the carriage along the horizontal guide includes of an endless flexible linkage whose position is space is set by master guide; the shape of these master guides in the rectangular system of coordinates x, y depends on the relation: ##EQU1## The flexible linkage is connected with the mandrel-rotating mechanism and with the traverse on which the thread guide is mounted.

Abstract: A machine for winding casings on mandrels, comprising a mechanism to rotate the mandrel, a carriage with a filament-guiding head moving in guides parallel to the axis of the mandrel, and a mechanism to move the carriage. The latter mechanism includes an endless Gall's chain whose shape is defined by curved guide plates and which transmits motion from the uniformly rotating mandrel to the non-uniformly reciprocating carriage by means of a pin of a vertical slide which is hingedly connected to a link of the endless chain. The shape of the guide plates is chosen so that with a uniform continuous-path movement of the chain link, the carriage with the head moves in conformity with an equation of motion of its feed eye, as a function of the angle of rotation of the mandrel, to wind closed casings of any chosen shape along geodesic lines.