Abstract: A machine that has an assembly formed from a frame on which is rotatably mounted on a drum with parallel winding cores. This assembly is mounted so as to move translationally in a horizontal direction perpendicular to the axes of the drum and of the cores, while the sheet product feeding mechanism is fixed. The translational displacement of the movable assembly allows its gradual advance as the diameter of a reel being formed grows and also makes it possible to leave, between this assembly and the sheet product feeding mechanism, a gap available for an operator, for the purpose of introducing the leading edge of the sheet product onto one of the cores.