Abstract: The invention provides a transfer device comprising at least one gripping member (19) mounted for pivoting about a first shaft (19a), on a support (16) mounted for rotation about a second shaft (16a). The support (16) rotates through three angular steps per revolution to place the gripping member (19) in three successive positions (P1,P2,P3), in which it is respectively opposite the posts for precutting, finishing cutting and rolling of the foils. An orientation means (24) associated with a means (57) for adjusting the starting orientation of the gripping members, further allows each of these latter to be pivoted between its first (P1) and second (P2) positions, through an angle depending on the conicity to be given to the finished articles, and maintaining it as far as its third position (P3) in the orientation which it has in its second position (P2).