Abstract: A winding apparatus for winding a web into rolls comprises a rotatable assembly having plural winding sleeves mounted thereon for movement between a winding position and an unloading position. The sleeves can have any one of a plurality of different diameters, and are so mounted on the assembly that when each empty sleeve reaches the winding position its periphery passes through the same predetermined point on the turning circle of the rotatable assembly regardless of the diameter of the sleeve. The apparatus also includes a web transfer unit comprising a plurality of rollers and a cutter device which is movable into an operative position adjacent an empty sleeve at the winding position when it is desired to sever the web. The rollers redirect the web so that it passes more than half way around the empty sleeve at the winding position, and the cutter then cuts the web at a position on or inside of the turning circle adjacent the predetermined point through which the sleeve periphery passes.