A web rewinding apparatus comprising a turret winder and a cupping assembly is disclosed. The turret winder has a rotatably driven turret supporting a plurality of rotatably driven mandrels capable of engaging cores upon which a web material is convolutely wound thereabout. The cupping assembly has a plurality of cupping arms each cooperatively associated with one of the plurality of mandrels and having a mandrel cup for releaseably engaging the unsupported ends of the cooperatively associated mandrel. The rewinding apparatus also provides a first actuator for disposing the cupping arm from the hold-open position to the hold-closed position. Each of the cupping arms is disposed radially about the cupping arm turret and is carried in a radial orbital path about the cupping arm turret central axis while disposed in either of a hold-open position or a hold-closed position.