A take-up spindle carries axially spaced chucks each having a body carrying a plurality of chuck members for gripping the inner face of a hollow take-up core. Each chuck has a plurality of concentric springs which urge an actuator into a gripping position to cam the chuck members into gripping engagement with the core. Release mechanism concurrently urges the actuators of all the chucks to a released position whereupon the chuck members of each chuck are urged to a retracted position by an annular spring received in notches in generally radial faces of the respective chuck members. The chuck members are small and light weight to effectively eliminate resultant centrifugal force deforming the core, and are mounted to maintain a normal gripping force on the core although the core may tend to move axially of the spindle and chucks.