improved pneumatic shafts , chucks and lifts for roll stock and methods of construction and operation comprising an air bladder housed within a pair of concentrically disposed , longitudinally slotted sleeves . upon inflation of the bladder , the outer sleeve expands against the roll stock , or the core supporting the roll stock , providing full length grip . the inner sleeve expands against the outer sleeve while protecting the bladder from being pinched . the bladder is preferably a vinyl polymer plastic containing substantially inelastic roving to provide controlled and limited expansion . the combination permits true centering of rolls for rotational balance and constant tension , true running .