An air valve is provided in the stub shafts of roller
. Inflation helps hold true roundness of the roller and also resists indentation during use. In operation, a single thickness of the goods is pulled off the supply roll, usually by the first processing machine following the inflatable slide manufacturer. The sheet may contact one or more rollers not shown before it reaches the inflatable air dancer roller. It enters through entry slit, then curves downward about perforated pipe which receives air from the compressed air source and directs the air through the perforations of the pipes. The air forms a layer of compressed air escaping through the perforations and holds the goods out of contact with pipe, while being very rapidly displaceable sufficiently to absorb high-frequency but low amplitude changes in included length so as to prevent sheet breakage under the usual conditions. The sheet then moves to and underneath movable roller and upward to perforated pipe 14b, forming a bight which supports roller and the gear segment assemblies and gear racks. Compressed air in the cavity above roller adds any desired extra tension to sheet. The movable roller sub-assembly moves vertically in its range to pay out or to take up as necessary to maintain the desired tension in sheet. Because of the lighter construction made possible by the apparatus of the present invention, roller 40 can respond to sudden, larger changes in included length than conventional designs. At perforated pipe the same conditions exist as at pipe in the same manner absorbing rapid sheet oscillations "downstream" from the inflatable air dancer roller. The sheet leaves the inflatable air dancer roller unit through exit slit, and continues through the series of processing machines (not shown) to be rewound as finished roll.