A cushioning conversion machine located below a work table includes a stock supply assembly, a conversion assembly for converting the stock material into a cushioning product and providing it through a machine exit, and a pad transferring system including an upper series of rollers arranged in a path, a lower series of rollers arranged in a path and a motor for powering the rotation of the drive elements, the upper and the lower series of rollers defining a path therebetween leading from the machine exit to a passage in the work table.