A power sanding machine (10) has three circumferentially spaced cogged belts (40) to drive three discs (52) rotatably mounted to an inner bowl (30) which is rotatably mounted to a housing (12), which in turn is connected to an operating handle (14). Mechanical lock can rotationally affix the inner bowl (30) to the housing to circumferentially position a pulley at the left or right edge (326, 322) of the sanding machine or at the front end (330) of the sanding machine. Power cleaning and sanding machines (412, 500, 600) incorporate the three disc (52) arrangement or a direct-drive one disc arrangement (572, 672). The machines (412, 500, 600) include multiple floor finishing units (420, 514, 614) ganged together in unique arrangements.