A floor polishing or grinding pad assembly is provided. In one aspects a polishing or grinding pad assembly employs a flexible pad, a reinforcement layer or ring, and multiple floor-contacting tools such as disks. In yet another aspect, at least one of the floor-contacting tools has a workpiece-contacting bottom plane having angle offset from that of a base surface of the tool, a flexible pad and/or a flexible reinforcement layer. A further aspect employs a smaller set of disks alternating between and/or offset from a larger set of the disks.