A floor polishing or grinding pad assembly is provided. In one aspect, a polishing or grinding pad assembly employs a fibrous pad, a reinforcement layer or ring, and multiple floor-contacting disks. In another aspect, the reinforcement layer includes a central hole through which the fibrous pad is accessible and the fibrous pad at the hole has a linear dimension (x) greater than a linear dimension (y) of one side of the adjacent reinforcement layer. In yet another aspect, at least one of the floor-contacting disks has an angle (α) offset from that of a base surface of the disk, the fibrous pad and/or the reinforcement layer. A further aspect employs a smaller set of disks alternating between and/or offset from a larger set of the disks. In another aspect, the reinforcement layer includes a wavy or undulating internal edge shape.