Apparatus and methods adapted to polish an edge of a substrate include (1) a polishing tape having a polishing surface and a second surface and (2) a polishing arm having a longitudinal axis and adapted to force the polishing surface of the polishing tape into contact with an edge of a substrate. The polishing arm includes i) a polishing head adapted to contact the second surface of the polishing tape, ii) a rocker arm coupled to the polishing head and adapted to rotate the polishing head around the longitudinal axis of the polishing arm and iii) a load arm extending adjacent to the rocker arm and adapted to move the polishing head in a direction perpendicular to the longitudinal axis of the polishing arm. Numerous other aspects are provided.