Abstract: A portable abrading or polishing tool having a body adapted to be held by a user to manipulate the tool and carrying a motor which drives orbitally a part to which a head or shoe adapted to carry a sheet of sandpaper or the like is detachably connected for orbital abrading or polishing movement with the part. The head is attached to the part by a fastener, preferably a screw extending through an opening in a backing plate of the head, and is retained against rotation by an essentially tubular member or boot of flexible preferably elastomeric material extending between the body structure and the head. The tubular member has a first end which may be disposed about a portion of the body structure and be clamped thereto to detachably secure the head assembly to the body, and has a second end which is detachably connectable to the head, in a manner enabling alternate use of any of two or more heads of different shapes and sizes with the same motor and handle assembly.