Patent ID: 7150676

Claim:
A polishing tool comprising: a) an arbor that includes: a1) a shank having a first cylindrical axis; a2) an offset cylinder extending from the shank, the offset cylinder having a second cylindrical axis, the first cylindrical axis being offset from the second cylindrical axis and parallel thereto, the offset cylinder terminating at a distal end thereof with a support surface that is angled in a range of from about 1° to about 20° from perpendicular to the first and second cylindrical axes; and b) a toroidal polishing head supported on the support surface, rotation of the shank causing an oscillating rotational movement of the toroidal polishing head; wherein the oscillating rotational movement of the toroidal polishing head includes an in-plane motion to alleviate grooves and an out-plane motion for facilitating polishing liquid transfer between the toroidal polishing head and a work piece surface; and wherein the in-plane motion of the oscillating rotational movement of the toroidal polishing head is described by: X = ⁢ [ ( D CS 2 + D ID 2 ) / cos ⁡ ( β ) + ( D CS 2 ⁢ sin ⁡ ( α - β ⁢ ⁢ cos ⁡ ( θ ) ) ) / cos ⁡ ( β ) + ⁢ ( D CS 2 [ 1 + cos ( α - β ⁢ ⁢ cos ⁡ ( θ ) ] ⁢ tan ⁡ ( θ ) ) ⁢ cos ⁡ ( β ) ⁢ cos ⁡ ( θ ) + ( Ecc ) ⁢ cos ⁡ ( θ ) ] / cos ⁡ ( α ) .