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I know that drilling is an accepted method of repivoting and will produce a part that is good enough to work in a watch or a clock, but the result will not be as concentric as a turned part. Drill bits are double lip cutters and a force on one side of the cutter will push the other side into the work removing material. This is called drift and drills drift. If you magnify a drilled hole enough times it will not even look round; it will have a lobed cam shape. This is the reason jig bores are used in tool and die work. If a part requires a precisely located round hole, the hole would first be rough drilled to hog the metal out and then bored with a boreing head. This process would gurantee that the hole would be precisely round and precisely located. This could never be achieved with drilling.The process I described will also produce a hole that will be slightly off but if it is followed up with a turning operation It will put the new pivot precislsely on center.