Reasons why turning eccentric parts should use ball centres, radised centre drills or a combination of both.

Parlo

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This demonstration highlights the use of a radiused form centre drill and a ball centre. A radiused form centre drill must be used when eccentric turning to allow the workpiece to pivot correctly on a standard centre. A ball centre does the same but in a tapered recess, any angle can be used to locate the ball and the workpiece can pivot on the ball. The reason these two principles are important is that when using a standard centre drill with standard centre the workpiece will not run concentrically on a centre when turning eccentrically. When a workpiece is held eccentrically between centres the clamping distance between standard centres inside standard tapered centre drilled holes can vary especially if the centre recesses are different diameters.
 
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