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The second coordinate system is called the Part Coordinate System where the 3 axes relate to the datums or features of the workpiece.

Before the introduction of computer software to coordinate measurement, parts were physically aligned parallel to the machine's axes so that the Machine and Part Coordinate Systems were parallel to one another.  This was very time consuming and not very accurate.  When the part was round or contoured, rather than square or rectangular, the measurement task was nearly impossible.