We use a coordinate system to describe the movements of a measuring machine. The coordinate system, invented by the famous French philosopher and mathematician René Descartes in the early 1600's, lets us locate features relative to other features on workpieces.

A coordinate system is a lot like an elevation map where the combination of a letter along one edge of the map, a number along the other, and elevations shown throughout uniquely describes each location on the map. This letter/number/elevation combination is called a coordinate and represents a specific place relative to all others.

Another example is a street map with buildings shown (Figure 1). To walk to your hotel room at the Ritz Hotel from the train station (your origin), you walk 2 blocks along Elm street, 4 blocks on Maple and up 3 floors in the Ritz. This location can also be described by the coordinates 4-E-3 on the map, corresponding to the X, Y and Z axes on the machine. These coordinates uniquely describe your room and no other location on the map.

A coordinate measuring machine (CMM) works in much the same way as your finger when it traces map coordinates; its 3 axes form the machine's coordinate system. Instead of a finger, the CMM uses a probe to measure points on a workpiece (Figure 2).  Each point on the workpiece is unique to the machine's coordinate system. The CMM combines the measured points to form a feature that can now be related to all other features.