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"Measurements" 
The Coordinate System
The Coordinate System is a system for identifying elements in a set of
points by labeling them with numbers. The numbers are called coordinates
and can be thought of as giving the position of a point on a map. The
system of latitude and longitude is an example of a coordinate system that
uses two coordinates to specify the position of a point on the surface of
the earth (Figure 1). To walk to your favorite restaurant from the bus
station (your origin), you walk 3 blocks along college Avenue, 4 blocks on
state and up 2 floors in the Paper Valley.
Alignment Whenever you must measure a part relative to a part coordinate system, you must somehow take into effect how the part is setting on the table. With a street map, we do this automatically by spinning the map so that it is parallel to street (datum) or to a compass direction (i.e., north). When we do this, we're actually locating ourselves to the "world's coordinate system". With today's CMM software, the CMM measures the workpiece's datums (from the part print), establishes the Part Coordinate System, and mathematically matches it to the Machine Coordinate System. The process of relating the coordinate positions of the part and coordinate positions of the machine is called alignment (Figure 3).
Datum A datum is a location. We use datums as guides to tell others where we are or as directions on how to get to places. On the map, the Paper Valley Hotel is a datum. So are streets, the bus station, the museum and the restaurant. Thus, by using an origin, datums, directions and distances people have all the information they need to get from one location to another. For example, to get from the bus station (origin) to the restaurant, you walk 2 blocks north on College Avenue (datum), take a right, and walk 2 blocks east on State Street (datum).
Translation
To do this you would first measure the central hole, translate the origin to the center of this hole, and then measure each of the four surrounding holes. Moving the starting point (origin) of the measurement from its present position to another place on the workpiece is called translation. The CMM does this mathematically when you request an alignment routine from its geometric measuring software. In terms of our street map, once you arrive at your hotel and decide to eat at a legendary restaurant on your visit to the city, you need to find it on the map. The hotel now becomes your new starting point, or origin. By knowing your location, you can tell by looking at the map that you will have to travel two blocks west along State Street to reach the restaurant . Qualifying Probe Tips
