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Understanding the Coordinate Measuring System

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.
These coordinates uniquely describe only your restaurant and no other location on the map.

Figure 1. Your restaurant has a coordinate location of 4-D-2.

We can also use a coordinate system to describe the movements of a machine. The coordinate system, invented by the famous French philosopher and mathematician Rene Descartes in the early 1600's, lets us locate features relative to other features on workpieces. The location of your favorite restaurant is much like the locations of the X, Y and Z axes of a machine.

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

Figure 2. The hole (feature) in the workpiece has a definite X,Y, and Z coordinate.


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).


Figure 3. Alignment compensates for misalignment between the machine axes and the part axes.


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).

In metrology, a datum is a feature on a workpiece such as a hole, surface or slot. We measure a workpiece to determine the distance from one feature to another (Figure 4).

Figure 4. Datums


Suppose you need to know how far a specific feature of a workpiece is from another feature (Figure 5). Take, for example, the distance to the centers of each of four holes from a central hole.

Figure 5

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

Probe Compensation

CMMs generally gather their data by touching the workpiece with a probe (either a solid probe or an electronic touch trigger probe) attached the machine's measuring axis (Figure6).


Figure 6. Electronic (soft) touch probe.

Although the tip of the probe is very accurate, once the probe is attached to the CMM, the location of the tip to the machine's coordinate system must be determined prior to measuring. Since it's the tip's circumference that touches the part, the probe's center and radius are determined by measuring a very accurate sphere (requalificafion sphere) (Figure 7).

Figure 7. Qualification Sphere.

Once the center and radius of the tip are known, when the probe contacts a workpiece, the coordinates of the tip are mathematically "offset" by the tip's radius to the tip's actual point of contact (Figure 8). The direction of the offset is automatically determined by the alignment procedure.

Figure 8. The center of the probe is automatically calculated.