Coordinate measuring machines are used to measure geometric features of workpieces such as size, diameter, angle, angularity and parallelism. In principle, relatively complex shape, size and position measurements are reduced to the determination and mathematical evaluation of the spatial coordinates of discrete points. The results of these measurements can be displayed in both graphic and tabular form. Almost all machine designs are based on linear axes arranged according to the Cartesian coordinate system with corresponding linear scales. The measuring carriages are moved in the coordinate axes either manually or by motorized drives. One of the coordinate axes, usually the vertical Z axis (or “ram”) is equipped with a sensor for detecting the measured points. If a common tactile sensor is used, the positions of the three measuring carriages are read out to determine the point coordinates on the surface of the work piece. Some opto-electronic sensors (for example, image processing sensors) have their own, usually two dimensional measuring range. Using such sensors, it is possible to measure several points of a geometric element simultaneously without any movement in the coordinate axes. Using this approach, smaller object features can be detected completely. This is referred to as measurement “in the image”. If (in contrast to this) the sensor is moved over an extended object to measure one element or feature, this measurement is called measurement “on the image”. In either case, the sensor coordinate system is superimposed over the machine coordinate system.

Seen in above image: Measurement in the image:  Distance d2 is measured at sensor position  x2, y2.  Measurement on the image: Distance d1 is measured at sensor positions x1, and x2, y2.