Point Count, Aspect Ratio and Accuracy in Indirect Measurement of Points

Abstract

A common item in the “metrology toolkit” is indirect, or inferred, measurement. Vector bars, hiddenpoint rods, T-Probes, and B-Probes, are all examples of tools that capture indirect measurements. The theory is to very accurately measure all critical features of a rigid body, and record those measurements for later use. Later, when some of those critical features are hidden, the visible features are measured and the location of the hidden features can be inferred. This process is done frequently as often there is no alternative. However, when a customer recently challenged our use of the procedure, we were compelled to generate some data to support the use of inferred points, and to quantify the uncertainties associated with such a process. To this end, we developed a testing procedure to quantify the uncertainty of an inferred point using a laser tracker and standard targets. This procedure begins with measuring 10 points from multiple stations (unique, set, tracker locations) in order to establish a nominal value for each of the 10 points. The same 10 points are then measured from a new series of stations. These measurements were then broken into subsets of data, each individually fit to the nominal values. Each subset was defined by a varying aspect-ratio, and an also varying number of points that define each aspect-ratio.