The examination of compliance with specified geometric and form tolerances requires acquisition of numerous measured data points and extensive computation. Traditionally, the required computation and the software analyses are performed in three major sequential tasks. The first task is to develop a data sampling plan. The sampling plan needs to be developed based on the workpiece’s characteristics
and also type of the employed measurement equipment. The number and locations of surface measurement points are amongst the most important parameters that influence the accuracy and validation of the whole assessment process. However, optimum determination of these parameters is often a difficult and challenging process and no standard procedure or guideline has been developed for it yet. Next, conformance of the actual geometry to the desired tolerances is evaluated by fitting a substitute geometry to the data points captured by a Coordinate Measuring Machine (CMM). The third task is to calculate the geometrical deviations associated with the measured part. This task needs to be conducted based on the deviations of the data points from the best substitute geometry and to estimate the uncertainty of the assessed inspection results. Numerous research projects in the area of evaluating the geometric deviations based on the discrete measured points have been undertaken. However, the partitioning of these three key tasks is the prevailing theme in most of the reported approaches. Alternatively, these three tasks can be performed concurrently with continuous feedbacks or as the elements of a closed-loop. This integration and communication between the different modules enhances the level of the certainty, which results in more reliable decisions made by each individual task. In a closed-loop system, an estimation of the form and nature of the geometric deviations can be used to acquire the most useful data-set from the part. Knowing the characteristics of this data-set improves the estimation of the optimum substitute geometry and reduces the corresponding computation cost.
