Inspection planning and verification procedures are central activities in any inspection using Coordinates Measuring Machines (CMMs). The objective of tactile CMM inspection planning is to establish the best sequence of inspection steps with a detailed inspection procedure for each inspection feature or cluster of measurement points. Algorithms are then used to interpolate these points and generate their mathematical model(s). Complex surfaces may need to be decomposed into several patches which are interpolated separately then joined in a single model by determining their intersections. These models (curves and surfaces) are then used by tolerance analysis algorithms to verify if tolerance specifications are met by comparing the interpolated model representing the actual surface and the CAD model representing the theoretical surface.

This dissertation presents a computer-aided CMM inspection planning system as well as new tools for the interpolation and manipulation of measured features. The inspection planning system is modular and integrates all planning tasks.

A new algorithm is developed for determining inspection accessibility domains (or cones). An improved discrete accessibility algorithm is developed for probes with discrete possible orientations. A novel formulation of the problem of measurement points clustering and probe orientation selection in terms of operations sequencing and resources allocation is devised and adopted. A method for optimum clustering and sequencing of measurement points has been developed. The criteria in this case are the minimum number of clusters, the minimum number of resources used and finally the minimum distance travelled by the probe. A collision-free shortest probing path algorithm is enhanced. A modular Computer-Aided Inspection Planning (CAIP) system which integrates inspection planning tasks was developed and validated. Examples of actual parts have been used, tested and simulated.

A new method for the incorporation of uncertainties as well as linear constraints in the interpolation model based on dual Kriging interpolation has been developed. A new curve/surface formulation of dual Kriging as a combination of interpolation profiles is proposed, hence extending its use for solids and n-D entities interpolation, as well as sweeping, skinning and blending. In addition, dual Kriging was generalized to incorporate NURBS and B-splines. Finally, geometric algorithms, as opposed to numerical, analytical or differential algorithms for the intersection and manipulation of curves and surfaces are developed. Algorithms for the intersection of parametric/implicit and parametric/parametric entities (curves and surfaces) as well as for the projection of points on Curves and surfaces have been developed, implemented and validated.

The results of this work are intended to fill voids which exist in previous works in inspection planning and verification. These are:​ the integration of the different tasks involved in CMM inspection planning in order to develop an automated and robust inspection planner based on formalized and integrated approaches for accessibility analysis, optimum measurement operations sequencing and resources allocation, and accurate representation and manipulation of measured curves and surfaces.