A variety of inspection equipment exists in industry to capture the points on a surface that will envisage manufacturing form errors. Manufacturing inspection faces a problem of finding optimal methods to capture an evenly spread distribution of points on the surface. Sampling does not yield complete information about a surface. Each material removal process leaves a unique pattern on the surface of the workpiece, which has to be taken into consideration while developing the sampling strategy. For instance, round patterns left by face milling at low feeds on flat surfaces, and spiral patterns left during surface milling and turning operations on surfaces of revolution. Two new methods have been developed to improve sampling using the coordinate measuring machine (CMM) for inspection of flat and revolved surfaces. These are the Spiral, and Hamspi sampling methods.The Spiral method focuses on the centre of the area and uses the Archimedean spiral. Hamspi is a method that combines both the Spiral and randomized Hammersley to measure points in the middle as well as the outer zone of the workpiece. Mathematical comparisons of these methods have been made to establish feasibility. An experiment was performed to determine the accuracy of these models using two dependent variables: inspection time and minimum zone. The minimum zone was (statistically) significantly affected by only two factors: sample size and workpiece shape. The sampling time was however affected by sample size, workpiece shape, and the interaction between them. This study observed that the beginning and ending cutting zones of spherical surfaces were the most significant regions to verify. It was found that the Spiral and Hamspi methods had similar point distributions as the Hammersley method while placing more emphasis on the origin of the workpiece.

Flatness, circularity, and straightness have been studied quite extensively in literature. Forms such as torus are seldom studied. Yet, parts such as ball bearings and Toroidal-CVT have torus features that must be inspected for three-dimensional (3D) form. This research studies the torus form tolerances, herein termed torisity. Mathematical representation for coordinate form verification and fitting methods are each developed for torus forms for the very first time through this research. Three known sampling methods (Hammersley, Aligned systematic, and Random), 3 sample sizes (40, 80, and 120), 2 analysis approaches (horizontal and vertical), and 2 fitting algorithms (least squares and linear optimization) are developed and studied within a designed experiment for torus verification. Analysis shows that different combinations of the above factors lead to different outcomes. It is hoped that this analysis provides the foundation for the development of a future decision support system that can further lead to standards and solutions.

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Nonlinear forms such as the cone, sphere, cylinder, and torus present significant problems in representation and verification. In this paper we examine linear and nonlinear forms using a heavily modified support vector machine (SVM) technique. The SVM approach applied to regression problems is used to derive quadratic programming problems that allow for generalized symbolic solutions to nonlinear regression. We have tested our approach to several geometries and achieved excellent results even with small data sets, making this method robust and efficient. More importantly, we identify process or inspection tendencies that could help in better designing the processes. Adaptive feature verification can be achieved through effective identification of the manufacturing pattern.

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