The need for increased product variety and improved aesthetics require the manufacturing enterprise to reduce time to market and to increase use of free-form surfaces in the form of the product. These changes lead to problems in the traditional approach for specification and verification of tolerances especially for a free form surfaces. In the case of freeform surfaces, the desired performance of a product depends on its geometry and is often controlled by intrinsic parameters such as curvature. Design intent therefore requires control on variations in these parameters. Ideally therefore, tolerances have to be applied on these parameters to prescribe allowable variations in the geometry of free-form surfaces. Since only the geometry of the product is controlled in manufacturing, tolerance specification has to ensure that the tolerances specified on the part geometry will ensure that the resulting value of the parameter of interest is within the limits prescribed by the designer. Relationship between allowable range in design parameters and that in geometry is not linear. Tolerance specification therefore becomes a trial and error process requiring considerable expertise and time. This thesis provides designers with a tool to automatically derive the corresponding tolerances to be specified to the manufacturing process to realize the final shape, such that the parameters that are used to control shape of the surface are within the prescribed variations. Automation in acquiring inspection data has brought dramatic changes in procedure for tolerance verification too. Optical scanners and similar non-contact devices provide large amount of points on the surface of the part quite rapidly. The unstructured point data are then processed to determine if the part complies with the given tolerance specifications. For freeform surfaces, current methods of verification uses minimum distance criterion between the nominal surface and unstructured point data. This ignores the correspondence between the points in the two data sets and may result in the rejection of good parts and acceptance of bad parts. There are other unresolved such as the singularity at corners of polyhedral shapes and handling datum. A new approach based on the Medial Axis Transform (MAT) has been proposed. It has been shown that reasoning on the MAT of the nominal model and the measured point set respectively enables the identification of corresponding points in the two sets. Verification of the tolerance allocated is therefore free from the problem mentioned above. MAT exhibits dimensional reduction and hence reduces verification time. It also eliminates surface fitting for detected feature. Results of implementation are provided for tolerance specification and verification using MAT.

This research investigates tolerance strategies for modular systems on a project specific basis. The objective of the proposed research is to form a guideline for optimizing the construction costs/risks with the aim of developing an optimal design of resilient modular systems. The procedures for achieving the research objective included: (a) development of 3D structural analysis models of the modules, (b) strength/stability investigation of the structure, (c) developing the fabrication cost function, (e) checking elastic and inelastic distortion, and (f) constructing the site-fit risk functions. The total site-fit risk function minimizes the cost/risk associated with fabrication, transportation; alignment, rework, and safety, while maximizing stiffness in terms of story drift values for site re-alignment and fitting alternatives. The fabrication cost function was developed by collecting 61 data points for the investigated module chassis using the SAP2000 software while reducing the initial section sizes, in addition to the fabrication costs at each step (61 steps). With the reduction of the structural reinforcement, story drift values increase, therefore there will be a larger distortion in the module. This generic module design procedure models a trade-off between the amount of reinforcement and expected need for significant field alterations. Structural design software packages such as SAP2000, AutoCAD, and Autodesk were used in order to model and test the module chassis. This research hypothesizes that the influential factors in the site-fit risk functions are respectively: fabrication, transportation, alignment, safety, and rework costs/risks. In addition, the site-fit risk function provides a theoretical range of possible solutions for the construction industry. The maximum allowable modular out-of-tolerance value, which requires the minimum amount of cost with respect to the defined function, can be configured using this methodology. This research concludes that over-reinforced or lightly-reinforced designs are not the best solution for mitigating risks, and reducing costs. For this reason the site-fit risk function will provide a range of pareto-optimal building solutions with respect to the fabrication, transportation, safety, alignment, and rework costs/risks.