This Small Business Innovation Research (SBIR) Phase I project addresses a unifying mathematical framework for three-dimensional tolerance analysis which can quantify the flow of variation through a product based upon design specifications and associated manufacturing processes. The hallmark of this innovation is a system of geometric constraint equations that are a function of kinematic degrees of freedom (DOF). The constraints define the feasible space for features, components, and part-to-part (assembly) relationships due to geometric topology, tolerancing, and the manufacturing process. Sets of equations are solved for the particular homogeneous transformation matrices that systematically vary the features and components of the resultant feature-based assembly model, allowing for accurate calculation and assessment of dimensional requirements. The innovation will provide a unity calculus for variational modeling at the feature, component, and assembly levels, with Phase I emphaizing the crucial assembly level. Overall benefits of this innovation include boarding the application base, ease-of-use, and appeal of tolerance analysis, as well as enabling a compelling synchroneity with Computer-Aided Engineering (CAE) systems. Applications of computer-aided tolerance analysis are anticipated in the design and manufacture of mechanical and electrical systems, robust product and process design, simultaneous engineering, rapid prototyping, and product quality enhancement.
