CAREER: Geometric Singularities in Engineering Design and Manufacturing: A Generic Spacetime Approach

University Of Connecticut, Storrs CT

Investigators

Abstract

The research objective of this Early Faculty Career Development (CAREER) award is to develop a generic theoretical framework and computational algorithms for predicting, quantifying, and correcting potential malfunctions induced by geometric singularities, such as undesired loss of contact or changes in the prescribed motion of moving bodies in the presence of uncertainty. The research takes a new approach to the characterization of geometric singularities in the envelopes of families of both rigid and non-rigid moving shapes by reframing the problem in terms of the so-called "fold points" and "fold regions" in the neighborhood of these singularities. Based on this duality, the problem of detecting geometric singularities is recast into Point Membership Classification tests in the original d-dimensional Euclidean space, eliminating the need for envelope computations. In turn, this will result in improved detection and corrective capabilities of such potential failures. If successful, the results of this research will advance the state of the art in computer aided manufacturing, path planning, and geometric modeling by providing algorithms which will, for example, significantly improve on-line testing of tool paths and CNC codes for arbitrarily complex shapes and motions that will reduce under- or over-cutting in machining, improved swept volume calculations and improved collision detection. New curriculum will be developed and integrated into the mechanical engineering program. Outreach to an all women's college to encourage and actively recruit female students into mechanical engineering and collaboration with a successful existing K-12 outreach program will be performed as part of this project.