Kinematics Driven Geometric Modeling for Virtual Design and Manufacturing

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This grant provides funding for the development of an integrated computer-aided design/computer-aided manufaturing system for design and manufacture of kinematic freeform surfaces. The kinematic freeform surfaces have integrated geometric and kinematic control structures that embody the geometry of tool motions required for Computer Numerically Controlled (CNC) machining processes. Algorithms for synthesizing and analyzing rational Bezier and B-spline (or NURBS) based multi-parameter freeform motions will be developed. Kinematic freeform surfaces generated by the multi-parameter NURBS motions will be developed for commonly used cutting-tool geometries such as lines for wire-cut Electric Discharge Machining (EDM) processes, planes for 5-axis grinding processes, and cylinders for 5-axis milling processes. Multisensory virtual environments with multi-resolution rendering capabilities will be developed for design, approximation, and fine-tuning of kinematic freeform surfaces. Methods for analyzing and minimizing the machining errors due to discretization will be developed for generation and optimization of tool motions. A 5-axis virtual milling machine with visual, aural, and haptic feedback capabilities will be developed to simulate not only the position but also the velocity and acceleration of tool motions. The research results of this project will be validated on a real 5-axis CNC milling machine. This project represents an extension of NURBS geometry from the purely geometric domain to the kinematic domain. It offers an integrated framework for addressing geometric and kinematic problems in various stages of the virtual design and manufacturing pipeline. By incorporating kinematic issues early in the design stage, the project, if successful, would yield a new methodology and a software tool for designing sculptured shapes that are free of geometric machinability problems such as under- and over-cut. The project results will also provide a basis for concurrent design and manufacturing of dies, molds and other sculptured shapes for automobile and aerospace industries.