Kinematics-driven geometric modeling: a framework for simultaneous NC tool-path generation and sculptured surface design

Current practice in CAD/CAM separates the process of geometric shape design from that of CNC (Computer Numerically Controlled) tool path generation. Although successful for 3-axis machining, this strategy is not as effective for 5-axis machining of sculptured surfaces due to the difficulty in generating accurate and gouge-free 5-axis tool paths from the CAD models. This paper presents a framework for a new, kinematics-based methodology for geometric modeling that integrates sculptured-surface design with too-path generation for 5-axis CNC machining. In particular, sculptured surfaces are represented directly in terms of rational Bezier and B-spline motions of the cutting tool. The proposed framework brings together the fields of Kinematics and Computer Aided Geometric Design as well as the recent results in Computer Aided Motion Synthesis and Swept Volume Modeling and provides a basis for concurrent geometric shape design and manufacture.