Date of Award


Project Type


Degree Name

Doctor of Philosophy

First Advisor

Robert B Jerard


This dissertation presents four new tool path generation approaches for numerically controlled machining of sculptured surfaces: TRI$\sb-$XYINDEX, FINISH, FIVEX$\sb-$INDEX, FIX$\sb-$AXIS$\sb-$INDEX. All of the above systems index the tool across the object surface in the Cartesian space so that evenly distributed tool paths are accomplished.

TRI$\sb-$XYINDEX is a three-axis tool path generation system which uses a surface triangle set (STS) representation of the surface for tool position calculations. Surface edges are detected with local searching algorithms. Quick tool positioning is achieved by selecting candidate elements of polygons. Test results show that TRI$\sb-$XYINDEX is more efficient when machining surfaces which are relatively flat while the discrete point approach is faster for highly curved surfaces. FINISH was developed for generating three-axis ball-end tool paths for local surface finishing. It was based on the SPS. Given a surface with excess material represented by a set of discrete points, FINISH automatically identifies the undercut areas. Results show that FINISH provides significant improvements in machining efficiency.

FIVEX$\sb-$INDEX is developed for generating five-axis flat-end tool paths. It uses an STS approximation. Contact points on the surface are derived from edge lists obtained from the intersections of vertical cutting planes with the polygon set. The distances between adjacent end points set an initial step-forward increment between surface contact points. To verify tool movements, some intermediate tool positions are interpolated. The key features of FIVEX$\sb-$INDEX are: (1) a polygon set representing an object which may be composed of multiple surfaces; (2) Surface contact point generation by cutting plane intersection; (3) simple tool incrementing and positioning algorithms; (4) minimal user interaction; (5) user controlled accuracy of resulting tool paths.

FIX$\sb-$AXIS$\sb-$INDEX is a subsystem of FIVEX$\sb-$INDEX, generating tool paths for a tool with fixed orientations. Surface contact points are generated similar to FIVEX$\sb-$INDEX while tool positions are corrected with the highest point technique along the tool axis direction. Linear fitting is applied to output tool positions. FIX$\sb-$AXIS$\sb-$INDEX is preferred for machining surfaces curved in one direction, such as ruled surfaces. Test results show that FIX$\sb-$AXIS$\sb-$INDEX can serve as a three-axis tool path generation system but a five-axis machine is required to do it. (Abstract shortened by UMI.).