Sculptured surfaces are cornmon in a wide variety of products such as automobiles, household appliances, water crafi and aircraf? components. These surfaces may be required to reduce fluid drag or simply for esthetics. Machining is used in the production of most of these surfaces. Present day surface machining techniques generate the design surface at a single point on the cutting tool. Many closely spaced passes of the cutter are required to machine a surface to the required tolerance. In this thesis, a new 5-axis technique for machining sculptured surfaces with a toroidal or flat bottom end mil1 is presented. The proposed Multi-Point Machining tool positioning strategy advocates generating a surface at more than one location on the tool. More contact points between the surface and the tool will result in faster machining.

Equations were developed to mode1 multi-point contact between the workpiece surface and the tool. They were used to study the nature of contact between the tool and five quadratic surface forms:​ planar, parabolic, spherical, elliptic and hyperbolic. Two basic types of multi-point contact were found to exist;​ a circle of contact for planer and spherical surfaces and 2-point contact for parabolic, elliptic and hyperbolic surfaces. These results formed the bais of an exact multi-point tool positioning strategy for quadratic surfaces. Two algorithms were also developed to modify a multi-point tool position for non-quaciratic surfaces.

Cutting tests and simulations were used to investigate the properties of the multi-point tool positioning strategy. Multi-point scallops were found to be low and wide, giving the machined surface a much srnoother appearance than those produced by competing techniques. The size of these scallops were controlled by the tool geometry, separation between cutter contact points and feed direction. A big tool with small inserts will produce smaller scallops than a small tool with large inserts. The best feed direction is the direction of minimum curvature and the worst feed direction is the direction of maximum curvature.

Multi-point machining clearly offers the best performance of any tool positioning strategy. The results in this thesis show that the scallop heights produced by multi-point machining are about 0.0025, 0.04 and 0.5 times as large as those produced by the other leading tool positioning strategies:​ bal1 nosed, inclined tool and principal axis rnethods.