Kinematically generated ruled surfaces with applications in NC machining

The paths of cutting tools in Computer Numerical Control (CNC) machine tools are generated by approximating a desired machined surface with motions that can be generated by the CNC system. Kinematically generated ruled surfaces are surfaces that are created by the motion of a line. These surfaces are created in the same manner that the CNC system would use to machine them. This dissertation develops the algorithms necessary to create kinematically generated ruled surfaces. The algorithms are then used to solve problems in five-axis machining of contoured surfaces.; The kinematically generated ruled surface algorithms are developed by using line geometry to represent the rulings of the surface. The dual number system is used to represent the points in the line geometry. In this manner, the ruled surfaces are one-parameter curves on a dual unit sphere. The problem of generating ruled surfaces is then reduced to the problem of generating curves on a dual unit sphere. The curve generation is accomplished by creating line displacements which displace the lines on the surface of the sphere and generate the curves. Free-form curves are created by using a de Casteljau construction. Two-parameter motions are also created by using a de Casteljau construction.; These surfaces are applied to the problems of path generation and CNC interpolation for five-axis mills. The paths are specified using the tool axis to position the tool with respect to the desired surface. This method has the advantage that the path and the physical motion of the tool are closely linked. The paths are generated based on the kinematically generated surface that defines the desired surface. This is applied to problems in circumferential milling, face milling, and pocket milling.; Finally, the ruled surface path specification is used to create general CNC interpolators for five-axis milling. Algorithms for linear and parametric interpolation are presented.