This thesis presents the design, analysis, and performance evaluation of a polar based contouring system. The system consists of a contour digitizer and an NC machine. The contour digitizer may be a template digitizer or a software digitizer. The combination of the template digitizer and NC machine (TD/NC machine) operates as a copying machine. While the combination of the software digitizer and NC machine (SD/NC machine) resembles in operation a conventional NC system.

The polar contouring system employs an open loop digital control scheme that does not require an on-board computer.

The system offers a number of desirable features over both conventional copying machines and NC systems. Speed scaling, and scaling of contouring speed without the need of reprocessing the contour information are among these features. Furthermore, when operated as an SD/NC machine, the system is capable of tracking a contour with constant speed.

A detailed description of the polar contouring system and the salient features of the prototypes of the template and software digitizers, and of the NC machine that has been built is presented. An analysis of the contouring error due to the incremental approximation of the contour is carried out. An optimization procedure that locates the contour pole with respect to the machine pole for a minimum area error is outlined. Test results of locating the poles of three test contours for a minimum area error are also presented. A dynamic analysis of the NC machine that includes the type of contour, the type and magnitude of the load, and the contouring speed is presented. The results of the analysis indicate that in general, increasing the magnitude of the load or the contouring speed increases the torque required from the axes-drives. It is also shown that the torque increases rapidly with the decrease of the radius of curvature of the contour. The maximum allowable load and contouring speed are shown to be a function of the location of the contour pole with respect to the machine pole. An optimization procedure to locate the contour pole relative to the machine pole is presented for maximizing the allowable limits on load and on contouring speed. A procedure using composite graphs is provided for rapid calculation of the maximum torque required and available from the axes-drives in different contouring operations.