Symbolic and computational conjugate geometry for design and manufacturing applications

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Virginia Tech


Development of a methodology of applying symbolic and computational models of conjugate geometry to several problems in design and manufacturing areas forms the basis of this study. The philosophy of this work is the development of generalized symbolic models for two-dimensional and three-dimensional conjugate geometry applications. The generalized models have been implemented using what seems to be the best tool for these kind of applications - a symbolic manipulation system. The unique feature of this research is reflected in the fruitful combination of the elegance of conjugate geometry theory and the inherent versatility of a symbolic manipulation system.

The generalized conjugate geometry algorithms were programmed and run using MACSYMA. Typical cases in design of mechanisms have been studied using these symbolic programs. The manufacture of helically swept surfaces is of special interest to this work. Helically swept surfaces have been designed and three schemes of manufacturing these surfaces are presented here. Examples of these three schemes of manufacturing helically swept surfaces have been carried out using the symbolic program in MACSYMA. The results of all the examples have been presented both analytically and graphically.