| Summary: | 博士 === 國立成功大學 === 機械工程學系 === 87 === In terms of principal, conjugate theory is a branch of differential geometry. It is included in differential geometry. But the detail content doesn''t find in the books of differential geometry. Little content maybe included in differential geometry. However, their mathematical forms don''t conveniently apply to conjugate surface''s theory. Conjugate theory mainly applies to solve these questions, such as, machine design, manufacturing, confirmed surface of a tool, straightening roll machine, conjugate surfaces, and so on. In order to solve these questions, the conjugate theory is develop and forms an object of application.
Based on the conjugate theory, homogeneous coordinate transformation, differential geometry, and computer animation, a series of mathematical models of screw motion mechanisms, such as straightening machine, gear pump, multi-wave tubes, and rolling balls are derived. Using the derived mathematical models establishes the cutting tool path, and their geometric models. Based on the conjugate theory and the developed mathematical models investigate the contact condition between generating surface and generated surface. Envelope of the two-parameter family of surfaces or envelope of the three-parameter family of curves can straighten bars along the straightening line. Moreover, in the present dissertation, assembly errors of screw gear pumps are studied by conjugate theory. By the way of analysis, an error of center distance doesn''t influence the kinematic error.
In order to investigate the properties of the surface profile, in the present dissertation, the famous Gaussian first and second fundamental forms have been studied. Combined with the results of mathematical models, the geometrical properties which include the normal curvature, the principal curvature, the principal direction, the first limit curves, and the second limit curves are investigate. In order to synthesize the conjugate pair with the better lubrication and form a hydrodynamic lubricating conditions, the analysis of curvatures are necessary and fundamental. Moreover, the cutting tool path, undercutting, the generation of singular points, the design process of rolling contour, and their mathematical models are supplied in the present dissertation. These results can be important in designing, manufacturing, and detecting.
Although the establishment of these models are based on screw motion mechanism. A little change of the process is necessary in solving the similar and relative problems, therefore, it is worthwhile to apply this utensil widely.
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