Geometry of five-axis motion of two-parameter families of surfaces in Minkowski space

This thesis consist of six chapters. The first chapter has been devoted to the introduction. In the second chapter; fundamental definitions and theorems of Minkowski space and surfaces are given. In the third chapter, structure of surfaces are given in Minkowski space. The fourth chapter contains original part of our study. In the fourth chapter; 5-axis canal and tube surfaces for spacelike and timelike the center curve of a moving sphere are examined in the Minkowski 3-space. The Gaussian curvature, mean curvature, first and second fundamental form of coefficients of 5-axis canal and tube surfaces are examined. The parallel surfaces of 5-axis canal surfaces are obtained. On the other and, harmonic evolutes of 5-axis surfaces in Minkowski space are given. Finally, derive the corresponding equations for the inextensible flow of a 5-axis canal surface are given. In the fifth chapter; 5-axis canal and tube surfaces are given with some applications. The sixth chapter has been devoted to the conclusion. Keywords: Minkowski space, 5-axis canal surfaces, 5-axis tube surfaces, 5-axis motion, 5-axis machine.