On kinematic geometry of curves and surfaces

At first part of this thesis, it is mentioned the studies in literature about this subject. Second chapter consists of fundamental concepts and some important theorems about dual numbers, quaternions and dual vectors. In third chapter, it is mentioned screw motion and then it is given that translation and rotation motions which are the special cases of the screw motion. Forth chapter deals with the fundamental concepts and theorems which are situated in curve and surface theory and are needed for this study. In fifth chapter of this thesis we define screw surface and give some characteristics of these kind of surfaces. Then, it is obtained that Darboux frame and Frenet frame of a curve's image on screw surface of the surface on which the curve lies on. At the final part of this chapter, an example of screw surfaces is given. At sixth chapter, we give the definition of screw surfaces at a constant distance from the edge of regression of a surface M. After that, we compute the shape operator screw surfaces at a constant distance from the edge of regression of a surface M and by using this we calculate Gaussian curvature and mean curvature of these surfaces. Finally, we complete this chapter with an example of screw surfaces at a constant distance from the edge of regression. Final chapter consists of a summary of the study and some advices for autors who want to study on this subject.