M.Sc Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: In a spatial motion, the differential geometry of trajectory-ruled surfaces which belong to oriented lines of the mobil system is important in the mechanisms theory especially in the rational design of robots and their control. In such a closed motion, the trajectory-ruled surface of a x-oriented line which belongs to the mobil system can be characterized through two well-known real integral invariants, - the angle of pitch and - the pitch of this surface. The aim of this study is: To examine the relationships between the invariants of new trajectory-ruled surfaces. These invariants were obtained from the well-known real integral invariants of trajectory surfaces and recently dual integral invariants and the area vector belonging to the spherical images of these surfaces are defined. Thus while developing new geometrical interpretations related to space kinematics and trajectory-ruled surfaces. To contribute to the mechanisms theory especially to kinematics for robotics.The original section of this study is composed of three chapters. In the first chapter, at first we obtained the dual relationship among the dual area vector of dual spherical representations of a x-closed ruled surface drawn by a x-oriented line which is fixed in the mobil system of a closed spatial motion, the dual Steiner vector of the motion and the dual angle of pitch of this surface. Then we give some relationships and interpretations among the invariants of x- closed ruled surface and other escorting surfaces. Also the dual projection area of the dual closed spherical representation of the x-closed ruled surface is defined and then we showed that is an other invariant of the surface. In the second chapter, the dual characterization of Bertrand offset-surfaces are given and the relationships among the integral invariants of these surface offsets are also obtained.In the third chapter, the ruled-evolute surface offsets are defined. Also generalized relationships between the invariants of concecutive ruled-evolute surface offsets are obtained. Key words: Angle of Pitch and Pitch, Dual Angle of Pitch, Area Vector, Projection Area, Bertrand Ruled Surface Offsets, Ruled-Evolute Surface Offsets | |||||||||||||||||||||