Alternative frames and one-parameter motions in the curve kinamtics

This thesis consists of six chapters. The first chapter contains an introduction that includes literature studies and the purpose of the thesis. The second chapter covers basic definitions and concepts related to the geometry of motions, curve and surface theories in 3-dimensional Euclidean space. In curve theory, the Frenet and alternative frame formulas defined along a curve, special curve types such as helix, slant helix and curves with constant precession are discussed. In surface theory, ruled surfaces and their geometric properties, such as the striction curve, are specifically examined. Kinematic properties such as acceleration centers, instantaneous pole point, axode, sliding velocity, and absolute velocity are discussed at the end of the section. In the third and fourth chapters, Frenet motions and a one-parameter motions referred to as alternative motions defined along a space curve, as found in the literature, are discussed, and their kinematic properties are described based on relevant sources. In the fifth section, orthonormal frames are obtained using Frenet planes, and alternative one-parameter motions are defined using the frames obtained along a space curve. Their kinematic properties are examined, and the necessary theorems are provided. Finally, the sixth section presents the conclusions of the thesis and suggestions for future studies.