Sequential and modülar slerp interpolations in spherical mechanisms

This thesis consists of five chapters. In the introduction chapter; we give some information about the historical developments of our study. In the material and method chapter; basic definitions and theorems about the quaternions, dual numbers, dual vectors, dual quaternions, quaternion interpolations, dual quaternion interpolations and Blaschke frame were given and various examples were made. In the main results section; the sequential and modular SLERP interpolations were applied in the spherical mechanisms. The spherical motions were examined with the help of SLERP interpolation in the spherical mechanisms. The Geometric Slerp's Frenet frame and the curvatures were calculated. Furthermore, sequential Slerp interpolations were applied on the dual unit sphere in the dual spherical mechanisms. After the definitions of fast dual spherical interpolation and fast screw linear interpolation, the Blaschke frame of the unit dual spherical interpolation curve were calculated. In the fourth chapter, after the conclusions and suggestions of our study were given, the bibliography was written in the last chapter.