On differential geometry of fixed back-distance kinematicfactorable surfaces and transfer surfaces in 3-dimensionaleuclide space

This thesis consists of three parts. In the first part, basic concepts related to dual numbers, dual vectors, quaternions, dual quaternions, and rigid body motions are given. In the second part, the curves, surfaces, and monge surfaces used in the third part of the thesis as well as the special cases of monge surfaces that can be factorable and transferable are given. In addition, parallel surfaces, surfaces with fixed ridge distances, kinematic surfaces with fixed ridge distances, some basic definitions, and theorems belong to them are discussed. In the third part, some basic differential geometric properties of these surfaces are obtained by performing kinematic factorization and translation of surfaces with fixed ridge distance. Then, these obtained fixed ridge distance kinematics can be factorable as special cases of translation surfaces, fixed ridge distance surface, screw surface, parallel surface factored and translated surfaces are solved.