The kinematics of rigid bodies in 3-dimensional Lorentzian space

In this thesis, the forward and inverse kinematics of rolling contact motion without sliding of a moving spacelike (respectively, timelike) surface on a fixed spacelike (respectively, timelike) surface in Lorentzian 3-space was investigated. This thesis consists of seven sections. In first section, literature notion about rolling contact motion is given. In section two, the theory of curves and surfaces in 3-dimensional Euclidean space is given in detail. In section three and four, the theory of the forward and inverse kinematics of rolling contact motion in Euclidean 3-space is given. In section five, basic concepts, the theory of curves and surfaces in 3-dimensional Lorentzian space are given in detail. In section six, the forward kinematics of rolling contact motion without sliding of a moving spacelike (respectively, timelike) surface on a fixed spacelike (respectively, timelike) surface was investigated and the velocity equation of this motion in 3-dimensional Lorentzian space was obtained. In section seven, the inverse kinematics of rolling contact motion without sliding of a moving spacelike (respectively, timelike) surface on a fixed spacelike (respectively, timelike) surface in 3-dimensional Lorentzian space was solved by a polynomial equation.