"The research of the project proposed focuses on Mechanism Design in its interdependence to Motion Design with regard to spatial motion problems occurring in Solid Mechanics. That is, the design of motions interpolating a sequence of positions of a spatial system will be combined with the design of suitable mechanisms which can guide these positions.In engineering practice, one has to decide whether a mechanism or manipulator should be used to guide a required motion weighing up the technical and economic reasons.Currently, spatial motion problems are often solved by manipulators which beside high purchase costs raise problems relating their control, required space etc. Their flexibility is not essential for many applications. Therefore, solutions of spatial motion problems using mechanisms seem often rather reasonable in the context of economic expediency.From a kinematic point of view, one has to assign the determination of a suitable interpolating motion to the determination of a mechanism whose end-effector is capable of attaining these positions. This research will be done using geometric approaches coming from Computer Aided Geometric Design, Algebraic Geometry, Computational Line Geometry, Kinematics et al. The geometric idea behind it is to connect the modeling of motions either mathematically defined or implemented by mechanisms with well-known design of curves and surfaces.Concerning the career development, the main aim of the project proposed is to widen the scientific profile of the applicant in order to achieve an independent research career. One main objective is to establish an independent research group in this field. In order to achieve this goal, the project partly aims at the advancement of collaborations in this up-and-coming research field, in the frontier area between Mathematics and Machine Engineering. Furthermore, the advancement of research and knowledge management is a further training achievement."