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Stereotactic neurosurgery is a highiy precise intervention method that supports procedures in which instruments must be placed accurately and reproducibly at a certain location within the brain while minimally damaging overlying structures. The current state of the art is the use of targeting systems. These provide guidance assistance for the instruments, which must move along a given trajectory. However, such systems are often not flexible enough. They may restrict the surgeon in trajectory planning, depending on the used targeting system, or for multiple trajectories within one intervention the adjustment of the mechanical systems is time consuming. To overcome such restrictions, different surgical navigation or robot systems were introduced. A group at the German Cancer Research Center, Heidelberg is also developing a new system for stereotactic neurosurgery. The new system StereoMan is based on a highly precise 5-axis measuring machine. It is specified to combine the advantages of current systems, the flexibility of a free movable navigation arm and the motorized precise movement of a robot. Further it is designed to work as a tool-holding device in brain and spine surgery with more degrees of freedom than current targeting systems have. The main goals of the study are (1) the specification of the requirements for a neurosurgical high-precision manipulator and (2) the presentation of methods for very precise determination of the manipulator's transducer values for given stereotactic coordinates in Cartesian space (inverse kinematics). The latter also includes the kinematic modelling and precise determination of the kinematic parameters by calibration methods. By the methods, developed in the thesis, it is now possible, not only to make StereoMan mechanically accurate, but also to develop other surgical robots or manipulators, which are not constraint to simple kinematics. So far the arm constructions were simple because of the necessity to care for solvability of the inverse kinematics problem. In future it is possible to develop surgical robots with problem oriented kinematic structures. Further the accuracy of such systems can be ensured by proper calibration and kinematics algorithms. After the first developments of algorithms and software for an accurate, precise and safe neurosurgical manipulator, the StereoMan project will be continued with the set up of a final prototype to proceed with first preclinical tests.