This paper presents the design and optimization process of a permanent magnetic excited transverse flux machine, which shall be used as a shoulder joint motor in an articulated six axis robot arm in service robotics. Starting from given application specific requirements, a parametrized model of the machine is presented. For transverse flux machines, the typically high number of design parameters leads to a large parameter space. A full factorial analysis simulating every possible parameter variation would lead to simulation times in the order of years. Therefore, a suitable classification of the parameters is proposed, which is used for an iterative optimization algorithm performing several parametric sweeps in a three dimensional finite element simulation. Results from the sensitivity analysis and the final optimization results are discussed.