As part of the priority program "Small Machine Tools for Small Workpieces," a planar multi-coordinate drive was developed at Leibniz University Hannover, which utilizes the force effect of air free jets on drive profiles on the carriage. Building on this, Tim Schumacher designed a new profile and nozzle arrangement during this work, allowing for the extension of the translational drive with an unrestricted rotational degree of freedom. The geometric model developed for this purpose enables the automatic determination of suitable geometry parameters in conjunction with a computer-based evaluation. Based on the arrangements generated in this way, the development and optimization of a constructively feasible solution were carried out.