In the work the new concept of polar positioning system, alternative for Cartesian one, is presented. The mathematical model which allows calculation of the rotation angle of polar positioning system is considered. The Cartesian coordinates of formed points of object structure, received after discretization process of object are the inputs data to calculation. Output data however are rotation angles i.e. both working arm and rotation table angles. The influence of the stiffness of mechanical parts on the precision of instrument positioning and productivity of the presented polar device is defined.