This thesis briefly describes the history and development of CNC machines, it explains numerical control and gives an in-depth description of tool changers. A couple of concepts are taken into consideration and an optimal version is chosen. Afterwards, a calculation is made in the purpose of verifying the safety factor because all of the machine parts are intentionally over-dimensioned so that they could absorb vibrations and with that, enable high-accuracy machining. First calculations were made on the main motion assembly, which actually drives the tool. The forces and powers of cutting were calculated, shafts were checked for their safety factor and then the toothed belt was dimensioned. After that, the assembly for tool changing was calculated. By determining the dynamic moment of inertia, it was possible to calculate the necessary power for tool changing, and after that a worm gear reducer was dimensioned. Afterwards, all the screw joints that carry loads were calculated and a solution for the motion in x,y and z axes was briefly explained. Simultaneously to the calculation, a model was being designed in the program package CATIA. After designing the model, technical documentation of the main assemblies was made, which is attached to this paper. At the end of this paper a few design solutions, which solved the problem of positioning, were mentioned and explained.