The subject of the invention is a robotized system 10 of the type comprising a support onto which is placed an assembly of articulated arms at the end of which is disposed a tool 12 in contact with a determined work surface, the system allowing the displacement of the tool in rotation about the point of contact of the tool with the work surface, in accordance with signals for controlling a module 14 suitable for calculating them as a function of the remote handling of a virtual tool. The system is suitable for moving the point of contact of the tool in translation and this translation is controlled by the module in terms of polar coordinates, so as to have an angular displacement of constituent elements of said support and a radial displacement of constituent elements of this same support. The invention is more particularly useful in respect of tele-echography operations.