Robotized installation for the guided and controlled positioning and movement of a component or an instrument for diagnostic or surgical treatment at or around the head of a patient, whereby the installation includes a robotic device that forms a serial kinematic chain and carries component or instrument at its free and position-controlled end. The robotic device has three kinematic sub-assemblies that are mutually combined in series and include, a first sub-assembly in the form of a rotary-articulation mechanism corresponding to a serial-type, spherical kinematic arrangement with three degrees of freedom, a second sub-assembly in the form of a mechanism with linear translation along an axis, and a third sub-assembly in the form of a second rotary-articulation mechanism, integral with the moving part of the second sub-assembly and also corresponding to a serial-type spherical kinematic arrangement with three degrees of freedom.