A machining device has a machine head capable of displacement along at least three translation axes X, Y, Z for machining an immobile part fixed above the machining head. The machining head is maintained in a constant orientation by at least three articulated connecting rods. Two connecting rods define together with the machining head and with a first Y carriage, on which they are articulated, an deformable articulated parallelogram in the XZ plane. Another connecting rod is articulated on the machining head and on a second Y carriage and the second Y carriage is capable of displacement along Y on a second X carriage capable of displacement along X. The relative movement along X of the Y carriages results in a displacement in the Z direction. Several devices can be positioned in a plurality of tunnels, these tunnels being arranged so as to share several things.