Construction of the inner layer barrel drift chambers of the ATLAS muon spectrometer at the LHC

We have designed and built the facilities to assemble the inner layer of the precision tracking chambers (Monitored Drift Tubes, MDT) for the Muon Spectrometer of the ATLAS Experiment at LHC. This article describes in detail the tooling, the procedures and the quality control equipment used in the chambers assembly. Data are presented from the X-ray tomograph at CERN showing that the required chamber mechanical precision has been achieved.