To enable important scientific discoveries, ESO has defined a new ground-based telescope: the European Extremely Large Telescope (E-ELT). The baseline design features a telescope with a 39-m-class primary mirror (M1), making it the largest and most powerful telescope in the world. The M1 consists of 798 hexagonal segments, each about 1.4 m wide, but only 50 mm thick. In the last stages of the manufacturing process of these M1 segments, a nanometre-accurate metrology method is required for the M1 to be within specifications. The segments have to be measured on their whiffle-tree support structures with a nanometre-level uncertainty, with a total budget on form accuracy of 50 nm RMS for any segment assembly. In this paper a measurement machine design is presented based on a non-contact single-point scanning technique, capable of measuring with nanometre accuracy, being universal, fast and with low operational costs, providing suitable metrology for M1 segments. A tactile precision probe is implemented to be able to use the machine in earlier stages of the segment manufacturing process. In particular, this paper describes the design of the air-bearing motion system and the separate metrology system based on a moving Sintered Silicon Carbide tube, a fixed Zerodur metrology frame and an interferometric system for a direct and short metrology loop. Preliminary calculations show nanometre-level measurement uncertainty after calibration. (C) 2014 Elsevier Inc. All rights reserved.