One of the big research topics in modern cosmology is the mystery of dark Energy. To unveil the secret, cosmologists want to measure precisely the evolution of large scale structures in the universe. One way of doing so is to measure the 3D location of a high number of galaxies. By measuring the redshift of a galaxy, it is possible to find its distance. In order to measure a high number of galaxies in a practical amount of time, we need to observe multiple objects in parallel. Instead of a spectrograph, thousands of optical fibres are placed in the focal plane of a telescope. They will transmit the light of many objects to a spectrograph. Each fibre has to be positioned to several mu m precision in the focal plane of a telescope for each exposure. Each fibre is positioned by a 2-axis fibre positioner. In this paper such a fibre positioner with 24-mm diameter is presented. It is driven by two brushless DC motors in combination with a backlash free gearbox. The positioner has an optimal central fibre path and improved angular alignment. The fibre runs through the centre of the positioner and is only bent at the top to reach its target position. In this way, the flexion and torsion of the fibre are minimal. In addition to the high positioning accuracy, the design is optimized to allow a minimal tilt error of the fibre. This is demonstrated using a novel optical tilt measurement system.