75 mm stroke flexure stage for the LNE watt balance experiment

The LNE watt balance experiment aims at measuring the ratio of the Planck constant h to a standard mass m with a relative uncertainty smaller than 10⁻⁸. One step of our experiment requires to move a coil vertically inside a magnetic field along a total stroke of about 75 mm. To limit the uncertainty of our experiment, the velocity of the coil is servo-controlled at a constant value of 2 mm/s and the deviations of the trajectory from a rectilinear translation must be kept within 1 μm for straightness and within 5 μrad for yaw and pitch. These requirements must be performed along a useful stroke of 40 mm.To avoid play and friction, which are likely to perturb the feedback loop of the coil velocity, a flexure stage has been built to constrain the movement of the coil. For a 40 mm stroke, measurements show that the two straightness errors are smaller than 0.2 μm and 0.5 μm respectively, and that pitch and yaw are smaller than 4 μrad and 6 μrad respectively.