The Hita-STT is a five-axis parallel kinematics machine-tool designed for machining and polishing complex parts for applications in medical, automotive components, watch industries. The kinematics of Hita-STT prototype presents an over-constrained design in order to have constant stiffness in the entire workspace. This over-constraining is one of the causes of the hysteresis measured on the machine. Solutions to avoid hysteresis without degrading rigidity are presented. The machine has to be calibrated before its industrialization. A repeatability of 5 microns and an accuracy of 10 microns have to be reached in the entire workspace. Several calibration methods are presented and compared for the case of the Hita-STT machine-tool.