The Orthoglide project aims at designing a new 3-axis machine tool for High Speed Machining. Basis kinematics is a 3 degree-of-freedom translational parallel mechanism. This basis was submitted to isotropic and manipulability constraints that allowed the optmization of its kinematic architecture and legs architecture. Thus, several leg morphologies are convenient for the chosen mechanism. We explain the process that led us to the choice we made for the Orthoglide. A static study is presented to show how singular configurations of the legs can cause stiffness problems.