Many new machine-tool are based on a hexapod structure, a parallel robot with 6 DOF, While only 5 of them are needed for the machining operations as the rotation of the end-effector around its normal is not used. We have therefore an extra DoF: we propose an algorithm which is able to determine for almost any trajectory of the machine the values of the extra DoF to ensure that the trajectory lie within the workspace of the robot is singularity -free and furthermore optimize an arbitrary criterion