A 6-DOF monolithic nanopositioning stage is developed for three coordinate measuring machines (CMM) with nanometer resolution. The stage consists of a monolithic flexure hinge mechanism, six piezoelectric actuators and six fiber-optic displacement sensors. A mathematical model of the constraint optimization problem is presented. Based on the solution of the optimization problem, the final design of the 6-DOF stage is also presented. The numerical analysis on static and dynamic behavior of the stage is done by using the finite element method. The experimental results of the performance of the 6-DOF stage are presented.