## 5 Experimental Test  
In this section, a prototype of the 2-DOF CPM was fabricated and several experimental tests were carried out to evaluate its performance and demonstrate the effectiveness of the proposed design method. Referring to the optimized results, the dimensions of the prototype were selected as: \(L=50\) mm, \(t_{1}=3.5\) mm, \(t_{2}=2.5\) mm, and \(d=10\) mm. The 3-D model and the experimental table of the 2-DOF CPM are shown in Figure 21. The main body of the CPM was fabricated using the milling process with a single block of Al-7075. From the stress diagrams shown in Figure 19, we can see there is a concentration of stress where the leaf springs connect to the platforms and the fixed base. Therefore, fillets with a 2 mm radius were machined at both ends of the flexure members to reduce the effects of stress concentration. Two 60-um-stroke piezoelectric actuators (P-843.40 from Physik Instrument) were adopted to drive the stage. They were driven by a modular piezo controller & driver (E-621 from Physik Instrument), which generates voltage up to 120 V. Two force sensors (U93-1 kN from HBM) were mounted at the end of each actuator to detect their actuation forces. Compared to mounting them in front of the actuators, this installation type reduces the moving mass of the stage and thus improves its dynamic response. A four-channel high dynamic signal processor (MX410 from HBM) was utilized to amplify and record the analog voltage output of the force sensors. The displacement outputs of the terminal platform along the two axes were measured using two high precision length gauges (MT-1281 from Heidenhain). A DSPACE processor board DS1007 equipped with a 16-bit ADC card (DS2004), a 16-bit DAC card (DS2101), and a six-channel incremental encoder interface card (DS3002) was utilized to output the excitation voltage for the piezo servo controller and capture the data from the force sensor signal processor and length gauges. Preloads were applied along the two axes through preload baffles to prevent the piezoelectric actuators from suffering pulling forces during the motion process and to eliminate the clearances between the actuators and the mechanism. The preloading forces were detectable by the force sensors and they were set to about 300 N initially. The input axial stiffness along the two axes was tested first. The actuation forces were detected using the force sensors and the displacements were measured using the length gauges. Figure 22 shows the relationship between the tested actuation forces and the corresponding displacements along the two axes. The tested displacement-force curves fit into lines well and indicate the stiffness of the CPM is linear, which will be easy to control. The least squares method was utilized to fit the results and the input axial stiffness of the CPM was calculated as 3.87 N/um and 3.93 N/um, respectively. The axial stiffness measurements were greater than the theoretical and simulated results. The differences occur for two reasons. First, the fillets machined at both ends of the leaf springs increase their stiffness. Second, the displacement output of the terminal platform is larger than that measured at the actuation point, which results in a larger measured stiffness. Figure 20: First three vibration modes of the CPM. (**a**) First mode. (**b**) Second mode. (**c**) Third mode. The workspace of the CPM was tested through running a square trajectory in the open-loop control. The experimental result and estimated workspace are given in Figure 23. The measured workspace was 45.21 \(\upmu\)m \(\times\) 45.63 \(\upmu\)m, which is a little smaller than the estimated result. The decreased motion of the CPM lies in the deformations of the joint surfaces between the parts connected by bolts. Figure 21: 3-D model and prototype of 2-DOF CPM. (**a**) 3-D model. (**b**) Prototype. Figure 22: Experimental results of input axial stiffness. Then the natural frequency of the CPM was tested using the hammering method with the piezoelectric actuators dismantled.