## 5 Experimental Test
The flatness of the measuring datum planes was improved to 1 \(\upmu\)m. The preload forces along the two axes were set to 300 N. Then the output coupling of the CPM was re-evaluated and the results are given in Figure 20:4 It shows that the cross-axis outputs of the CPM are significantly reduced and the maximum output couplings between the two axes are only 0.105% and 0.045%, respectively. The actuation point deformation should be measured to evaluate the ICD of the CPM, which is impossible to be achieved experimentally in this prototype. To conquer this problem, we proposed utilizing the ratio of the axial deformations at the two actuation points to reflect the input coupling performance of the 2-DOF CPM. Because of the linear displacement-force relation as shown in Figure 22, the changes of axial forces along the two axes were detected to indirectly evaluate the input coupling of the CPM. Tests were run on the variations of axial forces along the two axes when the \(x\)- or \(y\)-axis is actuated, shown in Figure 20:5 The results show that when the CPM moves through the whole range along the \(x\)-axis, the changes of the axial forces along the \(x\)- and \(y\)-axes are 169.4 N and 0.41 N, respectively. When the CPM moves through the whole range along the \(x\)-axis, the changes of the axial forces along the \(x\)- and \(y\)-axes are 0.34 N and 170.2 N, respectively. The corresponding coupling ratios  
Figure 20:6 Output coupling evaluation of CPM through adjusting the preload forces. Figure 20:7 Coupling motion tests when the preload force along the \(x\)-axis changes. (**a**) Coupling motion along the \(y\)-axis. (**b**) Coupling motion along the \(x\)-axis. can be calculated as 0.24% and 0.20%, where the theoretical values calculated by Equation (28) are all 0.084%. The difference may lie in manufacturing and assembling errors. Regardless, this method provides a feasible way to evaluate the input coupling of the CPM and demonstrates this prototype's excellent input decoupling performance. This study also evaluated the contour tracking of the CPM for 2-D trajectories, to reflect the two-axis cooperative tracking performance. To adequately verify the decoupling performances of the CPM, the actuators in the CPM were controlled independently without any additional kinematic calibration or compensation. A Proportion-Integration algorithm was utilized to realize the closed-loop control. The 2-D tracking results for 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) lines with a contouring velocity of 40 \(\upmu\)m/s are shown in Figure 33a, and the corresponding contouring errors have been plotted in Figure 33b. The contouring error here is defined as the minimum distance between the actual position and desired trajectory along an orthogonal direction to the trajectory. The results show that the maximum contouring error is smaller than 25 nm. The experimental tests of circular contouring at different frequencies are shown in Figure 34, where the radius of the circles is 10 \(\upmu\)m. The measured circular trajectories are coincident with the ideal trajectory without elliptical distortion, which contributes to the identical dynamic characteristics and excellent decoupling performance of the two axes. To obtain a more intuitive comparison, the maximum and average contouring errors of the circular contour with different frequencies has been illustrated in Figure 20:8 The results show that the contouring errors grow up as the frequency increases, and the maximum error is less than 150 nm. The contouring accuracy can be improved with the help of an advanced control strategy, which will be investigated in our future work. Figure 20:9 Output coupling evaluation of CPM through improving the manufacturing accuracy of the measuring datum. Figure 23.0 Input coupling evaluation of CPM. Figure 23.1 Circular contouring performance at different frequencies: (**a**) \(f\) = 0.5 Hz; (**b**) \(f\) = 1 Hz; and (**c**) \(f\) = 5 Hz.