## 3 Results
### Reducing Stiffness in Compliant Joints Via Lattice Flexures: Comparison between FEA and Experiments  
A total of 75 tests using the LFHs with their respective lattice pattern topologies and a single test involving solid flexure hinges were performed. An example of a CCAJ under experimental loading during the test is shown in Figure 12a. This deformed shape obtained in the experiments was validated with FEA, for which an example is shown in Figure 12b. FE models were further used to predict the displacements of the CCAJs with LFHs. FEA predictions for the stiffness of each case were then compared with the experimental results. A comparison between FEA and experimental force-displacement curves is shown in Figure 13 for the stiffest and most flexible cases obtained for each lattice topology. The errors obtained from comparing FEA predictions and measurements of additively manufactured samples are listed in Table 1.  
Figure 10: Compliant cross-axis joint tests with different flexure hinges. (**a**) Use of normal solid flexure hinges. (**b**) Use of re-entrant lattice-flexure hinges with a 3.5 mm unit cell and 0° orientation. Figure 9: Types of lattice-flexure hinges used for the lattice-compliant cross-axis joint. Note that both the FEA stiffness predictions and the ML forecasting are included, with dotted lines, in Figure 13 (ML forecasting is discussed in an upcoming subsection). The stiffest values of the hexagonal LCCAJs were obtained for a configuration with a 3.5 mm unit cell and 0\({}^{\circ}\) lattice orientation (0.46 mm displacement) (Figure 13a), and the most flexible values were obtained for the configuration with a 3.5 mm unit cell and 80\({}^{\circ}\) lattice orientation (1.03 mm displacement) (Figure 13b). In the case of the re-entrant LCCAJ, the stiffest values were obtained with the configuration containing a 5.5 mm unit cell and 0\({}^{\circ}\) lattice orientation (0.58 mm displacement) (Figure 13c), and the most flexible values were those of the configuration with a 5.5 mm unit cell and 60\({}^{\circ}\) lattice orientation (1.41 mm displacement) (Figure 13d). Finally, for the square LCCAJ, the stiffest values corresponded to the configuration with a 3.5 unit cell and 0\({}^{\circ}\) lattice orientation (0.29 mm displacement) (Figure 13e), and the most flexible values to a configuration with a 3.5 mm unit cell and 40\({}^{\circ}\) lattice orientation (0.72 mm displacement) (Figure 13f). The case of the CCAJ with fully solid hinges resulted in a displacement of 0.14 mm upon applying a load of F = 0.04905 N. By comparing it with the other displacements achieved (for the same load), even for the CCAJs with the stiffest LFHs, the reduction in stiffness was successfully obtained. As stated before, the stiffest LFHs gave a resultant displacement of 0.29 mm, improving the range of motion of the CCAJ in the process. Finally, the less stiff LFHs gave a resultant displacement of 1.41 mm, influencing the range of motion of the CCAJ significantly. Among the lattices tested, the square topology was the stiffest. A visual comparison between the highest and lowest displacements obtained is presented in Figure 14.  
Deviations between the FEA predictions and the experimental results seen in Figure 13 can be attributed to various factors. To start with, the contact pairs in FEA were chosen carefully by analyzing the mechanical behavior of the LCCAJ. On the other hand, imperfections found in the additively manufactured LFHs (described in the previous subsection) caused variability in the experimental results. Some displayed a different depth dimension in the lattice part once the supports were removed. This action might have caused unwanted material to be retained or the removal of more material than intended from the lattice parts. Such defects could also have led to sliding or over-constrained assemblies at various contact zones of the LCCAJs tested. In addition, at a microscale level, irregular microstructural defects appeared during the extrusion of the samples from the 3D printer (Figure 11).