## 4 Experimental Analysis  
Today, because of the height level of technology development, the aim is to achieve full utilization of the material for the manufacturing of the external fixation device, because of that, working loads are pushed to their maximum. The first step is to do an analysis about stress distribution using experimental analysis. The next step is to carry out the optimization process to achieve lower mass in correspondence to allowed interfragmentary displacement and stresses at defined places of design. The verification of numerical structural analysis of external fixation device is done using experimental analysis on real design. Experimental testing is done in a laboratory for material testing, using tensometric analysis equipment from the laboratory for mechanical design testing. In real conditions, the external fixation device is loaded through the bone segment. In experimental analysis, the bone segment is replaced with, geometrically, the same segment manufactured from beech tree [15; 16; 29]. In addition, supports of the lower and upper parts of the bone segment are supported using spherical joint to the testing machine. The end of the spherical joint is connected to the force sensor (Figure 7). The proximal bone segment displacements were monitored by a displacement transducer, while the loading was controlled by a force transducer (type U2A from HBM-Huttinger Baldwin Mestechnik GmbH, Darmstadt, Germany). Testing machine was a machine for material testing (Zwick GmbH & Co., Ulm, Germany, model 143501). Stress analysis was carried out using tensometric analysis equipment using data acquisition (DAQ) system QuantumX MX840B (HBM) and strain gauge 3/120 LY11 (HBM), (Figure 7). The fixator tree is loaded with eccentric pressure load at the place of the proximal bone segment. Because of eccentric pressure, principal deformations consist of bending deformations and axial pressure (Figure 8); because of this, they can be defined using the superposition, as follows:  
\[\epsilon_{1}=-\epsilon_{\text{p}}+\epsilon_{\text{s}}=-\frac{\text{F}}{\text{ AE}}+\frac{\text{M}}{\text{EZ}};\;\epsilon_{3}=-\epsilon_{\text{p}}-\epsilon_{ \text{s}}=-\frac{\text{F}}{\text{AE}}-\frac{\text{M}}{\text{EZ}} \tag{4}\]  
where: \(\epsilon_{\text{p}}\) is the strain component caused by the axial compressive force, \(\epsilon_{\text{s}}\) is the strain component caused by the bending moment, F is the axial compressive force, A the area cross-section of the fixator connecting rod, E modulus of elasticity, M bending moment, Z section modulus of the fixator connecting rod. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{6}{c}{**Principal Stresses, MPa**} & \multicolumn{3}{c}{**Von Mises Stress, MPa**} \\ \cline{2-7}  & \multicolumn{3}{c}{**MP+, SG+**} & \multicolumn{3}{c}{**MP\(-\), SG\(-\)**} & \multicolumn{3}{c}{**MP+**} & \multicolumn{1}{c}{**MP\(-\)**} \\ \cline{2-7}  & \(\sigma_{1}\) & \(\sigma_{2}\) & \(\sigma_{3}\) & \(\sigma_{1}\) & \(\sigma_{2}\) & \(\sigma_{3}\) & \(\sigma_{\text{vm}}\) & \(\sigma_{\text{vm}}\) \\ \hline FEA & 330 & 0.2 & 0.001 & \(-\)0.003 & \(-\)0.4 & \(-\)355 & 330 & 355 \\ \hline Exp. & 334 & - & - & - & - & \(-\)368 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum values of principal and von Mises stresses at the measuring points. In this case, bending deformations are much larger than pressure deformations (\(|\epsilon_{\rm s}|\gg\epsilon_{\rm p}\)). According to that, this case of load has unequally distributed principal deformations along the longitudinal section of the tree. The neutral line does not match the axis of symmetry of the fixator tree (Figure 8). Because of this, two Wheatstone quarter bridges are applied and connected to the Quantum X system using two measuring channels. Wheatstone quarter bridges have one active SG and one compensation (passive)  
Figure 8: Placement of strain gauges on fixator tree. Figure 7: Experimental analysis of external fixation device for axial pressure load.