# Novel Instrument for Clinical Evaluations of Active Extraocular Muscle Tension
## 2 Materials and Methods
### Structural Analysis and Calibration  
Structural analysis was performed on the ATMD to investigate the sensitivity and mechanical stability of the composed components, as shown in Figure 5. The sensing unit was modelled in three dimensions using CAD software Solidworks 2019 SP3.0 (Dassault Systemes, Velizy-Villacoublay, France) and assembled, as shown in Figure 5a. Model simplification was carried out for efficient analysis and rapid computation: (1) screw threads were replaced as bonded contacts, (2) linear bashing and housing were integrated as single parts, and (3) additional components were excluded, including the cap, connector, bolt, and swab.  
Boundary conditions were determined and are displayed in Figure 5b [24; 25]. The enclosure parts (e.g., handle and case) were fixed, while the internal parts (e.g., linear motion (LM) guide, housing, shaft, and sensor PCB) were bonded. The shaft and housing were subjected to friction, where the pressure applied to the swab might be transferred to the force sensor. Pressure on the top of the swab and axial force by initializing the bolt were included as external loads, as shown in Figure 5c. Preloading using the initializing bolt could influence the normal friction force, and, thus, the resistance against the force transferred to the sensor could be varied. These were crucial factors for precise measurements using FGT as an ATMD [26; 27]. Finally, structural analysis was conducted to evaluate the stress distribution of each component, as shown in Figure 5e.  
Figure 4: Real-time waveforms of the force on the cotton-tipped swab (**a**) and the tilting angles of the three axes for the ATMD sensing unit: yellow for the x-axis angle, orange for the y-axis angle, and blue for the z-axis angle (**b**).  
The stress distribution of the sensing unit was calculated, as shown in Figure 6. Most of the stress was generated in the connecting pin that vertically supported the loading of the shaft. The maximum von Mises stresses of the pin were 2.896 \(\times\) 10\({}^{6}\) N/m\({}^{2}\), 5.793 \(\times\) 10\({}^{6}\) N/m\({}^{2}\), 1.448 \(\times\) 10\({}^{6}\) N/m\({}^{2}\), and 2.897 \(\times\) 10\({}^{7}\) N/m\({}^{2}\) for axial forces of the initializing bolt of 0.98 N, 1.96 N, 4.9 N, and 9.8 N, respectively, as shown in Figure 6. Aluminum (Al) 6061, which is one of the most common Al alloys in general-purpose use, was employed as the raw material. The yield stress of Al 6061 was 2.757 \(\times\) 10\({}^{7}\) N/m\({}^{2}\). We assumed that the maximum stress should be at least two-times lower than the yield stress for structural safety, and so an axial force of 4.9 N was determined for the initializing bolt.  
Figure 5: Summary of ATMD structural analysis: (**a**) three-dimensional (3D) modelling of the sensing unit, (**b**) simulated boundary conditions, (**c**) external forces on the top of the shaft and the axial force through the initializing bolt, (**d**) mesh generation, and (**e**) stress analysis of assembled components.  
Figure 6: Maximum von Mises stresses measured using the sensing unit as a function of axial forces: (**a**) 0.98 N, (**b**) 1.96 N, (**c**) 4.9 N, and (**d**) 9.8 N.  
The calibration process was performed for the assembled sensing unit of ATMD, as shown in Figure 7a. A tailored housing was three-dimensionally printed to stand upright beside the sensing unit to precisely measure the counterweight, as shown in Figure 7b. The correlation between the force sensor output and counterweight was determined as  
\[\text{y}=1.9061\text{x}-0.8025 \tag{1}\]  
where y is the mass in grams and x is the force sensor output.  
The R\({}^{2}\) value for Equation (1) was 99.95%, and the Pearson correlation coefficient, calculated using statistical software SigmaXL version 9.1, was 0.9985. These results indicate that the calibrated sensor unit is highly precise for FGT measurements [28; 29; 30].