## 3 Experimental Method  
The experimental framework of this study involved mechanical design, software development, and mechanical validation. In the mechanical design phase, the complete measurement system was modeled using Autodesk Inventor software 2017. CAD drawings of the propeller blades examined in this study were provided by the blades' manufacturer. These drawings were imported into the mentioned software to simulate operation of the developed system and verify that its mechanism achieves the desired surface measurement conditions. Once this verification was complete, the system hardware was created to implement the measurement mechanism, and the electrical control layout and configuration were then planned. Figure 3 illustrates the overall research process. To ensure the integration of virtual simulation and real-world implementation, the software development phase--particularly CAD-based simulation and mechanism verification--was conducted in parallel with the physical system design. This allowed iterative validation and modification of the design before hardware fabrication. As shown in Figure 3, hardware development followed the CAD-based simulation phase. The completed system was subsequently used in the verification and validation experiments described in Section 4. The developed system uses a PCL to perform motion control and data processing tasks. The PLC also reads measurement values from the displacement sensor. The system HMI enables the user to quickly configure measurement positions and view real-time readings. The acquired measurement data are transmitted to a personal computer through Ethernet. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Displacement Sensor** & **PLC** & **Expansion Module** & **HMI** \\ \hline Model & CITIZEN SA-S110 & DVP28 SV11T2 & DVP16 SN11T & DOP-107 IV \\ \hline Name & Servo motor & Servo motor driver & Screw-driven linear stage \\ \hline Model & ECM-B3M-C20604 RS1 & \multirow{2}{*}{ASD-B3-0421-L} & KK50-2P-300A1F1 \\  & ECM-B3L-C20401 RS1 & & ETH13-L5-100-BC-T40-C4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equipment list for propeller measurement experiments. Figure 3: Research process flowchart. The user can directly input desired coordinate positions into the HMI or utilize the teaching mode, which helps the user guide the sensor to the measurement position. In the system design, the measurement points on propeller blades are determined on the basis of the manufacturer's empirical knowledge, which indicates the regions prone to large deformation during production. These critical points are primarily along the leading and trailing edges and at the blade tips, which are areas particularly susceptible to cracking and warping during the postinjection cooling and drying stages. The developed system requires the following parameters for accurate measurement of manufacturing quality: the x-axis advancement distance of the three-jaw chuck platform, rotational offset angle of the propeller about the chuck platform axis (\(\gamma\)), inclination angle of the measurement axis relative to the x-axis normal vector (\(\alpha\)), and vertical advancement of the measurement axis (\(T_{L}\)). The procedure for capturing the spatial coordinates of measurement points is described as follows:  
1. A working plane perpendicular to the central axis at the measurement point is defined, and a line is drawn through the measurement point and the axis on this working plane. Measuring the length of this line yields the distance between the measurement point and central axis (Figure 4). 2. A second working plane perpendicular to the line drawn in Step 1 is defined. On this new plane, a tangent and a normal vector passing through the measurement point are constructed (Figure 5). 3. The completed auxiliary-line model of the propeller is positioned in an assembly drawing. The propeller is aligned under the measurement axis, and the axis and propeller are rotated so that the surface normal vector at the target point aligns with the measurement axis (Figure 6).