## 2 Experimental Setup  
Typically, the spatial position of a point on a propeller, relative to its central axis, is defined by the coordinates \(X_{n}\), \(Y_{n}\), and \(Z_{n}\). However, accurate surface measurement also requires the determination of the surface normal vector at that point, expressed as Alfan and Beta\({}_{n}\). Consequently, a mechanism with five degrees of freedom is necessary to perform fundamental measurements. Given that a propeller comprises three or more blades, this study adopted a measurement system designed with four degrees of freedom: two linear axes and two rotational axes. The linear axis in the x-direction and the rotational axis in the z-direction are designed with offset values to optimize measurement performance. Overall, the developed automatic measurement system has two main components: a measurement platform and a power control unit. The measurement platform can be positioned separately in a convenient operational area, and the power control unit can be independently installed in a control cabinet. The system is equipped with two linear axes and two rotational axes, with each rotational axis connected to a planetary reducer. Specifically, the linear axis in the x-direction, which is responsible for supporting the test object, uses a TECO ETH13 (HIWIN Technologies Corp., Taichung, Taiwan, and TECO Electric & Machinery Co., Ltd., Taipei, Taiwan) model screw drive with a 5 mm lead. Mounted on this linear axis is a rotational axis in the z-direction, driven by a 1:18 flange-type planetary reducer. The measurement axis comprises a rotational axis in the x-direction, which is driven by a 1:100 low-backlash, coaxial planetary reducer to allow for fine-tuned angular control. The measurement axis is mounted on a cantilever structure that uses a HIWIN KK50 ball (HIWIN Technologies Corp., Taichung, Taiwan, and TECO Electric & Machinery Co., Ltd., Taipei, Taiwan) screw linear stage. A 90\({}^{\circ}\) open fixture  
Figure 1: Process flowchart for the precision casting of marine propellers. is installed on this stage to secure the CITIZEN displacement sensor used for measurement. The overall mechanical arrangement described above is illustrated in Figure 2. For clearer understanding of the platform's motion and axis relationships, readers may also refer to the supplementary demonstration videos [18; 19] available on YouTube, which visualize both continuous and single-point measurement modes. A K-type bracket is installed on the measurement platform to elevate the measurement axis, ensuring that the center of the measurement rotation axis is positioned 235 mm above the surface of the three-jaw chuck table. The three-jaw chuck table is fixed on a linear guide in the x-direction. The center of the chuck table is 59 mm offset from the center of the measurement axis along the y-axis, and the displacement between the sensor's measuring terminal and the x-axis is 204 mm, as illustrated in Figure 2.  
The CITIZEN SA-S110 displacement sensor (Citizen Seimitsu Co., Ltd., Tokyo, Japan) is a high-precision device with a resolution of 0.1 um and offers absolute coordinate measurement. The sensor housing is manufactured through die casting, and the measurement probe features a 3.175 mm-diameter ceramic ball. The probe shaft is supported by a linear bearing, which enhances durability and reduces the likelihood of erroneous readings. Communication with the DVP28 SV11T2 PLC (Delta Electronics, Inc., Taoyuan, Taiwan) is facilitated through the RS-485 standard [20]. DVP28 SV11T2 is equipped with four high-speed counters and supports four-axis 200 kHz high-speed pulse output. The PLC is compatible with various motion control instructions, including absolute position control and relative position control. DOP-107 IV (Delta Electronics, Inc., Taoyuan, Taiwan) is a 7-inch HMI model from Delta's DOP-100 series. It is powered by a Cortex-A8 processor and supports communication through Ethernet and serial ports.