## 2 Research Methodology  
### Reconfigurable Fiducial-Aided Positioning System Design  
The fiducial-aided calibrating and positioning artefact is not only designed to explore its capacity for positioning freeform surfaces in the manufacturing cycle, including manufacture, measurement and evaluation, but also identify the errors (i.e., geometric volumetric errors) of the corresponding machine tool. As a result, the designed reconfigurable fiducial-aided model should suit the machining and measuring conditions well, such as the working space, machine kinematics, tool collision and clamping. Standard balls are good fiducials because their positions can be easily acquired by many touch probe-based on-machine CNC measurement instruments.  
The basic idea is the design of a workpiece fixture with a cuboid or cylindrical shape which is capable of being clamped easily in the machines. The ball bars are then assembled at the tips of rods which are mounted surrounding the workpiece with different heights so that a 3D space enveloping the machining work volume is established. The idea behind the variable heights of the balls is that richer information about the working space of the machines can be gathered as well as achieving additional geometric constraints. It is clear that the reconfiguration ability, depending on the working environment (i.e., machine tools, workpiece), is the most important feature of the new fiducial-aided design. It is noted that this characteristic provides the possibility of obtaining specific information in the desired areas. It has the ability to overcome the drawbacks of existing designs that require special fixtures for different workpieces as well as requiring additional equipment. Moreover, the fiducials such as standard balls can also calibrate the measuring systems. Once the fiducial-aided positioning system is established, there is no need for any manual operation to align the workpiece on the machine tool since the fiducials can provide the coordinate information.  
The key requirement of the design is the stability of the artefact geometry in the measuring process. Thermal sensitivity due to working temperature and elastic deformation under different gravitational directions are considered as the main factors which should be minimized. In order to limit the thermal expansion and deflection, the ball is made of Si\({}_{3}\)N\({}_{4}\)The fixture and the rods are made of steel. Moreover, some short stems made of steel are used to add to the height of the ball bars to control the deformation. A thermally controlled environment is always necessary in the current experiments. As for the gravitational effect, it can be calibrated on a CMM by rotating the fixture to change the direction of gravity in the process of calibration of the positions of the fiducials, and the details are shown in the following section.  
Figure 1 shows an example of the designed system consisting of five fiducials (\(N=5\)) mounted on a square fixture on a five-axis fly-cutting raster milling machine tool. Five fiducials (standard spheres) were designed to surround the workpiece in the 3D artefact. The heights of the sphere were 20, 25 and 35 mm, and the distribution of these fiducials is also shown in Figure 2.