## Concept and Kinematic Model Formulation
### Test-Bench Setup Validation and Procedure  
In the light of the obtained results from numerical simulations, a prototype (a milling machine ram) was fabricated and tested. The scope was to compare the numerical models with the experimental tests using the FBG sensors. Figure 5 shows an overview of the system prepared to perform the experimental tests. The test-bench was composed of the moving slide frame with the embedded FBG sensors, the interrogator, and a personal computer to process the collected data. The axis structure was constrained in \(x\)-\(y\) directions at the carriages location and in the \(z\) direction at the nut support location. The selected FBGs had the following characteristics:  
Figure 4: The Finite Element (FE) analysis results (strain-tensors) performed on the Carbon Fiber Reinforced Polymers (CFRP) beam with the embedded fiber Bragg grating (FBG) sensors applying a static load (2000 N) on the \(x\) (**a**) and the \(y\) (**b**) axis.  
Figure 3: Homogeneous Transformation Matrix system composition of subsequent reference plane.  
* peak resonance wavelength of 1549-1551 nm,
* length of active zone from 0.25 k mm to 10 k mm,
* length of passive zone from 1 m to 100 m,
* reflectivity close to 90%,
* peak amplitude equal to 15 dB,
* temperature sensitivity of 10.2 pm/\({}^{\circ}\)C,
* measurement precision lower than 0.2%,
* measurement resolution less than 2 \(\upmu\)m,
* Range Measuring System of operating temperature from \(-\)50 \({}^{\circ}\)C to +110 \({}^{\circ}\)C.  
The experimental procedure consisted of two main phases. In the first part of the test campaign, a set of static loads was applied to the structure in order to verify the effectiveness of the FBG sensors embedded in the prototype. These results were compared with the numerical model.  
The stresses measured by the FBG sensors through the modification of their characteristics were transferred to a PC. The signals were examined and saved by the sensing software. The obtained results were used in order to improve the regression model to compensate the TTP deviation.  
The second phase of the experiments was based on the time-variant thermal tests. In this case, the experimental tests were performed by varying the temperature of the structure over time (36 h). This part of the study sought to optimize the model and understand the effectiveness of the system in compensating the TTP position when the MT structure temperature varies.  
The measures of the FBG sensors were acquired by an optical reading unit (Fabry-Perot Interferometer), while the temperature changes of the MT ram were automatically collected by integrated circuit temperature sensors (LM35) located along the structure. A FBG interrogator was adopted to monitor the Bragg wavelength shift of the FBG under different stresses. It had a resolution of 1 pm and a sampling frequency of 1 kHz. In particular, two laser sensors were used to measure the TTP displacement. An auxiliary low conductive kit was used to represent the tool and tool-handler system. It was fixed to the bottom flange of the ram. The laser sensors were placed at 120 mm from the assigned tool tip point, measuring both displacements in the \(x\)-axis and \(y\)-axis directions. The laser sensor had a resolution up to 0.05 \(\upmu\)m and a linearity of 0.5 \(\upmu\)m.