# Measurement of Wheel Radius in an Automated Guided Vehicle
## 5 Discussion  
The results obtained from experimental studies are characterized by small dispersion and thus high accuracy. A comparison of coefficients of variation with the values obtained from the calculation of relative errors (Figure 10) indicates that appropriate precision and diligence are maintained during the tests. During the experimental tests, it was tried to make the oscillation and deviation values smaller to \(A\) = 0.025 m and \(C\) = 0.3 m. The calculated values of the coefficient of variation Table 2 for both wheels, except for the load with the force \(F_{N}\) = 1800 N, are comparable. For a force load of \(F_{N}\) = 1800 N, the coefficient of variation for the left wheel is 84% higher. The values of the coefficient of variation are influenced by the impossible to completely eliminate deviations and oscillations as well as, for example, unexpected accidental slips in the contact of the wheel with the surface and measurement errors in data recording. The calculations of the slip coefficients \(s\) as a function of load carried out show their linear relationship (Figure 14). Equation (10) used for calculations takes into account the elastic deformation of the wheel and microslips in the contact between the wheel and the surface. According to the information contained in a series of studies and in Figure 3, for low values of slips \(s\) < 2%, the relationship between the force acting on the wheel and the slip is linear.  
The diagram in Figure 15 clearly indicates the elastic properties of the belt material. This graph has the shape of a hysteresis loop. The field contained inside the hysteresis loop indicates the ability to damp vibrations.  
The test results and their courses presented in Figures 14 and 15 are compatible with the examples shown in many works [23; 24; 25]. This proves the correctness of the adopted methodology and diligence in the course of research.  
The results obtained and the relationships developed on their basis are very important for the automated guided vehicle. Especially in the vehicle shown in Figure 11. In the vehicle shown in  
Figure 14: Load dependence as a slip function for (**a**) left wheel; (**b**) right wheel.  
Figure 15: Deflection characteristics as a function of load.  
Figure 11, the rear wheels do not carry any driving or braking forces and are used to measure the distance traveled.  
During the tests, the force loading the wheel did not exceed 21% of the maximum wheel load. By increasing the wheel load by 1010 N from 790 N to 1800 N, the relative increase in the rolling radius was 0.12%. Because with the slip below 2%, all changes are linear, a further increase in the load by the force of 1010 N and 2020 N will result in an increase of the rolling radius by 0.24% and 0.36%. The increments of the rolling radius are related to the value obtained under the load of 790 N. In the last case, the total force on the wheel will be 3820 N. This is less than half the allowable force.  
Assuming that only one wheel is subject to load changes, the other wheel is loaded with a constant force \(F=790\) N, using the dependencies (1)-(4), it is possible to determine the deviation from the set route and the radius of the curve along which the vehicle will move. The results are presented in Table 3.  
The analysis of the data in Table 3 shows that the differences in the load on the wheels cause significant changes in the trajectory carried out by the vehicle. Correction of the above errors can be made through additional navigation systems or by taking into account corrections made to the control system, coming from the load measurement system of a given wheel.