## 4 Discussion  
The present methodology investigated the innovative use of the strain gauge method in combination with a structural modification of a manipulator link load-bearing element. The advantage of the proposed low-cost torque sensor using the strain gauge method is the possibility to register and evaluate the dynamic effects (vibrations) of the whole mechanical system during real operating conditions as well as their influence on the stresses in selected structural elements in case of setting a higher sampling frequency. Based on the deformation and stress analysis carried out in real operating regimes on a physical model, it is possible to verify the results obtained by numerical modelling on computational models and, thus, to verify the correctness of the boundary conditions used. The advantage of the presented methodology is the possibility to analyse the stress states depending on the parameter settings of the drive units. The force effects acting on the manipulator link can also be measured when it is braked.  
Based on a series of experimental measurements under static and dynamic loading and the results obtained by numerical modelling, the following can be stated:  
* Strain gauge measurements on the modified flange under static loading confirmed perfect agreement (less than 2%) with the numerical modelling results over the entire working range (28 Nm to 200 Nm).
* The measurements under dynamic loading were analysed by comparing the amplitude spectra obtained from time records of the strains and accelerations. The amplitude spectra documented perfect agreement between strain gauges and accelerometers, which can be used in practice for vibration analysis. The strain gauge measurements documented excellent agreement in the frequency domain compared to the accelerometers, even at low strain levels of the order of microstrain units (Figure 11a).
* Strain gauges provide information on the mechanical stress history, which can be used to investigate the influence of the number of cycling loads on positioning accuracy.  
Figure 12: Forced vibrations at low frequencies. (**a**) Time record of strains registered by strain gauges; (**b**) time record of accelerations registered by accelerometers; (**c**) amplitude spectrum of strains; (**d**) amplitude spectrum of accelerations.  
* The design of a low-cost torque sensor represents a simple solution to measure torque using a modified flange without intervention in other parts of the manipulator.  
The proposed methodology is mainly suitable for testing newly designed (prototype) manipulators. The use in long-term operation, for which the manipulators are designed (repeatability of operations), is possible by replacing the flanges with strain gauges as part of planned maintenance.  
Conceptualization, M.P.; methodology, M.P. and M.H.; validation, M.P., M.H. and S.G.; formal analysis, M.S. and S.G.; investigation, M.P., M.H. and S.G.; resources, M.S.; data curation, M.P. and M.H.; writing--original draft preparation, M.P. and M.H.; visualization, S.G.; supervision, M.P.; project administration, M.H.; funding acquisition, M.P. and S.G. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the following projects: VEGA 1/0516/22, VEGA 1/0509/23 and KEGA 011 ZU-4/2022.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon request.  
The authors declare no conflict of interest.