Theoretical modeling and error analysis of a compliant Y-shaped mechanism including beam joint stiffness and stress topology for size optimization of six-axis force/moment sensors

The novel compliant Y-shaped mechanisms have mechanical advantages for the multi-axis force/moment sensor since they yield more elastic deformation and more voltage output for strain gauge measurements compared to their common alternative cross-beam structures. This study includes stress topology and natural frequency approximations of the y-shaped structure by taking into account elastic beams and the stiffness of the beam connections. Subsequently, the stiffness and strain output accuracy of the model greatly improved compared to previous studies. The accuracy of the theoretical model is examined in a sensor dimension range by statistical error and parameter analysis. Comparing with the finite element model, results show that the percent error of the theoretical model is 2% for strain, 5% for stiffness, 3% for first natural frequency, and 8% for equivalent stresses, with all correlations above 98%. Comparing the optimization results with the literature, although the y-shaped structure shows similar mechanical behavior with the cross-beam structure, the voltage output of the y-shaped structure is increased up to \(100\%\) for force/moment axes. Moreover, the optimization process with MATLAB GlobalSearch lasts approximately 1 s for the theoretical model and 8 h for the finite element model.