Designing Multi-Axis Force–Torque Sensors by Minimizing the Amplitudes of Their Nonlinear Displacements

Abstract

Compliant multi-axis force–torque sensors play a crucial role in many emerging robotic applications, such as telemanipulation, haptic devices and human-robot physical interaction. In order to synthesize the compliant architectures at the core of these sensors, several researchers have devised performance indices from mechanism theory. This paper follows the same approach, but includes the innovation of using the changes in the compliant mechanism geometry as a new performance index. Once external forces are applied, the compliant mechanism deviates from its unloaded configuration, and thus, changes in geometry prevent the sensor from exhibiting a linear response. In order to minimize this nonlinear behavior, the potential sources of error are analyzed by applying linear algebra techniques to the expression of the Cartesian force mapping. Two performance indices are then presented and combined. The first index measures the variations of the Jacobian matrix about the unloaded configuration. The second index measures the amplification of the error arising from the joint displacements measurement. The resulting indices can be expressed symbolically, making them easier to evaluate and synthesize. Finally, we apply the performance indices we have developed to simple compliant mechanisms, and discuss the results.