“…Conventionally, in the 3-DOF spherical actuator literature, force and torque calculations are carried out by applying a change of coordinates in the derived magnetic flux models, parametrized with a set of three Euler angles to account for the orientation of the rotor. Several non-contact based methods were proposed to measure the orientation of the spherical rotor including, for example, vision based approaches [52,16,53,54], a laser-based apparatus relaying on flat reflecting plate [55], or an artificial neural network technique, which maps distributed 2-axis and 3-axis magnetic flux density measurements to the instantaneous orientation of the rotor [56]. Computing the orientation is not an easy task and, in general, although the relation between current and force and torque is linear, the relation between the rotor orientation parameters and the rotor magnetic flux density is nonlinear.…”