Polarization Criteria Detection of a Generalized Spatial Universal Rotating Magnetic Vector

Spatial universal rotating magnetic vectors (SURMVs) are generated by the superposition of three orthogonal sinusoidal magnetic vectors with the same frequency and widely used to drive magnetically actuated capsule robots. Although many forms of the superposition formula are proposed to guarantee the circular trajectory shape of an SURMV, there is no general research on how the trajectory shape will be if the actual amplitudes and phases of the three orthogonal sinusoidal magnetic vectors do not satisfy the proposed superposition formula. Thus, this paper presents an analytic model for the trajectory shape detection of a generalized SURMV which is the superposition of three orthogonal sinusoidal magnetic vectors with the same frequency but any amplitude and phase. After analytic analyses on the superposition formula of the generalized SURMV, the trajectory shape turns out to be classified as three types of polarization only: linear, circular, and elliptical polarizations in space. And the analytic expressions for the criteria of the three types of polarization are given and verified through both simulations and experiments, which could make the trajectory shape and error detection of an SURMV easier than direct measurement on magnetic fields before.