Deflection modeling of permanent magnet spherical chains in the presence of external magnetic fields

This work examines the interaction of permanently magnetised spheres in the presence of external magnetic fields at the millimetre scale. Static chain formation and deflection models are described for N spheres in the presence of an external magnetic field. Analytical models are presented for the two sphere case by neglecting the effects of magnetocrystalline anisotropy while details of a numerical approach to solve a chain of N spheres are shown. The model is experimentally validated using chain deflections in 4.5 mm diameter spheres in groups of 2, 3 and 4 magnets in the presence of uniform magnetic fields, neglecting gravitational effects, with good agreement between the theoretical model and experimental results. This spherical chain structure could be used as an end effector for catheters as a deflection mechanism for magnetic guidance. The spherical point contacts result in large deflections for navigation around tight corners in endoluminal minimally invasive clinical applications.