Manipulation of permanent magnet beads with head-to-tail ring formation on thin 3D surfaces

We propose a novel permanent-magnet-bead structure (PMBS) able to move on thin three-dimensional (3D) surfaces actuated by an external rotating magnetic field (ERMF). The proposed PMBS can sustain its structure without using mechanical linkages. It also has self-positioning capability, which can maintain its current position in the presence of external disturbances without the aid of an ERMF. The PMBS can move along a 3D surface with either rolling or walking locomotion under an ERMF depending on different geometric constraints. We calculated the magnetic torque and force of the PMBS to evaluate their self-positioning and locomotion abilities on a thin 3D surface. Finally, we conducted several experiments to demonstrate the controlled motions of the PMBS in complex surface environments.