Three-dimensional manipulation via magnetic levitation

Magnetic levitation (MagLev) of nonmagnetic materials in paramagnetic solution, also known as MagnetoArchimedes Levitation, offers a versatile method for density-based analysis and contactless manipulation. However, most extant MagLev configurations focus on optimizing the near-linear gradient of the magnetic field along the central axis to simplify the analysis and manipulation, disregarding the ubiquitous nonlinear magnetic field. In this study, we explore how nonlinear magnetic fields affect three-dimensional levitation behaviors of objects. We utilize the nonlinear magnetic fields generated by a pair of coaxially arranged ring magnets with like poles facing to levitate objects in paramagnetic solution, which we term "nonlinear MagLev". A systematic analysis on the magnetic field, magnetic potential energy and magnetic force is conducted to explain the levitation stability. To describe the three-dimensional levitation behaviors, a mechanical model that accounts for both the nonlinear magnetic field and mass distribution within objects is developed. Theoretical and experimental results demonstrate that the nonlinear magnetic field enables objects with different mass distributions to achieve distinct equilibrium orientations. The concept of leveraging the nonlinear magnetic fields in MagLev provides a general and feasible solution for contactless three-dimensional manipulation, extending potential applications in advanced manufacturing, sorting and self-assembly.