Dexterous magnetic manipulation of ferromagnetic objects is well established, with three to six degrees of freedom possible depending on object geometry¹. There are objects for which non-contact dexterous manipulation is desirable that do not contain an appreciable amount of ferromagnetic material but do contain electrically conductive material. Time-varying magnetic fields generate eddy currents in conductive materials^2,3,4, with resulting forces and torques due to the interaction of the eddy currents with the magnetic field. This phenomenon has previously been used to induce drag to reduce the motion of objects as they pass through a static field^5,6,7,8, or to apply force on an object in a single direction using a dynamic field^9,10,11, but has not been used to perform the type of dexterous manipulation of conductive objects that has been demonstrated with ferromagnetic objects. Here we show that manipulation, with six degrees of freedom, of conductive objects is possible by using multiple rotating magnetic dipole fields. Using dimensional analysis¹², combined with multiphysics numerical simulations and experimental verification, we characterize the forces and torques generated on a conductive sphere in a rotating magnetic dipole field. With the resulting model, we perform dexterous manipulation in simulations and physical experiments.

^{铁磁物体的灵巧磁性操纵已经很好地建立起来，根据物体几何形状1}可能具有三到六个自由度。有一些物体需要非接触式灵巧操作，这些物体不包含可观量的铁磁材料，但包含导电材料。时变磁场在导电材料^2,3,4中产生涡流，并由于涡流与磁场的相互作用而产生力和扭矩。这种现象以前曾被用于诱导阻力以减少物体通过静态场时的运动^5,6,7,8，或使用动态场在单个方向上对物体施加力^9,10,11，但尚未用于执行已用铁磁物体证明的导电物体的灵巧操作类型。在这里，我们展示了通过使用多个旋转磁偶极子场可以对导电物体进行六个自由度的操作。使用维度分析¹²，结合多物理场数值模拟和实验验证，我们描述了在旋转磁偶极子场中导电球体上产生的力和扭矩。使用生成的模型，我们可以在模拟和物理实验中进行灵巧的操作。