Reconsidering Six-Degree-of-Freedom Magnetic Actuation Across Scales

Magnetic actuation, also known as magnetic manipulation, refers to the use of controlled magnetic fields, generated by electromagnets or permanent magnets, to impart forces and torques on a remote magnetic object. The magnetic object is typically modeled as a magnetic dipole, affording five-degree-of-freedom (5-DOF) actuation, comprising 3-DOF force and 2-DOF torque. A method was proposed that uses a three-magnet object in which one magnet is used for traditional 5-DOF actuation and two auxiliary magnets achieve the sixth (torque) DOF via a force couple, and this object can still be modeled and controlled as if it exists at a single point in space, as in traditional 5-DOF actuation. We reconsider this method of 6-DOF magnetic actuation. We perform a numerical study of torque that can be generated on a multi-magnet object of varying shape (but assuming that the individual magnetization vectors are coplanar), size, and orientation, using a variety of well conditioned magnetic manipulation systems. We find that, in the limit as the magnetic object is reduced in size, there is an optimal arrangement of the magnetic object, which is invariant to the manipulation system. We find that the sixth DOF comes at a cost to the original 5-DOF, reducing them by 61% when using the optimal magnetic arrangement; this value is also invariant to the manipulation system. Finally, we find that the sixth DOF scales poorly relative to the other five as the size of the object is reduced, but can be relatively large as we consider objects that are large relative to the distances over which they are being actuated.