A multi-degree-of-freedom electromagnetic machine includes a spherical structure, a first coil, a second coil, a non-magnetic structure, and a Halbach array. The spherical structure has a first axis of symmetry, a second axis of symmetry, and a third axis of symmetry, and the first, second, and third axes of symmetry are disposed perpendicular to each other. The first coil is wound on the spherical structure about the first axis of symmetry, and the second coil is wound on the spherical structure about the second axis of symmetry. The non-magnetic structure is spaced apart from, and at least partially surrounds, the spherical structure. The Halbach array is mounted on the non-magnetic structure and includes N-magnets, where N is a multiple of 4. The spherical structure and non-magnetic structure are mounted to allow relative rotation between the non-magnetic structure and the spherical structure.