A multi-degree-of-freedom electromagnetic machine that may be operated as a motor, a generator, or a motor-generator, the machine comprising: a first structure comprising a first conductor, a second conductor, and a third conductor, the first conductor following a first general trajectory, the second conductor following a second general trajectory that is different from the first general trajectory, the third conductor following a third general trajectory that is different from the first and second general trajectories, the first, second, and third conductors together forming a general shape of a surface; a second structure disposed adjacent to the first structure and including a magnet that emanates a magnetic field, the magnet having at least one of its magnetic poles facing the surface; a pinion gear coupled to the second structure; an inner shaft coupled to the pinion gear; an outer shaft having an inner surface and surrounding at least a portion of the inner shaft, the outer shaft having an annular gear formed on at least a portion of the inner surface, the annular gear meshing with the pinion gear; and a control coupled to the first, second, and third conductors and configured to individually control current magnitudes and directions in each of the first, second, and third conductors to thereby control the relative movement between the first structure and the second structure, wherein the control is configured to independently control i) the current magnitudes and directions in each of the first, second, and third conductors and ii) frequencies of the currents supplied to each of the first, second, and third conductors to thereby control: i) a rotational speed of the pinion gear, whereby a rotational speed and direction of the outer shaft is controlled, and ii) speed and direction of an orbit of the pinion gear, relative to the annular gear, whereby a rotational speed and direction of the inner shaft is controlled, and wherein a Lorentz force affects relative movement between the first structure and the second structure when the magnetic field that emanates from the at least one magnetic pole interacts with electrical currents within any of the electrical conductors. a first structure comprising a first conductor, a second conductor, and a third conductor, the first conductor following a first general trajectory, the second conductor following a second general trajectory that is different from the first general trajectory, the third conductor following a third general trajectory that is different from the first and second general trajectories, the first, second, and third conductors together forming a general shape of a surface; a second structure disposed adjacent to the first structure and including a magnet that emanates a magnetic field, the magnet having at least one of its magnetic poles facing the surface; a pinion gear coupled to the second structure; an inner shaft coupled to the pinion gear; an outer shaft having an inner surface and surrounding at least a portion of the inner shaft, the outer shaft having an annular gear formed on at least a portion of the inner surface, the annular gear meshing with the pinion gear; and a control coupled to the first, second, and third conductors and configured to individually control current magnitudes and directions in each of the first, second, and third conductors to thereby control the relative movement between the first structure and the second structure, wherein the control is configured to independently control i) the current magnitudes and directions in each of the first, second, and third conductors and ii) frequencies of the currents supplied to each of the first, second, and third conductors to thereby control: i) a rotational speed of the pinion gear, whereby a rotational speed and direction of the outer shaft is controlled, and ii) speed and direction of an orbit of the pinion gear, relative to the annular gear, whereby a rotational speed and direction of the inner shaft is controlled, and i) a rotational speed of the pinion gear, whereby a rotational speed and direction of the outer shaft is controlled, and ii) speed and direction of an orbit of the pinion gear, relative to the annular gear, whereby a rotational speed and direction of the inner shaft is controlled, and wherein a Lorentz force affects relative movement between the first structure and the second structure when the magnetic field that emanates from the at least one magnetic pole interacts with electrical currents within any of the electrical conductors.