A multi-degree-of-freedom electromagnetic machine, comprising: a stator comprising a first stator conductor, a second stator conductor, and a third stator conductor, the first stator conductor following a first general trajectory, the second stator conductor following a second general trajectory that is different from the first general trajectory, the third stator conductor following a third general trajectory that is different from the first and second general trajectories, the first stator conductor, second stator conductor, and third stator conductor together forming a general shape of a sphere and being oriented at predetermined angles relative to each other, wherein trajectory means a geometric path traced by a conductor over a predefined length that is designed to contribute to generation of a Lorentz force; an armature disposed adjacent to, and movable relative to, the stator, the armature including an armature conductor and a plurality of magnets to provide a degree of position control of the armature, each magnet having at least one of its magnetic poles facing the sphere, the armature conductor encircling a portion of the stator; and a control coupled to the first, second, and third stator conductors, the control configured to: (i) supply direct current to the first, second, and third stator conductors, and (ii) selectively amplitude modulate the direct current supplied to one or more of the first, second, and third stator conductors, to thereby electromagnetically couple, via transformer action, the armature conductor to the one or more first, second, and third stator conductors, wherein, for a given amplitude magnitude of the direct current, the armature conductor is electromagnetically coupled more strongly to the stator conductors that are amplitude modulated at a higher modulation frequency, to provide an additional degree of position control of the armature to the said position control of the armature by the magnets. a stator comprising a first stator conductor, a second stator conductor, and a third stator conductor, the first stator conductor following a first general trajectory, the second stator conductor following a second general trajectory that is different from the first general trajectory, the third stator conductor following a third general trajectory that is different from the first and second general trajectories, the first stator conductor, second stator conductor, and third stator conductor together forming a general shape of a sphere and being oriented at predetermined angles relative to each other, wherein trajectory means a geometric path traced by a conductor over a predefined length that is designed to contribute to generation of a Lorentz force; an armature disposed adjacent to, and movable relative to, the stator, the armature including an armature conductor and a plurality of magnets to provide a degree of position control of the armature, each magnet having at least one of its magnetic poles facing the sphere, the armature conductor encircling a portion of the stator; and a control coupled to the first, second, and third stator conductors, the control configured to: (i) supply direct current to the first, second, and third stator conductors, and (ii) selectively amplitude modulate the direct current supplied to one or more of the first, second, and third stator conductors, to thereby electromagnetically couple, via transformer action, the armature conductor to the one or more first, second, and third stator conductors, wherein, for a given amplitude magnitude of the direct current, the armature conductor is electromagnetically coupled more strongly to the stator conductors that are amplitude modulated at a higher modulation frequency, to provide an additional degree of position control of the armature to the said position control of the armature by the magnets. (i) supply direct current to the first, second, and third stator conductors, and (ii) selectively amplitude modulate the direct current supplied to one or more of the first, second, and third stator conductors, to thereby electromagnetically couple, via transformer action, the armature conductor to the one or more first, second, and third stator conductors, wherein, for a given amplitude magnitude of the direct current, the armature conductor is electromagnetically coupled more strongly to the stator conductors that are amplitude modulated at a higher modulation frequency, to provide an additional degree of position control of the armature to the said position control of the armature by the magnets.