Spherical electromagnetic machine with two degrees of unconstrained rotational freedom

A spherical electromagnetic machine, comprising:

• a spherical stator body having an outer surface;
• a predetermined number of longitudinal slots (Nlongitude) formed in, and spaced evenly around, the outer surface;
• a predetermined number of latitudinal slots (Nlatitude) formed in, and spaced evenly around, the outer surface;
• a plurality of longitudinal coils wound around the spherical stator body, each longitudinal coil having a portion thereof disposed within a different one of the longitudinal slots;
• a plurality of latitudinal coils wound around the spherical stator body, each latitudinal coil having a portion thereof disposed within a different one of the latitudinal slots;
• a first hemispherical shell rotor mounted for rotation relative to the spherical stator body and spaced apart therefrom, the first hemispherical shell rotor surrounding a portion of a first half of the spherical stator body;
• a first plurality of magnets coupled to an inner surface of the first hemispherical shell rotor and facing the spherical stator body;
• a second hemispherical shell rotor mounted for rotation relative to the spherical stator body and spaced apart therefrom, the second hemispherical shell rotor surrounding a portion of a second half of the spherical stator body;
• a second plurality of magnets coupled to an inner surface of the second hemispherical shell rotor and facing the spherical stator body;
• and
• a gimbal coupled to the spherical body, the first hemispherical shell rotor, and the second hemispherical shell rotor,
• wherein:
• the spherical stator body, the plurality of longitudinal coils, and the plurality of latitudinal coils implement a stator having a predetermined number of poles (P),
• the longitudinal slots are separated from each other by a longitudinal slot pitch angle in radians defined, in radians, as
• π
• *
• P
• 2
• *
• N
• longitude
• ;
• and
• the latitudinal slots are separated from each other by a latitudinal slot pitch angle in radians defined, in radians, as
• π
• *
• P
• 2
• *
• N
• latitude
• .

A spherical electromagnetic machine, comprising:

• a spherical stator body having an outer surface;
• twenty-four longitudinal slots formed in, and spaced evenly around, the outer surface;
• sixteen latitudinal slots formed in, and spaced evenly around, the outer surface;
• a plurality of longitudinal coils wound around the spherical stator body, each longitudinal coil having a portion thereof disposed within a different one of the longitudinal slots;
• a plurality of latitudinal coils wound around the spherical stator body, each latitudinal coil having a portion thereof disposed within a different one of the latitudinal slots;
• a first hemispherical shell rotor mounted for rotation relative to the spherical stator body and spaced apart therefrom, the first hemispherical shell rotor surrounding a portion of a first half of the spherical stator body;
• a first plurality of magnets coupled to an inner surface of the first hemispherical shell rotor and facing the spherical stator body;
• a second hemispherical shell rotor mounted for rotation relative to the spherical stator body and spaced apart therefrom, the second hemispherical shell rotor surrounding a portion of a second half of the spherical stator body;
• a second plurality of magnets coupled to an inner surface of the second hemispherical shell rotor and facing the spherical stator body;
• and
• a gimbal rotationally supporting the spherical stator body, the first hemispherical shell rotor, and the second hemispherical shell rotor,
• wherein:
• the spherical stator body, the plurality of longitudinal coils, and the plurality of latitudinal coils implement a 4-pole stator,
• the longitudinal slots are separated from each other by a longitudinal slot pitch angle of 15-degrees
• (
• π
• 1
• ⁢
• 2
• ⁢
• ⁢
• rad
• )
• ,
• the latitudinal slots are separated from each other by a latitudinal slot pitch angle of 22.5-degree
• (
• π
• 8
• ⁢
• ⁢
• rad
• )
• ,
• and
• a Lorentz force causes movement of the first and second hemispherical shell rotors when electrical current is supplied to one or more of the longitudinal coils or to one or more of the plurality of latitudinal coils.