Spherical motor is a multi-degrees of freedom actuator which can be rotated in various directions. However, the control method of the completely arbitrary direction was not fully established in the conventional research. Usually, there were limitation of an angle and a problem of accuracy. In this paper, the general theory which generates torque in the arbitrary direction is proposed using a rotor which has arbitrarily arranged magnets, and a stator which has arbitrarily arranged coils. The theory uses the torque map which included the influence of all the magnets of the rotor. Desired torque is generated by resultant of the torque vector which the coils generate. Therefore, strict control is possible however complicated the pattern of the magnetic field is. First, the technique of the torque generation in the arbitrary direction and the creation method of a torque map are explained. Then, the basic experimental result in the case of the spherical motor with the hexahedron based rotor and the octahedron based stator is reported.