A rotor-stator structure for electrodynamic machinery is disclosed to, among other things, minimize magnetic flux path lengths and to eliminate back-iron for increasing torque and/or efficiency per unit size (or unit weight) and for reducing manufacturing costs. In one embodiment, an exemplary rotor-stator structure can comprise a shaft defining an axis of rotation, and a rotor on which at least two magnets are mounted on the shaft. The two magnets can be cylindrical or conical magnets having magnetic surfaces that confront air gaps. In some embodiments, substantially straight field pole members can be arranged coaxially and have flux interaction surfaces formed at both ends of those field poles. Those surfaces are located adjacent to the confronting magnetic surfaces to define functioning air gaps, which are generally curved in shape.