We aim to develop an X–Y linear synchronous motor where 360° rotational motion around the Z-axis is possible. We considered “rotational force characteristics around the Z-axis that use alternating magnetic fields orthogonal to the X–Y linear synchronous motor.” The stator of the linear synchronous motor has two pairs of three-phase field windings positioned orthogonally to each other. A two-pole permanent magnet and an iron core comprise the rotor (mobile element). We demonstrated the rotating magnetic field around the Z-axis generated by an alternating magnetic field intersecting on a plane. Further, we used magnetic field analysis to evaluate the rotational force characteristics working on the rotor. We also considered the impact of the position of the rotor magnetic pole on the output characteristics. We experimented with a prototype to evaluate the validity of the analytical result. The experimental result showed that a rotational drive force could be generated 360° around the Z-axis.