A positioning system used in assembling a scroll-type fluid machine includes a radial thrust mechanism driving motor for turning a radial thrust mechanism in synchronism with rotational phase of a rotary shaft, a vertical pressing mechanism for producing a vertical pressing force for pressing a stationary scroll against a frame, a displacement sensor for measuring horizontal displacements of a stationary scroll retaining mechanism from at least two directions, a first processor for calculating an orbital path of the stationary scroll from obtained measurement values, a second processor for evaluating stability of the orbital path of the stationary scroll based on vertical pressing force data and the orbital path of the stationary scroll, and a third processor for calculating a fixing point on which the stationary scroll is to be fixedly centered with respect to the frame when the orbital path of the stationary scroll is judged to be stable.