Abstract: The machine comprises a shaft mounted in a housing to rotate about a horizontal axis and arranged to carry the body of revolution in a concentric position. The shaft is also capable of oscillating in the housing about a vertical axis intersecting the horizontal axis near to an end of the shaft. An elongated indicator member is mounted in the axial extension of the shaft by a ball articulation. A measuring scale is mounted on the housing adjacent the free end of the indicator member. A deviating element is adapted, in the course of rotation of the shaft, to come momentarily in contact with the indicator member so as to deviate the indicator member relative to the scale to an extent which is a function of the magnitude of the unbalance of the body of revolution. An arrangement is combined with the ball articulation for ensuring the remanence of the deviation. The deviating element is in the form of a cam rotatable by a driving motor about an axis parallel to the axis of the shaft.