40 could be replaced by a second wheel 43 illustrated in broken lines in the latter case only the locking means 37 of the grinders 34 is necessary the grinders or other contact elements have so far been allowed to take on their working position simply by letting them bear against the rail but it would likewise be possible to force them into relative positions as a function of a predetermined curvature this is what has been done in the embodiment shown in fig8 here the frame 44 carries at each of its ends a grinder having a rigidly fixed position a third grinder 46 is provided between the two grinders 45 this grinder 46 being capable of being raised or lowered at will whereby to obtain with the two first grinders three points of contact located on a curve to be trued two auxiliary motors 47 secured to the frame 44 simultaneously actuate two screws 48 acting on a transverse support 49 of the grinding unit a chain 50 and sprocket wheels 51 ensure even rotation of the two screws and thereby displacement of the support 49 parallel to itself a finger 52 of support 49 and a scale 53 of the frame 44 make it possible with an appropriate division of the scale to determine according to the position of the finger the positive or negative radius of curvature which corresponds to the position of the central grinder 46 the screws 48 in themselves ensure the desired locking action all of the above embodiments have been described with.