The carriage of a digital document reader is shifted by means of a pair of worms rotatable in the frame and engaging two nuts borne by the carriage. The worms are rotated simultaneously, e.g. by a single stepping motor and a toothed belt engaging a pulley or by two separate stepping motors. For the purpose of reducing inertia, each worm is formed together with the driving pulley by moulding a layer of plastics material on a metal core tube which is formed with a shallow groove of coarse pitch to anchor the plastics layer. Each nut, also of plastics material, is formed with a series of axial notches which define an equal number of elastic sectors which allow any play on the worm due to wear to be taken up.