Rectilinear vertical reciprocating movement is transmitted to the needle-holder beam of a needling machine by a crank mechanism preferably comprised of two horizontal auxiliary connecting rods hinged to a support of the beam. The two auxiliary connecting rods are mounted to the two sides of the needle-holder beam and support. Each auxiliary rod includes an end hinged to a related main connecting rod, with the other end being joined to the structure of the machine by a sliding block and two conjugate profiles. One of the profiles is fixed and the other profile is mobile. The profiles form a rolling coupling, so that each sliding block that is hinged to the related ancillary connecting rod slides when the crank mechanism runs between two extreme axial positions. Simultaneously, each profile of the ancillary connecting rod rolls on the fixed conjugate profile to remain constantly in contact therewith, along lines that are always located on the horizontal plane in different vertical contact lines through the center of the main connecting rod small end.