A mechanism for converting rotary motion into linear motion includes a rod having a thread or threaded part at its outer peripheral surface, and a holder member on the outer peripheral surface of the rod, rotatable relative to the rod, and axially movable relative to the rod. Rollers are supported rotatably by the holder member and have annular grooves at their outer peripheral surfaces. Each roller is torsionally disposed at an axial angle greater than or equal to a lead angle of the thread with respect to a central axis of the rod. Both ends of the roller shaft are secured to the holder member, and the mechanism has a structure in which a hole having a diameter greater than that of the roller shaft is provided at one end of the holder member and the roller shaft is secured by a roller mounting member.