The invention relates to a cylindrical element connection device for connecting at least one pair of cylindrical elements with micrometric sections. The cylindrical element connection device includes a cutting means for cutting the tail end of the cylindrical element at a cutting step, a polishing means for polishing the cut tail end of the cylindrical element at a polishing step, a connection means for connecting at least two cut polished tail ends at a connection step, and a fixing means for fixing the cylinderical element, wherein the fixing means is formed by at least one single-piece part, which internally includes: at least one longitudinal hole having a cross-section complementary to the outer cross-section of the cylindrical element, and two slots for defining the fixing part and the movable part of the fixing means, wherein one of the slots is located in a longitudinal plane, and contains the axis through which the longitudinal hole passes and the other slot defines the clearance of the movable part; and the fixing means further includes a cutting plane perpendicular to the longitudinal hole.