The object of research is perspective mandrels with the pince fendues used for installing blanks such as rings, bushings and cups. These machine accessories are both high-precision and wide-range, but in previous articles it was found that there are reserves for expanding their technological capabilities. It was found that the shape and size of the articulation are key parameters and they significantly affect the allowable compression of the collet and its strength. Therefore, in this article, the finite element method solves the problem of determining the rational shape and parameters of the articulation to increase the compression of the collet while maintaining strength. Based on the manufacturability of the split collet articulations, various forms of articulations are considered by the method of iteration from the traditional rectangular to the idealistic semicircular. The configuration of the articulation shape, the chamfer angle that bevels a right angle in a traditional design, and the chamfer size varied. As a result of calculations, the maximum stresses and displacement of the ends of the articulation, which provides its compression were determined. This compression allows increasing the base diameter of the collet when loading, and the stresses ensure the strength of the collet. Two rational forms of collet articulation that have practical interest are defined. The first form, which is the easiest to manufacture, has a 45° chamfer and, with equal strength, provides almost 15 % more compression of the collet than for a traditional design. The second form, which is more difficult to manufacture, has chamfers of 30° and 60° and with equal strength provides 30 % more compression of the collet.