Fiabilitate si Durabilitate - Fiability & Durability No 1/ 2020 Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X 28 STUDY OF A MECHANISM GENERATING DUPLICATRIX CUBIC Prof. Emeritus PhD. Iulian POPESCU, University of Craiova, member of the Romanian Academy of Technical Sciences Prof. PhD. Liliana LUCA, University Constantin Brancusi of Targu-Jiu Assoc. Prof. PhD. Mirela CHERCIU, University of Craiova ABSTRACT. The ancient problem of the duplication of the cube, solved only in 1837, led to a mechanism generating this curve, duplicatrix cubic, given in the literature. In this paper the mechanism is structurally analyzed and the generated trajectories are studied . The closed loop method was used. The desired curve resulted, then the initial data of the mechanism were modified, thus generating a wide range of other curves. KEYWORDS : mechanism , duplicatrix cubic, different curves generated 1. INTRODUCTION A legend says that due to a plague from 430 BC. Chr., the greeks consulted the oracle of Delos, concluding that the volume of the altar where the oracle was, should be doubled. That is, having a cube with the side "a", its volume is , and doubled means 2 , so the side of the doubled cube being x, results , i.e. . The problem was to find the segment x only with the ruler and the compass. Many attempts have been made, the solution being given by the frenchman Wantzel in 1837, who proved that this problem cannot be solved only with the ruler and the compass. Ferreol indicates the polar and cartesian equations of the duplicatrix curve , [1] . Some geometric aspects regarding this curve appear in Sendai 's work , [2 ]. Other details are given by Masia in [3 ]. The problem is also mentioned in [4]. In the paper [5], Artobolevskii gives a mechanism generating this cubic curve, a mechanism studied below. 2. THE MECHANISM STUDIED Figure 1 shows the kinematic diagram of the mechanism according to Artobolevskii [5 ]. Fig. 1. The mechanism studied Structurally, the mechanism is analyzed and shown in figures 2 and 3 . The