(1) Background: The objective of this study was to develop the field of mechanisms that generate aesthetic curves, as they can be useful in designing machines for the manufacture of highly beautiful products. We started from the image of the Flower of Life and we set out to build mechanisms in the field of mechanical engineering that can generate this image. (2) Methods: First, we studied in detail the geometry of the figure. Secondly, based on the mathematical considerations, we made the synthesis of a mechanism able to trace this image, based on the Geneva mechanism with intermittent movement. We completed this mechanism with other kinematic chains, so we generated the proposed curve. Next, we made the synthesis of the second generating mechanism. This was a gear mechanism with compound profiles to which we added additional kinematic chains to generate the Flower of Life curve. Further on, kinematics was applied to confirm the drawing of the curves with the closed loop method. (3) Results: The results obtained following the study and presented in the paper show that the two created mechanisms generate images (trajectories) identical to the Flower of Life. Moreover, other images similar to the Flower of Life, with great artistic potential, were obtained. (4) Conclusions: The aim of the study was achieved, the authors proposed two new mechanisms which generate a highly aesthetic design image—the “Flower of Life”. The paper provides all the notions of structure and kinematics that are necessary to calculate the mechanisms and also analyzes other kinematic possibilities of the created mechanisms. The paper contributes to the development of a new field in the Theory of Mechanisms: generating aesthetic curves.