“…Later, they [7] investigated the deflections of a ring gear by finite element (FE) method and theoretical approach, respectively. Satoshi ODA et al [8] applied the FE method to study the root stress and the rim deformation of a thin-rimmed spur ring gear supported by pins. Abousleiman and Velex [9] developed a hybrid 3D finite element/lumped parameter model to analyze the quasi-static and dynamic properties of planetary/epicyclic gear sets, where the effect of a flexible ring gear was taken into account by using the beam elements for simple structures and the 3D brick elements for complex geometries.…”