A member for guiding an element mobile in oscillation or rotation is presented. The member has a body made of a hardened metallic material, provided with a bore for assembling the mobile element, having cavities that are distributed discontinuously in the bore and capable of acting as grease reserves, and having optional grease supply. In the bore are defined a bearing surface outside of the cavities and the grease supply, and a non-bearing surface in the cavities and the grease supply. The bore includes at least one zone with: cavities having a depth of between 2 and 5 mm, and a quantity of grease in the cavities per bearing surface of between 0.05 and 0.3 g/cm2. A mechanical system having such a member and a method for manufacturing such a member is also contemplated.