A rotary machine assembly for a turbomachine, such as a rotor, having a rotor wheel where a plurality of circumferentially spaced female dovetail slots are obtained. The rotary machine assembly also comprises a plurality of blades. Between each blade and the adjacent one there is an interface angle. Each blade comprises a male dovetail, configured to fit with a corresponding female dovetail slot of the rotor wheel along an insertion direction. The female dovetail slots are shaped so that the insertion direction of each male dovetail is convergent with the rotation axis of the rotor wheel, so as to form with it an insertion angle, so as to insert gradually all the male dovetails into the female dovetail slots and packing them also gradually. A method for assembling a rotary machine assembly, which does not require any specific tool, is also disclosed.