A rotary member assembly for a turbomachine operating with a fluid stream, the rotary member assembly comprising: a rotor wheel having a peripheral rim and configured to rotate around a rotation axis, wherein the rotor wheel has a plurality of circumferentially spaced female dovetail slots about the rim of the rotor wheel; and a plurality of blades, configured to intercept the fluid stream while the turbomachine operates, wherein each blade comprises a male dovetail, shaped so as to fit with a corresponding one of the female dovetail slots of the rotor wheel along an insertion direction, an airfoil, having a first end, connected to the male dovetail, and a second end, and an airfoil shroud fixed to the second end of the airfoil; wherein the rotary machine assembly is characterized in that each of the female dovetail slots is shaped so that the insertion direction of each corresponding male dovetail is convergent with the rotation axis of the rotor wheel, so as to form with it an insertion convergence angle ( α), so that the blade moves towards a closer position with respect to the rotor axis during the insertion, and in that, when the male dovetail of each blade is inserted in the corresponding female dovetail slots, the airfoil shrouds of each blade contact each other. a rotor wheel having a peripheral rim and configured to rotate around a rotation axis, wherein the rotor wheel has a plurality of circumferentially spaced female dovetail slots about the rim of the rotor wheel; and having a peripheral rim and configured to rotate around a rotation axis, wherein the rotor wheel has a plurality of circumferentially spaced female dovetail slots about the rim of the rotor wheel; and a plurality of blades, configured to intercept the fluid stream while the turbomachine operates, wherein each blade comprises a male dovetail, shaped so as to fit with a corresponding one of the female dovetail slots of the rotor wheel along an insertion direction, an airfoil, having a first end, connected to the male dovetail, and a second end, and an airfoil shroud fixed to the second end of the airfoil; configured to intercept the fluid stream while the turbomachine operates, wherein each blade comprises a male dovetail, shaped so as to fit with a corresponding one of the female dovetail slots of the rotor wheel along an insertion direction, an airfoil, having a first end, connected to the male dovetail, and a second end, and an airfoil shroud fixed to the second end of the airfoil; a male dovetail, shaped so as to fit with a corresponding one of the female dovetail slots of the rotor wheel along an insertion direction, an airfoil, having a first end, connected to the male dovetail, and a second end, and an airfoil shroud fixed to the second end of the airfoil; wherein the rotary machine assembly is characterized in that each of the female dovetail slots is shaped so that the insertion direction of each corresponding male dovetail is convergent with the rotation axis of the rotor wheel, so as to form with it an insertion convergence angle ( α), so that the blade moves towards a closer position with respect to the rotor axis during the insertion, and in that, when the male dovetail of each blade is inserted in the corresponding female dovetail slots, the airfoil shrouds of each blade contact each other.