A method for assembling according to a common axis a first and a second half-ring gears (7a, 7b) manufactured according to a pre-established manufacturing drawing, characterized in that, to align the teeth along said common axis, the method comprises steps wherein: - an angular positioning pin is provided for the half-ring gears in relation to each other, the pin to be received in first and second respective holes of the said first and second half-ring gears, must each have a final cross-section adapted to the pin; - with reference to the predetermined manufacturing drawing, the first and second holes (21a,21b) are drilled such that the first hole has a first cross-section that is smaller than the said final cross-section on the first half-ring gear and that the second hole has a second equal section to the said final cross-section on the second half-ring gear, - for each half-ring gear: - several teeth (13a1,13a2...) equidistant from each other are indexed or identified, with a first tooth (13a1) which is closer to the hole (21a, 21b) of its respective half-ring gear than the other teeth, to define a common index mark to both half-ring gears; - on each tooth identified, the multidimensional coordinates (x1, y1, z1), with respect to the centre of the half-ring gear, of a reference point (27a3) are determined; - the determined multidimensional coordinates (x1, y1, z1) are compared with theoretical coordinates (x2, y2, z2) of these same points from the pre-established manufacturing drawing; - a difference is recorded between the determined coordinates and the theoretical coordinates for defining a positional deviation of said points; - the first hole is re-drilled to said final cross-section, positioning it based on the positional deviations of the reference points of each half-ring gear such that, during assembly, each tooth indexed to the first half-ring gear facing a tooth indexed from the second half-ring gear, parallel to said axis, according to the common index mark, - and the first and second half-ring gears (7a,7b) are assembled by tightly engaging said angular positioning pin in the first and second holes, and by a tight fit of the half-ring gears together. - an angular positioning pin is provided for the half-ring gears in relation to each other, the pin to be received in first and second respective holes of the said first and second half-ring gears, must each have a final cross-section adapted to the pin; - with reference to the predetermined manufacturing drawing, the first and second holes (21a,21b) are drilled such that the first hole has a first cross-section that is smaller than the said final cross-section on the first half-ring gear and that the second hole has a second equal section to the said final cross-section on the second half-ring gear, - for each half-ring gear: - several teeth (13a1,13a2...) equidistant from each other are indexed or identified, with a first tooth (13a1) which is closer to the hole (21a, 21b) of its respective half-ring gear than the other teeth, to define a common index mark to both half-ring gears; - on each tooth identified, the multidimensional coordinates (x1, y1, z1), with respect to the centre of the half-ring gear, of a reference point (27a3) are determined; - the determined multidimensional coordinates (x1, y1, z1) are compared with theoretical coordinates (x2, y2, z2) of these same points from the pre-established manufacturing drawing; - a difference is recorded between the determined coordinates and the theoretical coordinates for defining a positional deviation of said points; - several teeth (13a1,13a2...) equidistant from each other are indexed or identified, with a first tooth (13a1) which is closer to the hole (21a, 21b) of its respective half-ring gear than the other teeth, to define a common index mark to both half-ring gears; - on each tooth identified, the multidimensional coordinates (x1, y1, z1), with respect to the centre of the half-ring gear, of a reference point (27a3) are determined; - the determined multidimensional coordinates (x1, y1, z1) are compared with theoretical coordinates (x2, y2, z2) of these same points from the pre-established manufacturing drawing; - a difference is recorded between the determined coordinates and the theoretical coordinates for defining a positional deviation of said points; - the first hole is re-drilled to said final cross-section, positioning it based on the positional deviations of the reference points of each half-ring gear such that, during assembly, each tooth indexed to the first half-ring gear facing a tooth indexed from the second half-ring gear, parallel to said axis, according to the common index mark, - and the first and second half-ring gears (7a,7b) are assembled by tightly engaging said angular positioning pin in the first and second holes, and by a tight fit of the half-ring gears together.