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As you can see from the image above, this UV is composed by 4 subparts, 4 rectangles. Each of them has exactly the same vertex number and the topology quite equal compared to the others so I could make them to perfectly overlap one over the other. Is there a way-out to do this automatically instead of repositioning all these vertexes one by one?
Here the file blend
Thank you!
Your 3D object looks like each arm is shaped irregular, meaning that the edge lengths won't be the same, meaning that the UVMap cannot be the same, if you want a map without stretching. However, if you just want each point to be identical, you can indeed achieve this by unwrapping in a strict order.
First, select one of the corner faces (remember which one!) on one of the four islands, and press L when the mouse cursor is over the matching island. Choose Seams as the limiting factor. Then, reset the UVMap. This will take each quad and set the UV coordinates to (0,0), (0,1), (1,0) and (1,1), no matter what the shape in 3D is.
Next, use Follow Active Quads as the unwrapping method. The active quad is still the one which was selected first, and its current UV position serves as the starting point for the follow active quad unwrap.
Next, select the corresponding face and island from the three other shells. I'm marking them in the GIF here before I unwrap the rest. This is important so the orientation of the resulting UV Map is identical to the others. The four resulting UV islands will have completely identical vertex positions, but, as stated initially, stretching for sure.
If stretching is not desired, all you can do is match up the boundaries of your map by snapping vertices. Snapping to vertices also works for scaling, as you can see in this little GIF here:
You can use this technique in tandem with the answers previously given here.
If I understand your question, there is a way you can perfectly snap multiple uv's to the same spot for perfect manipulation, which i figured out with some inspiration while trying to figure out this very same issue.
Using the 3D cursor (or in our case, the 2D cursor) we'll snap all of our desired selections to a single point. Here's my example, where you can see my similar UV's below:
Next, we'll use Blender's fancy-shmantsy cursor-snapping tools!
You can access Blender's Cursor-snapping tools using the hotkey ⇧ Shift + S or through the UV dropdown right next to the image-browser
Finally, we can get to the goodies! When we try snapping with the method presented above, (the method is Snapping > Selected to Cursor [Offset]) Each UV will be moved by its exact centerpoint, landing directly on top of the 2D Cursor! (Brilliant, right? Don't you just love inspiration?) Inspiring examples below:
Important Note: Make absolutely certain that you don't choose the default Selected to cursor option, and instead choose the Selected to Cursor (Offset) option! That Offset is your lifeblood, my young padawan! If you forget to choose the one with offset, your UV will collapse into an infinitesimally small point and cease to be recognizable as anything other than the essence and epitome of your sheer and utter failure to read a storming stack-guide. It is entirely unrecoverable, regardless of how many wanton tears you shed for it.
L, ⇧ Shift + S > 7
L while hovering over the desired UV to SELECT, and then you SPAM-SPAM-SPAM that ⇧ Shift + S > 7 combo, (pressing 7 is just a faster way of clicking that little Selected to cursor (Offset) thingy, allowing you to bypass the fiddling trouble with the mouse.
