for the bowl construction:
you will have to use a mould. In order to design and make it, you should first take some critical decisions.
First, notice the differences between the oud bowl shape (all ribs alike, the longitudinal section is identical to the soundboard’s outlines) and the baglamas / bouzouki / mandolin bowl: different shapes, due to different longitudinal section – outline’s traces.
Most important is to understand how the ribs are meant to hold together, while still having to transform the longitudinal section curve to the symmetrical sounborad’s outlines.
This is a critical as much as a difficult task, because the outermost ribs that support the soundboard have to be shaped and curved following different properties to each side : “internally” should follow the trace of the precedent rib, whilst “ externally” should have to be trimmed flush to provide the flat soundboard outlines.
This is the reason that these outermost ribs are generally made wider, providing enough surface to shape accordingly. But this practice creates the two next issues:
1) the mould sides to the soundboard outline edges (exactly at the areas that will be covered by the outermost ribs) must be absolutely flat crosswise (the wooden rib cannot be curved in two directions)
2) This is quite important: you need to determine the
"convergence point". It is the point that all ribs’ edges meet at the back of the bowl. Often, there are more than one of these “points”, in that case usually three: one for the central area ribs and (one + one) for each side (see the last picture attached).
……
I didn’t have time to search photos etc. Instead, I found a few videos that may help even better at this point:
Mandolin bowl construction
https://www.youtube.com/watch?v=45tqCDxOeaM (part 2)
https://www.youtube.com/watch?v=ObKHrcG3MfA (part 3) at 0:31.... notice the two outermost-wide staves
Here is the YouTube channel of a fellow amateur luthier (member here) about bouzouki construction with many helpful videos
https://www.youtube.com/user/TheBouzoukimaker/videos?view=0&sort=p&shelf_id=2watch this one
https://www.youtube.com/watch?v=UMiNrQfyMQcat 10:30... wide side-ribs
here are some photos of my first (bouzouki) bowl with a single "convergence point":
not a very nice work, but at the end this wide curved piece (I don't know the term, I will search for it) covers everything
and this is my first attempt (prior to actually working on the mould) to check the matching, point etc., maybe something like that will also help you
this is a 3 points mould (design of another fellow member): extending the rib lines you can "see" that clearly: the 7 "central" ribs will meet downwards, quite near to the "soundboard level line" at the bottom.
in this latter image you can also see clearly the "flat crosswise" surface of the outermost wide ribs at both sides.
Also notice this:
the number of the ribs is odd. It is easier to make it this way, achieving a good fit for the first (central) rib which later on will be used as a "guide" for the next and the latter for the next...and so on.
Happy homework!

I don't have a descent internet connection at home, so most likely I will not get in touch until after the weekend.