With the help of many posts in different discussions, I finally found a way to set my chain correctly :
In short, I added "associate parameters" to all the varied dimension of the individuals links so that I can call them in the relations.
I don't understand why but in relations at assembly level, calling the varied dimension with the parameter (w01:FID_74=width_main_link) works fine but calling the same dimension with the varied dimension (d0:6=width_main_link) leads to problems at a higher level assembly.
With this set up, I can assemble as many chains as necessary, all with different dimensions in a top level assembly and it works fine every time.
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so I am done for what I wanted to do, even if I still don't really understand why it works now ...
If anybody knows I would be glad to hear.