Time to continue the general lesson in odd bits of pterosaurian anatomy and here we have a real specialisation: the notarium. This is unique to larger pterodactyloids and is essentially a fusion of the vertebrae that make up the spine where the shoulder articulates with the back to produce something that looks rather like a pelvis at the front. It has some interesting connotations for pterosaur evolution and ecology, and that of the development of bone in general.
The notarium turns up in all the pterodactyloid lineages except the basal ctenochasmatids (which include Pterodactylus) or any of the rhamphorhynchoids. It does therefore appear to have evolved early on in pterodactyloid evolution and been present in all but the most basal clade (and several other individual taxa from around the pterodactyloid tree it should be added), and probably not coincidentally appears just as pterodactyloids (and by extension pterosaurs as a whole given the relatively small size of the rhamphorhynchoids) started to get big.
The notarium consists of a number of dorsal vertebrae fused together into a single functional unit with both the actual centra (the big bit at the base of a vertebra) and the neural spines (the tall bits on top that you can feel on your own back when you bend forwards) being fused. The neural spines don’t always ‘fill in the gaps’ though in the way that the pelvis generally does, so you do see spaces remaining between them.
Having taken a very brief glance at the pterosaur literature, no one seems to have bothered cataloguing how may vertebrae make up the notarium except in a few specific species but in my experience it’s typically over five.
Apart from the basic morphology of a notarium being just a bunch of vertebrae welded together they typically have a socket sunk into the neural spines for the scapula (shoulder blade) to fit into. This is because the basic function of the notarium is to provide a strong platform for flight. With big pterosaurs (and as noted, only the big pterodactyloids have a notarium) they need a secure base for anchoring the flight muscles to power the flight stroke (and pterosaurs, unlike birds have a quite a lot of muscles mass on their shoulders for the upstroke) and to anchor the scapula itself. It might also serve to support forces going through it with the kind of quadrupedal launch hypothesised by Mike Habib. The notarium then as essentially an anterior pelvis makes a lot of sense mechanically.
The interrelationships of the various pterosaur clades are somewhere between complex and controversial depending on exactly your view, and even while some clades remain pretty fixed, different species can flit between groups causing problems. While all pterodactyloid clades apart from the ctenochasmatids (assuming you even think they are a true clade) have taxa in them with notaria, several species definitively do not have them (we have a good skeleton and there’s no notarium) and others may not (we just don’t know as we don’t have a complete enough skeleton). The short version is that it tends to be absent (or apparently absent) in relatively small taxa (like Tapejara and Germanodactylus) and then present on the big ones. It’s not present in juveniles either, or of course in the relatively small rhamphorhynchoids.
The obvious conclusion then is that this has evolved multiple times in multiple clades because it is a functional necessity of large size in pterosaurs (or perhaps flying animals in general since we don’t have any really giant birds or bats to compare to them). The notarium provided a stable base for the attachment of flight muscles and to anchor the scapula for both flying and launching into the air.