Peters (2000, 2010, 2011) described PILs (Parallel Interphalangeal Lines) that can be drawn through any tetrapod manus or pes. Primitively three sets are present, medial, transverse and lateral. The lines indicate phalanges that act in sets while grasping (flexion) or during locomotion (extension). As digits are reduced, as in theropod or horse feet, the PILs tend to merge.
Figure 1. On left: Tylosaurus pelvis with an anteriorly-leaning ilium. Note the acetabulum is not facing the reader. This is the medial view of the pelvis. In the middle, the two sacral vertebrae of Tylosaurus. On right: Tylosaurus forelimb paddle. Note the PILs are not continuous but stop at digit 2, the main spar of this aquatic “wing”.
Tetrapods with flippers or paddles present a special case,
but even then, PILs are present. Recently I took a look at the manus of Tylosaurus and noticed that the PILs were not continuous from side to side, as they are typically (but not universally) in terrestrial tetrapods. With Tylosaurus the transverse set was not apparent. The medial set extended to digit 2. So did the lateral set. Digit 2 in the wing-like paddle of Tylosaurus is analogous to the main wing spar of an airplane wing. And that spar is not supposed to bend. Apparently in this case, the absence of transverse PILs that would have allowed flexion and extension showed that the flipper was most efficient when it did not flex and extend much.
In most tetrapods the ilium extends posteriorly. In many the ilium also extends anteriorly, creating a long lateral plate for the attachment of many large muscles. In aquatic forms the ilium is generally reduced. As you might expect, in some taxa that also reduces the number of sacral vertebrae. In others, oddly, the number of sacrals can double to four. In many aquatic taxa, and a few arboreal forms, the ilium has no posterior process, but extends dorsally. Rarely, as in Tylosaurus (Fig. 1) the ilium tilts anteriorly. Only the presence of the laterally-facing acetabulum assures you that this orientation is correct. I’m not sure why this is so. That ilium angle is 90º from the scapula angle in a bird, bat or pterosaur, animals that fly through the air and employ the scapula to anchor muscles that raise the wing (the details differ between all three flyers, btw, with birds employing a pulley-like bone to bend the action of a pectoral muscle to aid in wing elevation). Tylosaurus may have had the same problem to overcome, paddle elevation, but used a tall narrow anchor, rather than a low, long anchor to do the job.
Lingham-Soliar (1992) described subaqueous flying in a mosasaur, but concentrated on the pectoral area and forelimb, ignoring the pelvis and hind limb.
Lingham-Soliar T 1992. A new mode of locomotion in mosasaurs: subaquaeous flying in Plioplatecarpus marshii. Journal of Vertebrate Paleontology 12:405-421.
Peters D 2000. Description and interpretation of interphalangeal iines in tetrapods
Peters D 2010. In defence of parallel interphalangeal lines. Historical Biology iFirst article, 2010, 1–6 DOI: 10.1080/08912961003663500
Peters D 2011. A Catalog of Pterosaur Pedes for Trackmaker Identification. Ichnos 18(2):114-141. http://dx.doi.org/10.1080/10420940.2011.573605