First of all, I am only asking this question about true dinosaurs. I am aware of, but not asking about: Pelycosaurs, which lived before the dinosaurs; or Crocodilians, which lived before, with, and after them, etc... It seems that every purely carnivorous dinosaur fossil we have found has been a two-legged Therapod. We have found bipedal herbivorous dinosaurs, but no quadrupedal carnosaurs. Is there a theory as to a reason behind this? Were Therapods simply first and "guarded their niche" successfully, or is there a good reason why a quadrupedal carnosaur wouldn't be successful. Or, is it simply that we haven't found their fossils yet?

This question has been languishing a bit without response, and while I am not an expert on this topic I thought I'd offer a conjecture. I find it really interesting that ALL dinosaur carnivores known to date were bipedal (theropods), and ALL dinosaur herbivores known to date walked on 4 legs. I didn't know that prior to this post, so thanks for raising the question. Much has been written about the supposed advantages for predators who can stand upright and use their forelimbs (arms?) to grab and tear at prey. But by that same reasoning why don't mammal predators like lions and wolves stand on two legs? There really aren't any mammal predators who are bipedal - except man.

I am guessing that the difference is in the nature of the prey. Lions, cheetahs, wolves, etc typically hunt very fast animals like gazelle and deer. They have to run fast enough to catch such prey, and animals with four legs are typically much faster than those with two. But the prey for dinosaurs were much larger, and I suspect slower, so speed of the predator was less important. And to attack a large dinosaur there is advantage in being able to grab and hold on with fore limbs. So perhaps the answer is in the differences between the speed of the prey, and their size? Again, just a guess.

Not ALL herbivores found have been bipedal, that's kind of my point: We have found both quadrupedal & bipedal herbivores, but only bipedal therapod carnivores.

Also, as we have seen from human hunters, bipedal locomotion is more energy efficient over long distances than quadrupedal. Many humans used to (and the Bushmen of the Kalahari still do) hunt by the "persistience" method: they run down (chase) a quadruped until the animal collapses from exhaustion.

I think I found part of your answer, I am providing a link: http://www.vertpaleo.org/source/oldbones/post.cfm/classification-and-turtles

My thoughts are also conjecture.

Look at the tree, dinosaurs diverged from mammals at a common ancestor and it appears that the bipedal dinosaurs diverged again. I think your question is interesting and it makes me ask why we really don't see bipedal mammalian carnivores, the upright posture could have diverged for mammals as well. I suspect it has something to do with protecting the uterus, imagine a pregnant female lion running on her hind legs as a buffalo rammed her gut. Lions also use leverage to pull prey down by the neck and it seems that dinosaur carnivores may have picked their prey apart using their hind legs and teeth (beak) more like a bird of prey, which would leave them far more vulnerable since they have paws rather than talons.

I think it's most likely to do with speed. Although elephants can move fast, they can't actually run. Since in order to run an animal must lift all it's feet off the ground simultaneously and elephants always keep 1 foot on the ground they don't actually run.

So assuming the large 4-legged dinosaurs couldn't run, this would give 2-legged carnivores an advantage in that they would be faster than the 4-legged herbivores. A 4-legged large carnivore would therefore not have this advantage so it's unlikely they would have evolved.

Just my thoughts.