Tyrannosaurus rex is often distinguished from other theropod dinosaurs as having had "binocular vision" (a perceptual capability sometimes oversimplified to be either present or absent). Moreover, binocular vision is often assumed to provide the ability to "see in depth".

As I have studied human visual perception, and in particular this notion of "seeing in depth", I was drawn towards applying what we know about binocular vision in extant reptiles and birds towards several theropod taxa, including T. rex. You can read more about the results here.

At the "100 Years of Tyrannosaurus rex" symposium, I presented a talk called "Rex, sit." describing how this dinosaur might have descended to a resting position and stood up again. Sitting likely involved settling its weight slghtly backward (much as we would if descending first to a squat then resting back onto our posterior).

Getting up again was a different matter, and might well have involved using the forelimbs to stabilize the body as it was shifting its weight forward again. In addition to the talk slides, you can read more here.

The pubic boot has been proposed to bear the weight of this giant. Once sitting down, the hindlimbs no longer bore the weight of the body, and were free to assume any of a number of positions.