The Origins of T-Rex's No Lips

In the past, people have reconstructed a lot of dinosaurs that look sort of like crocodiles with no lips. We were curious if there was any actual evidence to support that and so we decided to try and investigate it. Jurassic Park is itself kind of funny because at the time it came out they tried to do their best to make things very accurate - but T-Rex had no lips. So why did this come about? Was this just because people wanted to create a fearsome image for dinosaurs and that fitted the bill? Or did they really have reason to suspect that because crocodiles have their teeth on show, that's probably what T-Rex did?