So, two questions here about the Dinobots, as shown in Age of Extinction:
Why were the Dinobots so much larger than the Autobots? They were nearly five times the size of Optimus Prime, and Prime himself is almost 1.5 times the size of the rest of the Autobots. Why were they so gigantic? Is it something referring back to the comic/anime versions?
Why do they have alt-modes as dinosaurs? All Transformers scan surrounding vehicles to gain their alt-mode. Where did the Dinobots acquire theirs?
Historically, the Dinobots were big compared to the average Transformer, and even to Optimus Prime.
Optimus, in turn, was larger than most of the other Transformers.
The new Dinobots of Age of Extinction seem to take at least a slight cue from the original Knights of Cybertron of the IDW comic continuity, where they were some of the original Transformers. In the movie continuity, the Knights were charged with protecting the Allspark. I cannot, however, find any reference to them being exceptionally larger than the average Transformer.
Why, exactly, did these new Legendary Knights transform into Dinobots? This was a little cluttered, glossed over and sort of only inferred.
In the opening scene, the "Creator" ships are shown scanning the Earth and sending out Seeds - Cyberforming everything they come across - including Dinosaurs.
Cut to millions of years later. Lockdown is in possession of a ship originally owned/piloted by (some of) the Legendary Knights, where he has (at least some of) them locked up. These Knights are the Dinobots.
There are three somewhat-logical possibilities here (well, as far as any logic goes in the live-action movies).
While I can't comment on the movie version of the Dinobots, their original origin came from the Transformers cartoon, where some dinosaur bones were found sealed away in the mountain that the Ark had crashed into. The Autobot medic, Ratchet, decided to try and put some new robots together based on the shapes of the dinosaur remains that were found. They were supposed to be the "answer" to the Decepticons' newest creation at the time, the Constructicons.
At first, Grimlock was a bit belligerent and chafed under Optimus Prime's leadership. In later seasons of the cartoon however, Grimlock mellows out considerably and ends up more as comic relief in the show in the vein of "Me Grimlock (insert joke here)".
Dinobots have always been historical depict as bigger than the average Transformers (both Autobots and Decepticons) although the animation errors in the G1 cartoon often cause inconsistence with the size of the Dinobots: in some scenes the Dinobots looked bigger, in some scenes smaller. This kind of errors were frequently in the G1 cartoon, keep in mind that american cartoons in the 80s were made by underpayed Koreans treated as slaves.
Most of the continuities and sagas that came after the cartoon have followed the idea of depicting the Dinobots as bigger than the other Transformers (look at Transformers: War for Cybertron/Fall of Cybertron). The movie just reprised the idea and made the Dinobots even bigger in order to allow the Autobots to ride them and to express their might better.
The Dinobots in the movie have dinosaur forms because they were among the Legendary Knights, the first Transformers made and, as we see at the beginning of the movie, the Quintessons/Creators terraformed the Earth an eon ago and mutated the dinosaurs into the Dinobots. The movie version of the Dinobots are the result of the cyberforming of the Earth's dinosaurs.
Quite simply, in one of the stories, Shockwave, the creator of the bridge to Earth (for the Decepticons) explored Earth, after the seeds were placed,he took studies off the designs of the dinosaurs encased in transformium, when he returned to Cybertron, he captured Grimlock and his team, and used them as science experiments before they broke out.
The tests damaged their communication systems giving them little to no speech ability. Optimus and the Dinobots used to be the same size, but Shockwave enlargened the Dinobots to represent the actual size of a dinosaur. Thus the creation of the Dinobots.
Prime is larger because the Matrix of Leadership makes him the perfect leader mentally and physically, the Dinobots are bigger because dinosaurs are bigger than cars.
They turn into dinosaurs because:
G1: volcanic activity near Autobot HQ revealed a cave filled with ancient fossilized Dino bones. Fascinated by this, Wheeljack thought "hey, wouldn't it'd be great if some dinosaurs worked for us!" So then Prime decided to Ok the project of building them.(Grimloc, Sludge, Slag first/ Snarl and Swoop came later)
TF4: I'm guessing the Quintessons modeled them after the organic life forms they killed to get the "transformium".
