[Petrochemicals (OP)]

Now I am not a dinosaur scientist (NON AVIAN BEFORE A HELPFUL SOLE FEELS THE NECESSITY TO HIGHLIGHT THE FACT THAT DINOSAUR ILK DID SURVIVE THE YUKATAN PENINSULA IMPACTOR EVENT AND SUBSEQUENT EXTINCTION PROCESS AS AVIAN DINOSAURS OR "BIRDS" AS THEY ARE CALLED IN COMMON SPEAK)  but the tyrannosaurus Rex has long been mocked for having diddy arms and many theories to why have abounded as to why, such as the theory it is to prevent injury.

It is my theory that the T Rex and his peers developed small arms due to smaller arms facilitating higher speeds when in locomotion, thus natural selection breeding a small limbed machine the retained clawed upper  limbs for grasping prey.

The spinosaurus was known for having large arms, but being an aquatic creature it is known to have had diddy legs and a paddle like tail, having a similar appearance to a duck crocodile, but with arms. It would not have needed to run fast as it was an aquatic creature. The T Rex and friends would have needed to hunt on land, other  creatures, probably quick creatures.

[alancalverd]

A bit like the kangaroo, then.

Evolution generally sheds unnecessary weight.

[Deecart]

It is my theory that the T Rex and his peers developed small arms due to smaller arms facilitating higher speeds when in locomotion, thus natural selection breeding a small limbed machine the retained clawed upper  limbs for grasping prey.

I agree.
You have the same with some lizards that can walk on their legs (without arms) :Big legs and short arms.
Per example : (Frill-Necked Lizard Escapes Python | Wild Monsoon) 

This lizard can also climb (so he also use his short arms for that), but i dont think (because of his weight) the T-Rex could climb.
Therefore, perhaps it is why the arms of the T-Rex are even shorter.
Other difference i noticed between T-Rex and lizards : The length of the tail, shorter for T-Rex (because he probably dont need to climb, and perhaps some big animal would be handicaped with a tail too long for fast running.)
Last but not least : The position of the legs.
They are not positioned like the one of the smaller lizards (lateral direction), but more like a bird (downside direction).
Would be funny if we finaly found that the legs of the T-Rex where in fact positioned like the one of the actual lizards (crocodile etc).

[Alex Dullius Siqueira]

Don't think in the terms of arms like tools as we have and do.
 Arms for dinosaurs were but proto wings.
 Likely it was for it to run faster, though, first comes the fact that it was not suitable for wings.

 So the arms do get smaller for it to run faster, but first and ultimately it happened for he would not be able to fly.

 Flying it's the first intuition for predators, insects, fishes also fly on their environment, if something eats too much it will be grounded, unsuitable for flying, and only after that the natural selection reduced it's arms.
  Not being able to naturally flying, they got extinct as they did not served their purpose by letting the environment and instincts dictate their evolution.
 Very fragile dinosaur compared to the other ones.

 Those still suitable for flying even without wings were able to develop them and also the inverse into arms.
 T-Rex allowed it's arms to be removed nearly entirely for lack of predators.

 Much like chickens, there's a reason why they can't fly, their food it's inside the ground, another predator emerges like eagle and their are doomed as well.

 "Running faster" wouldn't possible keep up with bird like dinosaurs of prey.

 Long years considering that packs of dinosaurs could easily prey on T-Rex, specialty weaker ones.

[Deecart]

T-Rex was not walking very fast accordingly to this last study (but perhaps his tail was usefull to run fast) :

On the big screen, the Tyrannosaurus rex is often depicted as a predator that could easily catch up to a speeding car with a few swift stomps. That's probably because paleontologists had suggested that the T. rex clocked a top speed of 30 miles per hour and a walking speed between 4.5 and 6.7 miles per hour, reports Jeff Spry for SYFY Wire.

Now, researchers from the Netherlands have used computer reconstructions of a T. rex tail to estimate that the walking speed of the carnivore was much slower. According to the new study published in Royal Society Open Science, the predators walked at just under 3 miles per hour, reports Katie Hunt for CNN.
..
Studying how dinosaurs moved can help paleontologists further understand dinosaur behavior and how they thrived in their prehistoric ecosystems, CNN reports. In future studies, the researchers plan to use this method to calculate the top speed of a T. rex when it's sprinting. Other researchers have surmised that the heavy body of a T. rex, weighing between 11,000 to 15,000 pounds, hindered its running speed. However, van Bijlert suspects that the dinosaur's tail may have absorbed the shock in a way that made it able to run faster without breaking any bones, Live Science reports.

https://www.smithsonianmag.com/smart-news/new-study-finds-that-t-rex-walked-at-slow-pace-of-3-miles-per-hour-180977572/