I think you are referring to the Universal Bar Link Springs, shown in the diagram here:

You need those springs to provide the tension to pull the type bars back; the tension of these springs provide the touch control for the action. Without the springs there is nothing to pull back the type bars after striking the key, except gravity and the bounce off the platen. To replace the springs you will need to pull them from a dead Royal standard. They used the same springs for decades, so it wouldn't have to be a KMM.
 

I can assure you that will not find a spring like that at a big box store. Just where to get specialized springs is a challenge; probably need to see if there are any specialized sellers on the 'net. But how do you know what spring tension to get? 

SquireDante wrote:

Now that I have both KMMs side by side I noticed that there isn't a spot for the springs on the '48. All those holes on the older one aren't there on the newer. And once I get the keys moving freely I don't see the point in having springs at all. My Underwood from '47 doesn't have springs either, so maybe it's just the evolution of the design. For reference the '48 Royal's serial number is 3737880 with a 10" platen. 

It is not an evolution of design, because they used the same springs on the KMG, which came after. Underwoods wouldn't have those springs as it is not the same mechanism. These springs are unique to Royal standards.

I was not aware they made KMM's without these springs, so I am curious to see a photo of the underside of your machine.
 

It is not an evolution of design, because they used the same springs on the KMG, which came after. Underwoods wouldn't have those springs as it is not the same mechanism. These springs are unique to Royal standards.
 

When I compared the Royal to the Underwood I meant that a typewriter from the same time didn't have springs, so it is possible they're not required.

I do wonder how much the size of the platen/carriage changes the overall design. I've been inside both the '40 (which has a 14" platen) and '48 quite a bit and there are subtle differences. Maybe they wanted the smaller KMMs to be easier to type and left the springs out. I changed the touch control on both of them and the '48 never needs as much force to type as the '40.
Or maybe the guy who was supposed to put in the holes and springs missed work that day. 
I personally like the snap and bounce of my Underwood better than either of these lumbering Royals. 

Here are some pictures of the '48. 

Aha! The springs are at the front of the typewriter. Novice that I am, I never studied the touch control on the '40 to see what it connected to. I wonder when and why they made the change.