Im confused..

Consider a robot with a constant punch force. (an actual punch, fist to the face)

The damage, simplifying, would be based on the arm weight x speed.

But speed would be, simplifying, Force / arm weight..

So..doesnt matter the weight, cause its the force ruling everything..Force is the damage regardless of weight :

slower + heavier == faster + lighter, pretty obvious since f = m.a, this is actually intuitive to me

What is not obvious is, the faster the punch the better (harder to avoid), since the force is constant, you would always prefer a lighter arm..that doesnt make sense.. Its more intuitive to want a heavier arm for a strong punsh.. But to keep speed youd need more force...but if you will have more force, and force rules everything, youd keep it lighter @.@

In real life, Im pretty sure a robot arm with a supper engine, but made of plastic, wouldnt do much damage

So what Im not taking into account here, what would make heavier better withouth altering force?

Weight is not really important then?

Im getting that the force an object keep when put in motion (momentum?) is not what gives impact damage? A plastic punch would probably just bend elasticaly and not do anything to an iron target...

So the most destructive punch ever, wouldnt be necessarily from a heavy arm, but from a fast and very hard metal? Is that correct?

Not interested in deep maths, just the superficial logic, so I can make some design choices on a robots game.

Say I want to modify an robot to have a stronger punch, what would I do?

Yes, a punch from a really thin, pointy piece of light metal would be extremely destructive.

Actually the metric you are looking for is not force, but force over surface area (also known as pressure). An extremely strong punch distributed over a large surface area is going to do far less damage than a weak punch concentrated into a tiny surface area. Also see beanbags vs bullets. Similarly, a fast-moving object has a lot of energy, because kinetic energy scales with the square of velocity; so all things equal, the faster object will probably do more damage than the heavier one.

The actual damage imparted to the target depends on the consistency of the weapon and the consistency of the impacted area, as you correctly identified a plastic punch won't do much to an iron target, because the plastic will crumple on the iron and absorb the force of its own impact. If you can't penetrate the iron armor, you can still try and hit it really hard, which will set up a shockwave through the iron (because it's not completely rigid) which can damage whatever is behind (this is the basis for https://en.wikipedia.org/wiki/High-explosive_squash_head weapons). Sufficiently loud sounds can be very damaging because of the amplitude of the sound waves generated; that's why for instance water was being poured onto the launch pad for space shuttle launches to dissipate acoustic energy, so that the sound waves wouldn't shake the shuttle to pieces; if you were standing next to that your internal organs would be instantly turned to mush.

How accurate do you want to be?

Not accurate, just needs to make sense.

Perhaps a "Density" attribute to make impact attacks stronger/weaker.

Im thinking really in the upgrades, to make an arm better: change the material, stronger engine, make it lighter, etc..

Interesting:

https://en.wikipedia.org/wiki/Terminal_ballistics

An early result is due to Newton; the impact depth of any projectile is the depth that a projectile will reach before stopping in a medium; in Newtonian mechanics, a projectile stops when it has transferred its momentum to an equal mass of the medium. If the impactor and medium have similar density this happens at an impact depth equal to the length of the impactor.

For this simple result to be valid, the arresting medium is considered to have no integral shear strength. Note that even though the projectile has stopped, the momentum is still transferred, and in the real world spalling and similar effects can occur.