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I'm working on ideas for a game that will involve mechs of varying sizes and shapes and I am trying to establish an upper limit of size for humanoid mechs. This isn't about practicality, that is something I will consider separately. I'm just trying to establish a maximum possible size.

The mechs will be designed to mirror the movements of the operator. They will either move via advanced servos, motors or artificial muscles (or a combination of all three.) Whatever drives them, they will be able to match the movements of a human inside at near 1:1. This obviously will become a problem with larger mechs as they could easily damage themselves with the amount of force needed to move that fast.

What I want to know is how large can these mechs be built, using modern known materials, before trying to move near 1:1 with the operator would require enough force applied to the mech's components that the mech would risk damaging itself or wearing itself out too quickly to be useful?

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    $\begingroup$ You are looking at the strength of the wrong material. The real material whose strength is important is dirt. That is, a machine which looks like a human will begin sinking into the ground long, loooong before reaching the structural limits of steel. Ever wondered why buildings need those things called foundations? Because dirt is soft.) $\endgroup$
    – AlexP
    Mar 31, 2021 at 17:39
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    $\begingroup$ @AlexP - Arvex's mechs all have on snowshoes. They are badass combat snowshoes with spikes. Some have cross country skiis instead. $\endgroup$
    – Willk
    Mar 31, 2021 at 17:58
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    $\begingroup$ @Willk: That would just postpone the inevitable, and not by all that much. They need caterpillar tracks! $\endgroup$
    – AlexP
    Mar 31, 2021 at 18:02
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    $\begingroup$ Humanoid mechs are overrated. Snake, centaur, or insectoid/arachnid/centipede mechs to distribute ground pressuure are where it's at. $\endgroup$
    – DKNguyen
    Mar 31, 2021 at 20:49
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    $\begingroup$ @DKNguyen I like cartwheeling robots, like this: businessinsider.com/… $\endgroup$ Apr 1, 2021 at 10:35

3 Answers 3

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Ground Pressure

If you aren't taking the practicality of a mech into consideration, the primary limiting factor won't be absolute height, it'll be ground pressure. As long as you keep the ground pressure below about 40 psi/275kPa it should be able to operate on firm soil. If you keep it below about 10psi/70kPa it'll be able to go anywhere a human could go (assuming it fits). However, thanks to scaling effects (square-cubed law) the contact area under the feet will have to increase proportionally to maintain acceptable ground pressure.

If you double the linear dimensions of an human you increase their mass 8 times, but only increase the surface area by 4 times, so their feet must double in area (41% increase in width and length) to maintain the same ground pressure. A mech will likely be not just larger than a human, but denser, requiring even larger feet proportional to their size. Eventually the dimensions of the mech will make it incapable of replicating human motion, even if the structure and actuators are up to the task.

If these mechs are little more than parade floats, they can be as large as you want, with a minimal weight external shell supported not just by the feet but also by lifting gasses. This may be less of a classic mech, and more of an oddly-shaped articulated terrestrial zepplin, but if there are no practical considerations it could meet your requirements, and it would actually get easier to meet those requirements as it got larger. In this case the square-cubed law would actually be working in your favor, and increasing the lifting force you had to work with faster than the necessary weight of the structure increased.

True 1:1 Motion

If you want the mech to match an operator's movements 1:1 not just in terms of motion profile, but also speed (the mech doesn't just make the same motion, it makes it in the same time, and the operator's motions are not restricted to allow for the mech) there's a more concrete size limit. Bear in mind the numbers below are very approximate, since this isn't a technology which has been seriously pursued and developed to maturity in reality. Also, I use "a human" as a reference below because all else being equal, a smaller human will be able to make proportionally faster (though not necessarily absolutely faster) movements than a larger human, which will in turn scale to faster movements of the mech.

As you scale an object up, it will increase in mass with the 3rd power of its linear scale (2 times the linear size, 8 times the mass), and the necessary accelerations will increase linearly (double the distance an object must move in the same time, double the acceleration) meaning the forces required will increase with the 4th power of the linear scale. Meanwhile the structural strength of the object will only increase with the 2nd power of linear scale (2 times the linear size, 4 times the cross-sectional area). Thus, the stresses that would be placed upon the structure if it were required to match a given motion will increase with the 2nd power of linear scale. If you switch from flesh and bone to titanium you can increase the strength to weight by about 6 fold, but this will only allow you to make a mech about 2.5 times larger than a human. If you use modern composites you could build a mech a little under 9.5 times as large as a human. With the strongest known materials (graphene or nanotubes) you could make a mech about 38 times as large as a human, though it would be hard to call this "modern" technology.

As far as actuators, power tends to scale with the 3rd power of linear scale, while the force they can apply only increases with the 2nd power of linear scale (the force a hydraulic cylinder or a bundle of muscle fibers can apply is proportional to cross sectional area). As such, the force the actuators can apply will probably limit your mech's mobility before their power output. With hydraulics the limit is about 7.5 times the size of a human. Other types of actuator currently under development could increase that to about 11 times (relaxor ferroelectric polymer). If the current technical problems with shape memory alloys can be resolved, it would be possible to build such a mech about 24 times the size of a human.

These approximations, of course, assume you maintain the same proportions of structure and actuator that you see in the human body. If you were building a mech using titanium and hydraulics, you could use proportionally smaller actuators and a proportionally more robust structure. A fit human male is, for reference, about 82% muscle and about 14% bone by weight, so a mech using hydraulics and titanium that was about 60% structure and 40% actuator by weight, could replicate such a pilot's movements at a little over 5 times human scale.

Bear in mind, this does not account for ground pressure, the weight of the power plant, the weight of the cockpit, the weight of motion controllers or other hardware, or any armor or equipment the mech is carrying. All you're getting here is an empty frame and the actuators to move it.

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  • $\begingroup$ Very insightful. This actually lets me account for multiple size classes and define limitations of them accordingly (and which size classes can only exist with fictional materials.) $\endgroup$
    – Arvex
    Apr 10, 2021 at 18:39
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10 meters.

storm the puppet

https://www.dailyrecord.co.uk/news/scottish-news/thousands-watch-huge-puppet-storm-21308724

What are the largest humanoid figures currently constructed? Giant puppets! These must bear their own weight, and not fall apart. Depicted: Storm, a 10 meter articulated marionette who walked down the street to inspire the people of Scotland. It looks to me like she is largely made of plastic and fiber. I also found a very cute 8 meter marionette made of wood. I am not sure which would be a better look for your mechs. The lifelike girl mech has not been done to my knowledge.

The builders of these puppets could have used aluminum or titanium; these giant puppets are prestige projects, not built cheaply, and I think if lightweight metals offered an advantage they would be used. But to my eye they are not. Maybe there is an invisible skeleton. I think plastic and fiber are the way to go for giant articulated puppets / mechs.

I have a vision of a mech of this sort which could be lighter weight because like these giant puppets it is all plastic and fiber, and it contains no machines. The feet are two normal tanks with treads, and articulation cables for the mech above are based in the tanks. That puts the motor low and in a proven vehicle. The mech would move like it was wearing roller skates. It would tower above the tanks and fulfill your mechly needs. The tanks could keep their guns which would also make your mech lighter because it would not have to carry guns.

I think it would be safest to have the person who the mech was emulating down in one of the tanks, not up in the head Pacific Rim style. That way the mech could get shot in the head or groin or wherever and it would be fine.

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Go Gundam!

Actually someone has been working on this. Well kinda.

18mt Gundam

The world's largest humanoid robot is being developed in Yokohama (Japan of course, who else?).
The size will be 18mt (60 feet) tall, 25 tons and 24 degrees of freedom.
The hands alone will be about 2mt (5.5 feet) and weight 200kg each.
The engineers have to plan carefully materials and motors to avoid the structure tearing itself apart.
Here is the link to a full article with videos.
Gundam Robot

Of course it depends on what your robot should do. This one will simply walk around and move in a limited area. Maybe wave at the crowd? It's not like it will be able to walk around in the countryside.

UPDATE January 2023 You have until March to visit the Gundam factory park in Yokohama. See article

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  • $\begingroup$ Wait, that thing will move? I was under the impression it was just basically a statue. Cool. $\endgroup$
    – Len
    Apr 1, 2021 at 17:31
  • $\begingroup$ @Len They have setup a statue for the meantime. But the project I linked is about a robot with 24 degrees of freedom. Yes, it will be able to walk. I don't think it will be able to fight Godzilla, sadly, or even mimick tai-chi moves... $\endgroup$ Apr 1, 2021 at 17:40

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