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In The War of the Worlds the Martian fighting machines are tripods. Aliens are also moving around in tripods also in The Tripods.

Let's assume that there are good reasons to build legged vehicles to begin with. But what would be the reason to give them exactly three legs?

Edit: To make it clear, my question is not just three legs versus two, but three legs versus any other number. Indeed, I originally had "only three" in the question, but then replaced the "only" with "exactly" before posting, remembering that two-legged would also be an option.

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    $\begingroup$ My answer would be because its the minimum number of legs to sit at rest without needing to balance (efficient to a fault), but that's really short so I'll leave it here $\endgroup$ – Sarfaraaz Aug 31 '16 at 8:23
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    $\begingroup$ Recommended reading: Why are four-legged chairs so common? on Physics. $\endgroup$ – a CVn Aug 31 '16 at 12:11
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    $\begingroup$ Worth noting, though it may not factor into an answer: In War of the Worlds the narrator observes no signs that Martians have discovered or have made use of the wheel. This speaks to the alien-ness of their psychology. $\endgroup$ – rek Aug 31 '16 at 13:20
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    $\begingroup$ Three legs good! Two legs bad! Napoleon is always right! $\endgroup$ – Aron Aug 31 '16 at 14:22
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    $\begingroup$ At some point within the The Tripods series, a human character speculates that the aliens' planet is very swampy, thus making wheeled vehicles impractical and very tall walking vehicles ... not good, but one of the only workable options. $\endgroup$ – zwol Aug 31 '16 at 18:46
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I think it is because 3 contact points on a surface are the minimum to be stable and the maximum to not be statically indeterminate.

To rephrase it, I am pretty sure you have already seen a four legged table or chair which was wobbling but never seen a three legged wobbling stool. It is because you can always find a plane which contains 3 random points in a 3D space but you may not find a plane which contains 4 random points, and so your table with 4 contact points will hesitate between 2 different planes that contains 3 of its legs. This is why cars have car shock absorber and tables have screws on legs which can be extended or reduced to fit to the ground.

Furthermore, below 3 contact points it becomes hard to be stable (remember when you were in class and you tried to get the equilibrium on two legs of you chair).

However, for the movement process, if you are not rolling, you need to remove briefly at least one point of contact to move it then reiterate the process with the other legs. So you lose one point of contact. Thus, a logical idea would be "so why not 4 legs ? You can stay stable with 3 while moving the fourth". I think it is because in order to be quick you have to lose your stability. When you run (or even walk) you are constantly trying to catch the projection of your center of mass on the ground with your feet. This makes you move faster than always assuring your equilibrium (like most of biped robots do), but it is more hazardous (if something hold one of your foot back, you will fall...).

Another argument could be that it makes those alien machines more... aliens. Making them one footed would be hilarious as they are bouncing everywhere, two feet are too "human" and so, not really scary and four legs would be too "animal". There are a really few number of things on Earth that moves with 3 legs, which drives the spectator to an unknown thing and thus a more frightening thing.

Finally, aliens come from space, and to go to space to invade a planet you need tremendous machines. Two legs are not really stable (furthermore if you are not really sure about the gravity which occurs on the planet), and more than 3 would be too much weight to carry over some light-years !

So three legs are a good compromise between stability, simpleness and lightness (space travel is all about mass).

Oh and they can also abuse our trust by saying that they are here to give us our dose of vitamin C

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  • $\begingroup$ Fewer legs is also more space-efficient in addition to the reduced-weight. Your spaceship is only so big, and you need to store these somewhere until you get to the planet. After that, less space will likely result in better aerodynamics for those pesky planets with atmospheres. $\endgroup$ – David Starkey Aug 31 '16 at 13:46
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    $\begingroup$ +1 for 'stable and not statically indeterminate'. I'm an engineer, nice to see this in the first sentence of the accepted answer. $\endgroup$ – Lamar Latrell Sep 1 '16 at 1:22
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    $\begingroup$ Obviously the bureaucrats in the EU are also aliens, since their standards for chair safety (stable and not statically indeterminate) involves having 5 legs on office chairs! $\endgroup$ – Thucydides Sep 1 '16 at 3:03
  • $\begingroup$ @Thucydides there is good reason why office chairs have 5 legs, there is question about this very topic somewhere on SE, very interesting read $\endgroup$ – Lope Sep 1 '16 at 8:33
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    $\begingroup$ @Lope Just the link, for those interested. Really interesting read indeed. $\endgroup$ – EngelOfChipolata Sep 1 '16 at 8:39
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Well in the movie made in in 2012, the aliens were also tripods, so perhaps for the same reason that theoretical police robots are humanoid, they are based off of the creation species.

After all, three legs are better than two.

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    $\begingroup$ The aliens are tripods in the sequels to The Tripods; it's not just something the movie makers thought up. $\endgroup$ – wizzwizz4 Aug 31 '16 at 10:26
  • $\begingroup$ oh, well my point remains, I haven't found a copy of that book yet $\endgroup$ – TrEs-2b Aug 31 '16 at 10:33
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I'd assume the creatures of the planet were three legged and trilateral.

While humans are bipedal, most common creatures of earth are bilaterally symmetrical. The 'classic' automobile has 4 wheels, much like a horse has 4 legs. While trucks have more sometimes, it's still adding on to the rear wheels more than anything else. Tanks might be an exception, but they are kind of reminiscent of sleds.

So, we'd need trilateral symmetry to inspire that sort of design. Wheels would not work too well (Unless they somehow designed something like the omniwheel). Biomimicry or even bioengineering would explain three legs. They build off what they see, as we do.

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  • $\begingroup$ Not necessarily. There are multiple animals that use their tail. Two legs and a tail might be a start for a tri-legged animal. $\endgroup$ – darthzejdr Aug 31 '16 at 8:07
  • $\begingroup$ A tail would be used for balance, and very few creatures use a tail for weight/ground support in motion. An artillery style unit might do that I guess. $\endgroup$ – Journeyman Geek Aug 31 '16 at 9:54
  • $\begingroup$ Yes, but i wanted to show a tail as something in bilaterally symmetrical creatures that is already useful and give a odd number of parts. Also, yes tail is more commonly used for balance than as a third appendage, but there are some animals that use it. It would definitely be useful if said mech has some weapon with strong knock-back. $\endgroup$ – darthzejdr Aug 31 '16 at 10:52
  • $\begingroup$ @JourneymanGeek I for one welcome our new tripedal kangaroo overlords (or pentapedal in fact) $\endgroup$ – Chris H Sep 2 '16 at 11:11
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Building a three-legged walking robot is easier than a two-legged walking robot, and more than three legs can add to the complexity (depending on the design).

This TED talk by Dennis Hong covers some of the advantages of three-legged robots, in the first robot he describes in this talk (STriDER). Specifically:

  1. If you have to use legs at all, passive dynamic locomotion is an efficient way to move (it's how humans walk), and it's easier to build a robot that uses passive dynamic locomotion on three legs than on two.
  2. This robot moves by flipping its body upside down, swinging one leg between the other two legs, and catching itself. It would be awkward to swing more than one leg between the other two, so more than three would get in the way.

computer simulation of STriDER walking

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    $\begingroup$ While flipping the body may produce a more efficient and stable use of three legs, it doesn't produce the most efficient gait (lots of lateral movement needed to go forward) and flipping the crew and cockpit with every step is going to be disorienting. $\endgroup$ – rek Aug 31 '16 at 17:44
  • $\begingroup$ @rek Good point. Maybe the aliens naturally use this gait, so they're used to it? It's hard to picture what this would look like biologically, but they are aliens... $\endgroup$ – browly Aug 31 '16 at 18:40
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Three legs provide a good, stable base. A tripedal mech is harder to tip over than a bipedal one. Perhaps the aliens have some extremely powerful weapon with high recoil. A bipedal mech that fires this weapon forward will tumble backward; a tripedal (Y-shaped, with presumably 120 degrees between each leg) mech will have 1 leg in the back to support it.

Having three points of contact is also common safety procedure when operating dangerous objects (e.g. ladders), because of the stability that it provides. Perhaps the alien terrain is very mountainous and two-legged mechs are unsafe, thus leading to three-legged mechs becoming industry standard?

enter image description here

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    $\begingroup$ In the middle diagram, which limb will move next? In the other two it’s clear that 3 of 4 limbs are planted while the 4th moves to a new spot. $\endgroup$ – JDługosz Aug 31 '16 at 7:44
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    $\begingroup$ That explains why not only two legs, but not why not four. Especially when moving, there will be one leg removed from the floor most of the time. Rebalancing with three legs seems more complicated to me than rebalancing with either two or four. $\endgroup$ – celtschk Aug 31 '16 at 8:09
  • $\begingroup$ @celtschk I did not watch the movies, but it is not a problem if the tripods move with wheels. $\endgroup$ – SOFe Aug 31 '16 at 9:24
  • $\begingroup$ @JDługosz, his left hand will move next to make contact with the truck bed, then this lower foot will move up. $\endgroup$ – JPhi1618 Aug 31 '16 at 14:15
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Big walking things are not really a good solution, because it doesn't take much to trip them up. (See The Empire Strikes Back or Return of the Jedi for examples.) If your big walking things have super-awesome point defences then fair enough, but it's probably unnecessary.

Tripods are statically stable, which makes them seem like a good idea. However in order to move they have to lift one leg, and that makes them unstable. A stable walking thing will need at least 4 legs, moving only one at once. You can walk a tripod, but it's unstable. For a person falling a few feet, no big deal. For a 50ft killer robot, that's basically game over.

You're also limited in how fast you can travel by your leg length. There are huge stresses involved in the legs and in the joints, and pushing that much mass backwards and forwards takes a lot of energy too. The ultimate limit is the speed of sound in air, which is 340m/s. You can only move one leg at once, so movement of the whole thing is down to 80m/s for a 4-legged walking thing. That's around 180mph, which is pretty fast but still a sitting duck for military aircraft.

Mimicking the alien race is a nice idea. However we're a race of bipeds, and we're well aware that there are no practical purposes for bipedal killer robots. For all that fiction is full of the things, it's very clear that this is simple Rule of Cool and is completely impractical in reality.

Ground-based travel for general use, combined with air support from proper aircraft, is always going to be far superior to a big walking thing (regardless of the number of legs). If you want your ground-based travel to be largely immune to terrain, make it a tracked vehicle. If you want to get somewhere quick, hop in a jet.

So basically we're looking at Rule of Cool as pretty much the only reason to go there. Not just a 50ft tall war machine, but a 50ft tripedal war machine. With death rays. And huge killer tentacles. And they want to drink our bluuurrddd...

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  • $\begingroup$ I don't know; it seems to me like this explains about the downsides of a three-legged moving structure, not why someone would choose to build one like that, which is more along the lines of what the question is about. Could you perhaps clarify? $\endgroup$ – a CVn Aug 31 '16 at 12:21
  • $\begingroup$ I can't help thinking that only tripedal aliens would build tripedal robots. On Earth we can study quadrupeds and if we want a walking robot with more stability than a biped, we're likely to imitate nature. This said, there are pseudo-tripedal beasts here on Earth: kangaroos. They can move darned fast across rough terrain. I think this weakens the argument against tripedal designs in general. Hopping killer robots, anyone? Also how many feet does a galloping horse have in contact with the ground at once? $\endgroup$ – nigel222 Aug 31 '16 at 12:44
  • $\begingroup$ @nigel222 An elephant and a horse have identical body plans, but an elephant simply can't move like a horse does. A giraffe is closer to the tripod situation in how they'd move, but giraffes have big stability issues which makes them a dubious proposition as a weapons platform. Giraffe cavalry was never going to be a thing. :) $\endgroup$ – Graham Aug 31 '16 at 14:20
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    $\begingroup$ @MichaelKjörling The OP starts with a dubious assumption - that there are good physical reasons. Problem is, it doesn't take much inspection to find that there aren't good physical reasons, so we're left with Rule of Cool as pretty much it. I've edited the answer to say that. $\endgroup$ – Graham Aug 31 '16 at 14:24
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    $\begingroup$ @nigel222 Hopping also puts huge stresses (even more so than walking) on joints. See for example en.wikipedia.org/wiki/Kangaroo#Adaptations. $\endgroup$ – a CVn Aug 31 '16 at 14:30
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Versatility

We know that the aliens that are visiting are advanced, because they've crossed the stars. Therefore we know that they're engineering their vehicles using advanced technology and can find elegant solutions that aren't trivial. A key to an elegant solution is reducing it to the absolute minimum.

Given this, why do three legs work better than four? While it's been rightly noted that four legs allows the minimum three-for-stability and the fourth leg can move, humans (amongst other creatures) prove that you can balance on two legs. Indeed, you can balance on one leg, if your reflexive balancing systems are sensitive enough and strong enough. Taken to the extreme, you could balance on a pin - your reflexes and strength just has to be high enough.

Acrobat Balancing On A Point

Standing in place isn't the same as moving, however, which is presumably necessary. To efficiently move at a gallop, you really only need two points of contact, but it helps to have 'pushing'. When we look at a cheetah running, we see that the back feet are largely 'pushing' and the front are 'guiding'. If we posit we have the strength and reflexive balance at an advanced level, we only need one guiding foot, and can rely on the pushing feet for speed. A similar but reverse example of this is how the striders in Dark Crystal move.

But, if we assume all three feet have equal capability we get something even better than that: the ability to immediately change direction with the minimum number of limbs. If traveling in some direction, switching to a direction that is 120 degrees offset becomes trivial.

Also as noted in another post, three limbs makes climbing easy. If you've been rock climbing you have seen people using a deadpoint technique that utilizes dynamic momentum to bring their hands within reach of a good hold. These sorts of techniques make climbing much more graceful and use less energy than static three-point holds while a fourth limb is moving. Assuming the tripod is required to climb at some point, it really only needs three limbs to execute quick climbing manuevers: one 'swing point', one 'reaching point' that is about to take a hold and one 'stable point' that is about to let go once the new hold is secured.

Finally, three limbs are useful in the water. Assuming an undulating motion, similar to octopodes, any number of limbs past two would be useful. But the difficulty with only two limbs is that some degree of stabilizer is needed to maintain orientation - a fin or a third (or more) pushing appendage. Additional limbs can cause, at the least, additional drag, while their marginal utility is unclear.

Given a three dimensional space and sufficient reflexive systems and strength technology, three limbs seems like a reasonable, minimum number when the environment you're in is potentially quite variable.

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Because it's natural for them.

Our land-dwelling forms of life are mostly directional: predators have a "front" where they look for and where they run in, they only need to put some prey in front on them. They are way less efficient in moving to other directions. Prey looks around itself (field of vision is wider) but still has 1 direction where it's most efficient to run, they only need that direction to point away from predator.

What if specialising for one direction was not a winning move? At least for prey, having field of vision of 360 would be nice. If it's movement strategy is "move to the desired direction" instead of "point your front to the desired direction and then move" then having 3-way symmetry would be pretty viable (albeit more redundancy would be better, so creatures may be 6-way symmetrical).

If species in question evolved from something omnidirectional then using tripods may feel natural for them - it provides omnidirectional movement on surface with least number of legs. (they probably have budgets too)

Now, the trick is how to make directional specialiastion not a winning move.

Maybe they're sort of starfishes? Usually they have 6 "rays" but when they "mate" each parent sheds 2 of those and they join into a new being. Then missing rays are regenerated by all 3 beings. Note that "newborn" would also have some neural parts of both parents, somewhat resembling tines.

Maybe running is simply not their thing, their strategy relies on noticing the threat and counter-attacking immediately (venomous spikes or whatnot). Sticking with nautical theme, if visibility is very low where they live, they would have little time to react if ambushed. Thus, turning around is not an option (too slow), each "ray" is on a lookout for its part and reacts immediately for an attack.

Then they discover agriculture and space travel and sliced bread and you have your invaders rocking some tripod mechs.

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Note that in Wells' War of the Worlds the narrator rebukes some images of the walkers "He presented them as tilted, stiff tripods, without either flexibility or subtlety, and with an altogether misleading monotony of effect."[1] This seems to indicate that the robots have flexible legs more akin to a tentacle than what we traditionally think of as legs, which is made more likely by an earlier part of the book "... I could see, intermittently and vaguely, the gigantic limbs churning the water and flinging a splash and spray of mud and froth into the air. The tentacles swayed and struck like living arms..."[2] makes it more likely that the fighting-machines have tentacles instead of rigid legs. The Martians are also described as having at least sixteen tentacles originating around the mouth (see book 2, chapter 2). While my reading that the Martian vehicles have tentacle-like legs may be incorrect, the motion of the vehicles is still described as "...swift, complex, and perfect..." so maybe the Martians have exceptionally complex robotics by our current standards.

So at least in Wells' novel the Martians might have found a way to move easily with three tentacle-like legs instead of the four which a human might entertain as the most efficient model of a robot. That being said, gravity on mars is only about 38% of the gravity on earth, meaning that the three-legged model would work much more effectively there for both vertical movement and in making most likely long low hops along the surface of the planet. Also note that the Martians in Wells' novel have a significantly greater understanding of science and robotics than any current human could hope to have based on the size of their functioning walkers and things like the heat-gun.

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