# The Naked Scientists Forum

### Author Topic: Would a walking machine work with three legs?  (Read 2997 times)

#### Eric A. Taylor

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##### Would a walking machine work with three legs?
« on: 30/07/2010 09:36:35 »
I've just read War of the Worlds (again) and it reminded me of a question I've had from the first time I read the book.

The Martians use a walking vehicle with three legs (like a stool) I've tried hard to imagine how it might work and I would think that unless it used large heavy gyroscopes it would fall over if it lifted one leg to take a step. Using heavy gyroscopes would be bad engineering because the weight of the gyroscopes would cost you maneuverability, top speed and cargo capacity. None of which you would want to sacrifice in a combat vehicle.

H.G. Wells was so brilliant in other parts of the book (like the heat ray (laser?)) I find it hard to imagine he screwed this basic engineering problem.

#### daveshorts

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##### Would a walking machine work with three legs?
« Reply #1 on: 30/07/2010 09:59:28 »
But on that argument humans should need big heavy gyroscopes, a three legged gait is not intrinsically stable, so you would need complex control algorithms but probably not as difficult as a 2 legged one.

#### LeeE

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##### Would a walking machine work with three legs?
« Reply #2 on: 31/07/2010 10:42:46 »
I agree that neither three-legged nor two-legged gaits are stable (in either axis i.e. forwards/backwards or side-to-side).  However, I believe that a two-legged gait is actually more simple than a three legged gait.

With a two-legged structure you have a limited choice of configurations i.e. laterally, with the legs beside each other, or longitudinally, with one in front of the other, and then either move the legs alternately i.e. walking, or together i.e. jumping/hopping.  With a three-legged structure though, you have to decide not only upon how they're configured i.e. in a line or in a triangle (I think we should discount asymmetric configurations), but also how they're going to be moved because you can't simply alternate between three legs i.e. instead of a flip-flop you have to have a sequence.

Fortunately, evolution has resulted in bipedal organisms having their legs oriented laterally i.e. side-by-side, and although this requires a corresponding transfer of balance from side to side as each leg moves through the different points in the walking cycle it means that the legs can swing past each other without colliding; if we had our legs one in front of the other, the swing of our legs would be restricted by the leg in front/behind, unless we 'crabbed' slightly, so that the legs passed to one side of each other (many quadrupeds have to 'crab' when they trot for precisely this reason; this is something that's easily observed when watching a relatively long-legged dog trotting away from you).

With our laterally oriented legs then, there's only the issue of the side-to-side transfer of balance to worry about, while the forwards/backwards balance issue stays pretty much constant.  With a three-legged triangular gait though, there's also going to be a forwards/backwards transfer of balance to be considered, as well as the side-to-side transfer of balance.

Probably the best configuration for a three-legged walking structure would be to have them in a line, laterally orientated, rather than having them set out in a triangle.  This would remove the forwards/backwards balance transfer issues of a triangular configuration but would still bring the benefits of static stability of having three legs i.e. when standing still you could have the two outer legs forwards and the center one backwards (or visa-versa).

With two legs too, there is a simple symmetry in the action of each leg, the action of one leg simply being needed to be mirrored for the other leg but 180 degrees out of phase, alternately repeating the action on either leg, but with three legs this doesn't work because you have an 'extra' leg to consider.

Of course, with the three legs in a lateral line, you could mimic the two-legged gait by grouping the two outer legs together i.e. alternating between the outer two legs and the single middle leg, and this would do away with the side-to-side balance transfer issue too, but unless the outer legs were less strongly built they'd be unnecessarily 'over-engineered' as they'd only need to carry half the weight and handle half the force of the center leg.

The benefits of two legs then, are that the two legs can be identical and that the same single control algorithm can be applied to either leg, just requiring a phase difference between the two legs.  A lateral three-legged configuration, with the outer legs grouped, would require different legs and some differences in the control algorithms for the inner and outer legs, but would provide no advantages over two legs in terms of forwards/backwards stability (It would however, offer improved static stability).  A triangular configuration, as envisaged by H. G. Wells, seems to be the worst of the three configurations because as well as retaining the side-to-side balance issues of lateral bipedal walking, it also introduces a forwards/backwards balance transfer issue too, requiring even more complex control algorithms than the lateral three-legged configuration.

In summary then, I'd say that H.G.W. did indeed get it wrong and was only thinking of static stability when he gave his Martians three legs, oriented in a triangle.

#### Eric A. Taylor

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##### Would a walking machine work with three legs?
« Reply #3 on: 01/08/2010 10:36:13 »
But on that argument humans should need big heavy gyroscopes, a three legged gait is not intrinsically stable, so you would need complex control algorithms but probably not as difficult as a 2 legged one.

Humans have very sensitive accelerometers (in the ear) and very fast data possessors (called brains) that send signals to muscles that contract and relax to maintain balance. You don't notice but when you stand still your leg muscles are always contracting and relaxing. Humans already have computers that can do this even better than humans. Advanced fighter planes are unstable. If the computer fails the plane will crash because the computer makes control inputs that keep the plane in control.

One of the hardest planes to fly ever built was the Write Flyer. I saw a test where a highly skilled pilot tried to fly a replica and he could not do it. It was too unstable.

#### RD

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##### Would a walking machine work with three legs?
« Reply #4 on: 01/08/2010 11:25:41 »
Eric (from USA) may not have seen this prototype ...
« Last Edit: 01/08/2010 11:27:43 by RD »

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##### Would a walking machine work with three legs?
« Reply #4 on: 01/08/2010 11:25:41 »