Why do wheeled office chairs (and rolling hospital equipment) have 5 legs? Why not 3, 4, or 6?
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If you call a tail a leg, how many legs does a dog have? Five? No, four. CALLING a tail a leg don’t MAKE it one.
— Mark Twain (1835-1910), nom de plume of Samuel L. Clemens, American writer and humorist
Government regulations mostly. For a given rough area of the base of the chair 5 points touching the ground are more stable than 3 or 4.
Just seems to me it is more stable (much less likely to tip over) than a 4 leg chair. And more than five would likely be overkill. I’m gonna guess that lawyers or insurance companies were involved somehow.
Such chairs don’t have five legs, they have one leg, with five, errr, feet, I guess.
It’s easy to see why such a design with three or four feet would be bad. Unlike a stool or traditionally-legged chair, in a wheeled office chair, all the weight of the occupant is supported by the central shaft, which means it must be balanced by the foot assembly. With four feet, there is a full 90 degrees of unsupported area between each foot, which would make it very easy for the chair to tip. Three feet is even worse with 120 degrees between each foot.
This problem does not occur with a three-legged stool because the weight is divided equally among the legs instead of balanced on one center.
Yep, especially because the wheels would exacerbate the problem, since not only do you would you just fall over once you tip past the point of the center of gravity, but with wheels balancing on two legs at just about any angle is incredibly unstable. With five feet, and the smaller angle between any two legs, what I think happens is that it changes the center of gravity required to tip the chair on two legs to the point where it’s impractical to do it when the person is actually seated, or at least to tip very far. I’m experimenting with this now with my office chair, as a matter of fact. I can get it to go up on two wheels, but just barely, and it takes some effort.
My guess is, since you can obviously get away with only 4 legs on a regular chair, and we all know you can tip backward pretty easily in one of those to about 45 degrees before you fall over on your back, it’s the wheels on an office chair that require the 5th foot due to the instability of the wheeled feet. Just imagine leaning back at 45 degrees on wheeled chair feet. You probably wouldn’t make it to 30 before it started getting away from you.
“Man.”
Sphinx-like for Sphinx-like.
Aside from OSHA, an odd number of legs will always have SOME stable orientation on an uneven floor whereas a four-legged chair will rock.
And with wheels it will rock AND roll.
That’s obviously true for a chair with three legs, but in this respect, are five more stable than four?
Just this week I’ve replaced my 30+ year old 4 wheeled office chair with a shiny new 5 wheeled one. The only real problem with the old one is that the rubber tread came off one of the wheels and it squeaked a bit.
Quite the contrary: On any uneven floor, a chair with four legs will always have a stable orientation (usually, exactly two of them), but for almost all uneven floor surfaces, a chair with five will not.
And the existence of one central pillar versus multiple separate legs should matter not at all.
I found office chairs with six or even seven(!) legs searching Google.
I can’t for the life of me see why.
Nearly useless factoid.
Four points in a plane can be rotated such that all four points will contact a surface at one time, as long as the surface is continous.
Or something close. And IIRC this proof was proved not that long ago.
I suspect that an uneven floor will not be planar.
Even though it’s actually a very simple proof. Suppose you’re sitting in a chair that rocks front-left to back-right. Rotate the chair: Eventually you’re going to get to an orientation that rocks front-right to back-left. By the Intermediate Value Theorem, there must be some orientation where it doesn’t rock at all.
There are a few more details to it, but that’s the gist.
EDIT: The floor doesn’t need to be planar. If it is, then the problem is trivial. It can be any surface at all.
With 4 legs the weight on each caster wheel is 25% higher than it is with 5 legs, making it harder to scoot the chair while you’re sitting in it, especially on carpeting.
With 6 legs, your feet are less able to find the floor and more likely to hit a chair leg. So 5 legs makes the chair easy to scoot around in yet minimizes the interference to your feet.
But it is continuous, and the four points on the chair feet will be planar.
For a chair to tip over, the chair must rotate around a line formed by two feet that stay on the ground. On a chair with 5 feet, that line is further from the center of the chair than it is on a chair with 4 feet.
Because wheeled chairs are often rolled sideways, stability is more critical.
Three contact points at minimum are needed for stability (which can occur with two legs, if one foot has at least two points of contact and the other has one, but this is difficult to do because it requires the cg precisely within the triangle generated by those three points).
The problem with four legs is that the cg of the person/chair is usually located somewhere in the center of the “square”. But since three contact points are needed, the cg is almost always located close to the edge of the triangle generated by three of the legs. Once the cg relocates just a tiny bit, its outside of the first triangle and has to tip to find a new three points of contact, but the cg is still dangerously close to the edge, so the whole system constantly rocks back and forth, unless the floor is even and the chair leg length tolerances are tight, or there is deflection in the floor/chair legs.
five legs doesn’t have the same rocking problem, because there are multiple different combinations of three legs that allow for a wide shifts in cg from a central position while still staying within the same triangle generated by the contact surfaces.
With any given leg size, overturning stability is also affected directly by the number of legs, according to cos(180/#legs). Compared to an ideal infinite number of legs (a complete circular base), 3 legs are only 50% effective , 4 legs are 71% effective whereas 5 legs are 81% effective.