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Comment by keypusher | Hacker News Reader

I am fascinated by all the 3-legged furniture in the painting. The design guarantees stability due to all legs being on the same plane, solving the wobbling/instability problem so common in 4-legged tables and chairs. However, quadripedal tables and chairs are nearly universal in the modern day, with tripedal pieces being mostly reserved for eccentric art. I wonder at what point the trend changed, did it have to do with manufacturing techniques or simply aesthetics?

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Is there a relationship between 3 vs 4 legs and total weight bearing capacity? Maybe the tradeoff was stability for weight of furniture? I’m also not sure that three legs is more stable, wouldn’t it be more prone to tipping over, unless the three legs are splayed very far apart from the seat base? Remember the issue with furniture is a desire to keep it from tipping over, not stability in 3-space. You’d get no,wobble on three legs, but if you leaned or swiveled too much you’d find out that stability was an illusion, because you’d failed to take the vertical component into account.

A four-legged chair for example, regardless of how you lean (within reason) and distribute weight will maintain 3-point contact with the floor.

I imagine a lot of it is that floors are likely much flatter these days.

Stability is a big issue for chairs especially. Rolling office chairs are afaict all 5 legged these days, unless you happen to find an old one. OSHA mandate.

I think that’s for failure tolerance. Five isn’t much more stable than four, but if a wheel falls off then five remains stable.

From experience, if you lose a caster the chair won’t balance on the remainder, it will thud down on the leg. What more legs does however is more evenly distribute the load, which is important when rolling around, leaning back and all, of the other things we do in office chairs.

Im betting it has a lot to do with construction costs, especially with chairs. Chairs are very expensive and difficult piece of work with tons of pieces that need to take serious abuse, more legs means more pieces. Also if you have even the smallest imperfection in angles or squareness on a 4 legged piece of furniture it is immediately obvious. Joinery is what takes the most man hours, so hose stools for example have 24 mortises each, add another leg and you got 32 mortises, and a more expensive piece with more points of failure.

Another thing to consider, the floor. How flat would most floors be at the time? 4 legged chairs would almost always be rocking on 3 legs, causing them to fail and break more often. Shimming a short leg only works if it doesn't move or if the floor is almost perfectly flat.

Depends how you define "stable". Is it "less likely to fall over" or "less wobble"? That's basically the difference here.

A 4 legged chair is much less likely to fall over because it has more points of contact with the ground (yes, this extrapolates). While you're correct that a 3 legged chair isn't going to wobble, many would call it less stable because it is more likely to fall over. The force is distributed only across 3 points and if you sit at an edge that force is going to be highly concentrated along two points. In fact, those two points are always going to create a lever. In a 4 legged chair there are many edges that you can sit on where the weight will be distributed to three points, you have to be specifically on the edge where two legs create a plane to distribute the force to 2 legs (see why this extrapolates? More legs and it is harder to distribute force to only 2 legs).

Why 4 though? Well, I don't have a scientific answer. But it is pretty well balanced, doesn't increase cost much, nor weight. So probably just a compromise. Though in a lot of rolling chairs you will see that they typically have more than 4 points of contact with the ground (notice how much harder it is to tip these over?).

tldr: 4 is actually more stable in the sense of "you're less likely to fall out of the chair and bonk your head".

It's not exactly more legs -> less chance of falling, but rather it is larger footprint -> less chance of falling. The footprint is basically the shape made by the outermost points of contact. If the net force vector (generally just project center of mass in direction of gravity) goes outside the footprint, the system is unstable. You could absolutely have a chair with more legs be less stable than one with fewer legs, if the footprint is smaller.

You are correct, but I assumed that when people are creating their mental model that they envision regular polyhedra. Especially given the context. I felt that the distinction might make things more convoluted and I could leverage the likely mental model to my benefit. But you are technically correct.

Interesting you say that. When I grew up I was always told that four legged furniture was more stable than three legged ones. Three legged stools/tables were common (but not chairs I think) when I grew up and I was always cautioned against toppling. It could be because three legged furniture created a virtual triangle shape (Even if the top of the furniture itself was not a triangle, circular ones were very common) and when one puts weight on the side of the base of the triangle, like siting on the edge, the furniture is more likely to topple than a similar action on a four legged stool.

The floors were less likely to be perfectly level than modern floors so a three legged stool or table would be less likely to wobble.

For tables: leg room and leg exposure.

Simple three-legged saw horse:

https://www.toolsofthetrade.net/trucks-equipment/jobsite-equ...

Three legs are cheaper than four.

I don’t reckon it’d match today’s fashions.

Rocking tables are a pet hate of mine.

Maybe we could add ‘rocking table repair 10hrs a week’ to this list of items that allow you to fulfill the requirements to obtain welfare.

And / or it could be an option for those sentenced community service by the courts.

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