Stool Design Guide: Drop the Base

As a design warm up to the upcoming Shop Stool Build-Off, I'm putting together some design points to help you along in designing of your ideal shop stool. The first thing to address is how to attach to the ground, and how it moves. You may think that you don't want your stool to move, but unless your stool is a boulder or bolted down, it's going to move in some way or another as you interact with it. You should give some consideration to how/where you want that movement to occur.

Degrees of Freedom

Degrees of Freedom

Many engineers will be familiar with applying constraints to the needed 6 degrees of freedom. The concept is that a body (stool) needs to be restrained from translating (scooting) in 3 directions (forward/back), (left/right) & (up/down) it also must be prevented from rotating in 3 directions roll, pitch, and yaw. What motions might be (un)desirable? Only you can say what is needed in your shop. Some activities might benefit from motion, others might be impaired. But here are some possibilities for constraining your stool to the ground.

Some methods that deliberately leave degrees of freedom unconstrained and allow movement:

• Swivel casters allow you to slide in 2 directions and rotate in the yaw direction. (-3) 
• Spring loaded casters can retract when weight is applied Library stool
• Wheels might allow you to move in one direction only (side to side maybe) (-1 Translation)
• A swivel allows yaw  (-1 Rotation)
• A rocker allows pitch or roll (-1 Rotation)
• A sphere would allow pitch & roll (and an intense core workout) (-2 Rotations)

In addition to bases intended to move all the time via rolling, there are also bases intended to be static, but end up moving when the nesting force or center of gravity (CG) shifts. You've likely experienced this with a four legged stool. Because 3 contact points establish a plane. 4 points establish 2 planes. Either the ground or the stool prevent it from being perfectly co-planar. When your CG goes over one of the lines of the contact triangle, the stool shifts to the other plane or tips over. This can be annoying (Crossing the grey lines in the animation pitches/rolls a small amount) or dangerous (crossing the black lines may mean tipping over and on your head.) The annoying bit is exacerbated since all possible contact triangles in a 4 legged stool cross right through where your CG likely is (near your navel when standing, heart when sitting), in the center. Wobbling/shifting can be used to good effect, shifting between two distinct stable working postures as demonstrated in the tip-ton chair or to move around as in the Lee Valley walking stool (But why doesn't my 5 legged office chair wobble? I'll discuss that in "structure")

So annoying is this problem of 4 legs intermittently making contact with the ground that many people decide to make a tripod stool to eliminate that, with varying degrees of success. A problem with a 3 point connection to the ground is the ratio of inscribed circle (the tipping over on your head point) to circumscribed circle (how big of a footprint required) is quite large. Another negative is the tip-over point is significantly different based on what angle you are sitting on the triangle. Compared with 4,5,6 legs (regular polygons) it must be significantly larger to be as stable when leaning.

You can also go less than 3 and rely on your balance (legs) to constrain the remaining degrees of freedom. Strap-on, one-legged Milking stools exist on this principle. These force concentration on what is at hand and stay "in the moment" which might be useful for some tasks (Some autistic kids have found these helpful for focus.)

Tipping Zones of Various # Legs
(Stay out of the red zones with your CG)

But I would guess the majority here want nice stable stools, so how many contact points should your static stool have?

• You could have a single round base that also has an optimal tip over ratio (and can be moved by like rolling a barrel) but with a rigid base you are inviting another safe but annoying tip.
• Two points would be dangerous like a teenager tipping back a dining chair (-1 rotation pitch) or very like a bicycle at a stoplight (-1 rotation roll) 
• Three, discussed above
• 4,5 & 6 quickly improve on the stability, getting a close approximation of the stability of a pedestal.
• 7+ isn't going to be worth the effort, improved stability is marginal at best (see chart)

Gratuitously Geeky Chart

From a construction perspective, even numbers may have an advantage.  This explains why a 4 legged stool is common. It provides an easily manufactured, compact, safer-from-tipping over base, but unfortunately the annoying tipping point between stable positions requires only a tiny CG shift.

Another point to consider is that this assumes regular polygons (equally spaced legs) but you could design your stability envelope via irregular spacing to protect you in certain directions and allow closer access (with a little more tipping risk) in a direction you know your legs can assist or CG shifting is impossible. If you are thinking in this direction then you need to have a directional seat. You wouldn't want a surprise stability issue depending on how you sat down. (A tripod stool has this problem.)

However, if you are thinking about going more than the exactly constrained 3 legged stool, you are going to want to manage the extra constraints with your structure, otherwise the rocking will likely drive you crazy in time. I'll discuss more of this next time.