Degrees of Freedom
|Degrees of Freedom|
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)
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)
- 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|
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.