6 The self-restoring rule

AI workstation · 11 Oct 2026

Every stand so far tipped at a push of a few newtons. Before going further I made balance a formal requirement: every stand must be self-restoring. After any push below the tipping force it must fall back upright, so its centre of gravity stays inside the footprint with margin.

The equation

Take moments about the edge the stand would tip over. Gravity acts at the centre of gravity and holds it down; a horizontal push at the screen's top edge lifts it. At the point of tipping they balance:

$$M g \, (y_\mathrm{CG} - y_\mathrm{front}) = F_\mathrm{tip} \, z_\mathrm{push}$$

so

$$F_\mathrm{tip} = \frac{M g \, (y_\mathrm{CG} - y_\mathrm{front})}{z_\mathrm{push}}$$

Apply it to every edge: front, back and both sides.

A worked example

Stand v2: $M$ = 1.33 kg, centre of gravity 88 mm behind the foot's front edge, screen top about 0.31 m above the desk.

$$F_\mathrm{tip} = \frac{1.33 \times 9.81 \times 0.088}{0.31} \approx 3.7 \text{ N}$$

That matches the check script's 3.7 N forward. A light push with one finger is 5 to 10 N, so v2 fails the spirit of the rule even though it passes the 10° tilt test.

The ways to raise it

1. More mass, low down. Ballast in the foot. It raises $M$ without raising the centre of gravity.
2. A longer lever. Move the centre of gravity further from the edge: a bigger foot, or ballast placed away from the weakest edge (1 kg at the back of B3's foot took forward from 1.7 to 5.7 N).
3. A lower push point. A lower screen.

What height does and does not do

The height of the centre of gravity does not appear in $F_\mathrm{tip}$. A low PC does not raise the push to tip on its own. Height matters in the second test: the stand must stay up when tilted 10° any way, so the margin to every edge must exceed $h_\mathrm{CG} \tan 10^\circ$. A lower centre of gravity passes that test with a smaller foot, and the stand feels steadier.

The edge is where it touches

$y_\mathrm{front}$ is the edge the stand actually rests on, not the edge of the part you drew. Pads under a foot set it. Four round pads at 45° on a disc pull the front tipping edge in to about 70% of the radius. A ring of pad near the rim keeps it out (8.4).

Mind the material

PLA is light, so $M$ is small unless ballast adds to it. PLA creeps, so over time the screen and the centre of gravity can move towards an edge. Ballast must sit in parts that do not creep under it.

The rule is now in the repo's AGENTS.md, so every agent working on a stand checks it.