WING VII · MACHINA
Every exhibit in this wing is a different answer to the same question: what happens when a rigid shape is forced to move, bend, push a fluid, or simply vibrate. None of it needs a computer to be true — it needed only a computer to be watched this closely. This is the last wing. After this one, every discipline the museum promised exists.
EXHIBIT I · LINKAGES
Converting a circle's rotation into a straight line is exactly the piston problem in reverse, and for most of engineering history it had no exact mechanical answer — only approximations. Peaucellier proved an eight-bar linkage exists whose traced point is a genuinely straight line, no approximation at all.
Watt's and Chebyshev's four-bar linkages get close with far fewer parts — close enough that Watt trusted his to guide a steam engine's piston rod. Switch presets and watch exactly how much straighter Peaucellier's line really is.
pick a preset · drag a, b, c, d in free mode · watch the Grashof class change
EXHIBIT II · GEAR TRAINS
An involute tooth is the curve a taut string traces as it unwinds from a circle — and that single fact is why two gears cut with it mesh smoothly even if the centre distance isn't exactly nominal: the string's taut segment stays tangent to both base circles at once, no matter how far apart the centres sit.
Every tooth on this page is generated from that equation, not drawn by hand — change the module, the tooth counts or the pressure angle and the shape changes correctly, the same way a real hobbing machine would cut it.
module, teeth and pressure angle reshape the teeth · contact ratio must exceed 1
EXHIBIT III · FINITE ELEMENTS
A beam doesn't know it's "supposed" to deflect like PL³/3EI — that formula is what falls out of integrating the same physics a computer integrates one small element at a time. For a single load at the tip of a uniform beam, it turns out two-node beam elements get the exact right answer whether you use two of them or twenty — the entire premise of finite-element analysis stated as a number instead of a slogan is that this is provable, not merely convenient.
What genuinely gets harder as elements pile up is solving the resulting system — every element here is solved by Gauss–Seidel relaxation, not a shortcut direct solve, and a starved iteration budget shows up as real, visible error even though the mesh itself was never the problem. Choke the iterations on a fine mesh and watch exactly how badly relaxation methods can undershoot before they're given enough sweeps.
drag the tip load · starve the iteration budget to watch it undershoot
EXHIBIT IV · FLUID DYNAMICS
Push a fluid past a blunt obstacle fast enough and it can't decide which side to leave from — it sheds a vortex from alternating sides, over and over, forever. The shedding frequency isn't a free parameter: it locks onto one dimensionless number, the Strouhal number, almost independent of how fast the flow actually moves.
Every cell here runs a real D2Q9 lattice-Boltzmann solver — nine discrete velocities, colliding and streaming, cell by cell — not a shortcut. The Strouhal number in the readout is measured from the simulation's own shedding, not written in.
Reynolds slider · drag the obstacle · watch the wake lock into a rhythm
EXHIBIT V · PLATE VIBRATION
A vibrating plate has places that move a great deal and places that, astonishingly, do not move at all. Sand thrown onto the plate does the experiment for you: it bounces off everywhere except the places that are still, and comes to rest exactly tracing them.
Every pattern here is the real eigenmode of a simply-supported square plate — sin(mπx/L)·sin(nπy/L) — not a decorative texture. Sweep the frequency and watch the sand redraw a different, always-exact, nodal pattern.
sweep frequency to change mode · watch the sand settle on the quiet lines