ピタゴラ装置 A Pitagora-style chain reaction · 7 stages · 1 push
A mallet taps a marble, and everything after that is gravity and collisions: zigzag rails, growing dominoes, a counterweight lift, a toy car and a bascule sign. It's simulated as real tabletop physics. Press start to watch the perfect build, then build it a hundred times with slightly shaky hands and see which stage breaks first.
Released = potential energy given up as things fall (the lift wins some back). Almost all of it ends up as heat and clicks, which is exactly how a Pitagora device should spend it.
Every build is a little off. Each part lands within a random error of its design position, and friction, bounce and masses drift too. Build the machine many times over, see which stage fails, then change the design and try again.
One standard deviation of placement error. Friction also drifts by 6% and bounce by 0.03 for every millimetre of tolerance.
Each domino is this much taller than the one before. The first domino shrinks to fit, because the last one is always 9.5 cm.
Lifts a 36 g tray carrying a 5.6 g marble. The rail friction is worth about 4 g.
Balances the 10 g board the way a bascule bridge does. If it's too light, the car can't flip the board. If it's too heavy, the board pops up before the car arrives.
Builds #1–#N use the same random errors every time. Changing the design or the tolerance is therefore a like-for-like comparison.
You changed the design or the tolerance after this batch. Run it again to update.
No failures yet.
The dominoes are where most builds fail. This map runs 12 builds of every growth and spacing combination at your current tolerance, with the other design settings unchanged. Click a cell to use that design.
This is a rigid-body sim on Planck.js, a port of Box2D, stepped 240 times per simulated second. Lengths are in decimetres and masses in grams, so gravity is 98.1 dm/s². The glass marbles weigh 5.6 g and the steel ball 45 g, and the dominoes scale in mass with height³.
The lift is a pulley between the bucket and the tray, with Coulomb friction on the tray's rail. The sign is a bell crank with a counterweight. Once it passes vertical it falls onto a stop and stays up.
At the default ±2.5 mm, almost every failure is the same jam. Domino #5 leans on #6 and stops. The gap between them is designed at 23 mm. When a build closes it to about 21 mm or less, #5 hits #6 before it has picked up enough speed to tip a domino twice its weight. Wider spacing or gentler growth adds margin, and the design map shows how much.
Physics runs deterministically: build #17 is always build #17, so any failure can be replayed.
Inspired by NHK's PythagoraSwitch (ピタゴラスイッチ, on air since 2002), whose ピタゴラ装置 are supervised by Masahiko Satō and Masumi Uchino. This is an unofficial homage with an original machine and an original ending chime. Physics by Planck.js 1.4.2.