Mechanical
Systems using mechanical substrates
Systems using Mechanical
Antikythera mechanism
astronomical positions, eclipse prediction, Metonic calendar (multi-cycle gear ratios)
A hand-cranked bronze gearwork device built around 150–100 BC — the oldest known analog computer. Turning a single input crank advances 37 meshing gears whose tooth-count ratios encode the periods of ...
Billiard-ball computer
reversible boolean logic (Fredkin gate)
Proposed by Fredkin & Toffoli (1982). Balls travel on paths representing wires; presence/absence of a ball encodes a bit. Collisions at path intersections implement logic gates. Logically and thermody...
Coupled oscillator network (Kuramoto / XY model)
MAX-CUT / graph partitioning (approximate)
A network of identical oscillators — pendula, LC circuits, or CMOS ring oscillators — coupled to their neighbours by springs or resistive links. The Kuramoto model describes how each oscillator's phas...
Differential analyzer
solutions to systems of ODEs (via chained mechanical integration)
Built by Vannevar Bush and Harold Hazen at MIT in 1928–1931, the differential analyzer is a general-purpose analog ODE solver. The core component is a wheel-and-disk integrator: a disk rotates at rate...
Domino computer
boolean logic (AND, OR, NOT)
Standing dominoes propagate a falling signal. Fan-outs split signals, and careful geometry implements AND and OR gates. Signal is one-shot — must reset by standing dominoes again. Speed: ~1 domino per...
Galton board (bean machine)
Gaussian / binomial distribution
Balls dropped through a triangular array of pegs deflect left or right at each level. The distribution of balls in the output bins converges to a Gaussian as N→∞. Each peg is an independent Bernoulli ...
Hanging chain (catenary)
hyperbolic cosine / thrust line
A chain suspended from two fixed points and left to hang under gravity settles into a curve that exactly realizes the hyperbolic cosine. Gaudí used physical catenaries (inverted) to design the arches ...
Kelvin tide-predicting machine
sum of sinusoids / tidal height (Fourier synthesis)
Designed by Lord Kelvin (William Thomson) in 1872–73, this special-purpose mechanical analog computer performs real-time Fourier synthesis. Each tidal harmonic constituent (M2, S2, N2 …) is represente...
LEGO mechanical computer
arbitrary digital logic / sequential game state
A fully mechanical computer built from LEGO Technic with no electronics. Binary memory is stored as lever positions on a rotating drum (rod logic); a read/write head flips levers to write bits and sen...
MEMS accelerometer
Newton's second law (a = F/m) — continuous analog acceleration measurement
A microfabricated proof mass (typically silicon, ~1 μg) suspended by folded-beam springs. Under acceleration, the mass displaces by x = ma/k (Hooke's law + Newton's second law in equilibrium). Displac...
Marble computer
binary arithmetic / boolean logic
Gravity-fed marble runs with rocker/seesaw gates implement binary arithmetic and logic operations. One marble = 1 bit. The rocker flips state on each pass, implementing half-adders and logic gates. Th...
Mechanical fire-control computer
ballistic trajectory / gun bearing and elevation (multivariate real-time ODE)
Electromechanical analog computers installed on WWII-era warships (e.g. the US Navy Mark 1) continuously computed the correct bearing and elevation for naval guns from up to 25 live inputs: target ran...
Mechanical gyroscope
time-integral of angular velocity (orientation tracking)
A spinning rotor mounted in gimbals conserves angular momentum. Any external torque causes precession perpendicular to both the spin axis and the applied torque — rather than tilting directly. By read...
Planimeter
area enclosed by an arbitrary plane curve (∮ via Green's theorem)
A two-bar linkage with a tracing point at one end and a measuring wheel mounted on the tracer arm. When the operator traces the boundary of an arbitrary shape, the wheel rolls only in the direction pe...
Reservoir computer
temporal pattern recognition / dynamical system computation
Fixed nonlinear dynamical system (reservoir) coupled to a trained linear readout layer. Input drives the reservoir dynamics, output layer learns to extract desired computations. Echo state networks an...
Rubber-band Steiner tree
Euclidean Steiner minimum tree (approximate)
Elastic bands stretched between pins hammered into a board relax under tension to a state of minimum total length. Because each band pulls with a force proportional to its extension, the equilibrium c...
Slide rule
logarithm, multiplication, division, roots
Logarithmic scales engraved on sliding rules allow multiplication by physical addition of lengths (log a + log b = log ab). Precision is bounded by engraving quality and human reading resolution — typ...
Spaghetti sort
total ordering of positive reals (sorting) in O(n) physical time
Cut n spaghetti strands to lengths proportional to the n values to be sorted. Gather them loosely in a fist and lower them vertically onto a flat table so all strands stand upright. Lower a flat hand ...
Watt centrifugal governor
proportional speed regulation (continuous set-point tracking via negative feedback)
Two steel balls are mounted on hinged arms linked to a rotating vertical shaft driven by the engine. As engine speed increases, centrifugal force swings the balls outward and upward; through a collar ...