MB-01 · MECHANICAL BALLET · SHEET 1

DWG № MB-01 — A CHOREOGRAPHY FOR GEARS, PISTONS & LINKAGES

Mechanical Ballet

An SVG machine that dances. Every tooth, rod and pivot is computed from first principles — then a single GSAP master timeline conducts the tempo, six movements from overture to da capo.

MOVEMENT TACET
FLYWHEEL 00.0 RPM
SCROLL — THE PROGRAMME↓

ACT I

Pirouette— The Gear Train

Three dancers turning as one body. Each pair of meshed teeth reverses the sense of rotation: thirty teeth lead, fifteen follow at double speed, twenty-one answer in counter-turn. The ratio is the choreography — fixed forever by the count of the teeth.

TRAIN
30 : 15 : 21 T
MODULE
6 MM
SENSE
ALTERNATING
LAW
ω₂ = −(N₁/N₂)·ω₁

ACT II

Plié— Crank & Slider

The deep bend. A crank turns in place while the piston sinks and rises along its bore — pure rotation translated into breath. Its displacement curve is not a sine: the finite connecting rod sharpens the bottom of every bend, and the drawing plots it honestly.

CRANK
r = 56
ROD
ℓ = 170
STROKE
112
LAW
s = r·cosθ + √(ℓ² − r²sin²θ)

ACT III

Adage— The Four-Bar Linkage

The slow, extended line. Four bars, four pivots, a single degree of freedom — yet the coupler point writes a figure no compass could. The grey ghosts are the motion study, twelve poses held at once; the red line is the dance itself, solved each frame by intersecting two circles.

CLASS
GRASHOF CRANK-ROCKER
SOLVER
CIRCLE ∩ CIRCLE
OUTPUT
COUPLER CURVE
POSES
12 GHOSTS @ 30°

ACT IV

Petit Allegro— The Geneva Drive

Quick, precise steps. The driver turns without pause, but the star advances only while the pin rides its slot — a crisp quarter-turn, then perfect stillness for three beats. Intermittent motion is the machine's staccato, and the locking crescent is what holds the pose.

STOPS / REV
4
INDEX
90°
DWELL
270°
LAW
β = atan2(R·sinα, d − R·cosα)

INTERLUDE

Pas de deux— How Two Teeth Touch

Hold the scroll and the plotter zooms to the point of contact. Two wheels meet along one straight line — the line of action — tilted twenty degrees from the common tangent. Every construction on this sheet plots itself in order, exactly as a draughtsman would lay it down.

  1. 01 · BLANKS, HUBS & CENTRES
  2. 02 · PITCH CIRCLES — TANGENT AT P
  3. 03 · LINE OF ACTION, 20° PRESSURE
  4. 04 · DIMENSIONS & NOTES
PLOT 000%

THE SCORE

Tempo di ballo— Six Movements, One Variable

The ensemble never stores a pose. A single master timeline eases one number — angular velocity — and every mechanism integrates it into motion, the way an orchestra follows a baton rather than a metronome. Select a movement to cue the machine in the overture above; the score loops, twenty-eight seconds to the bar line, then da capo.

LINE CONVENTIONS

  • CENTRELINElong–short dash on every axis of symmetry
  • PITCH CIRCLEwhere two gears agree to roll without slip
  • DIMENSIONarrowed, measured, honest to the pixel
  • TRACEvermillion — the pen line a moving point leaves
  • GHOST POSEa motion study — twelve instants held at once
  • SECTION HATCH45° — material the cutting plane passed through

REVISION HISTORY

REVDATEDESCRIPTION
A07-19FIRST ISSUE — ENSEMBLE ASSEMBLED, FOUR ACTS DRAFTED
B07-20CHOREOGRAPHY ENLARGED TO FILL THE STAGE; DETAIL E (MESH, 10:1) PLOTTED UNDER SCROLL
C07-20SCORE TABLE CUES THE MASTER TIMELINE; DIMENSIONS NOW DRAW THEMSELVES. THIS SHEET.

INSTRUMENTS

  • GSAP 3.12.5 — master timeline, ticker, ScrollTrigger pin & scrub
  • FRAUNCES — display serif, optical size 144, weights 300/400
  • IBM PLEX MONO — annotations, dimensions, this very table
  • SVG + VANILLA JS — every mark computed at runtime; zero raster assets