Draw Me Watt's Steam Engine

The mechanism, in three motions

A slider-crank converts straight-line motion to rotation (or vice versa). The asymmetry of the piston's travel — slow near top dead centre, fast near the middle — is what makes it useful.

θ = 0

top dead centre

Piston fully out

The crank pin is on the cylinder axis. Piston extension is at its maximum (r + l). The piston is momentarily stationary — all forward velocity has been spent.

θ = π

bottom dead centre

Power stroke complete

The crank pin is on the opposite side. Piston extension is at its minimum (l − r). The asymmetry between this position and TDC is what gives the engine its working torque.

θ = 2π

cycle close

One full revolution

The piston has completed one out-and-back trip. In a four-stroke engine, every two revolutions produces one power stroke — the rest are intake, compression, and exhaust.

How Glyph drew it

Claude writes the JSON; Glyph samples the piston-position formula 360 times around the crank and emits a polyline. Same spec → byte-identical SVG, every platform, every run.

The Glyph spec JSON

// slider-crank.json — parametric piston-position curve
{
  "version": "glyph/0.1",
  "title": "Slider-crank (Watt 1769)",
  "data": {
    "function": {
      "shape": "function",
      "parameter": { "name": "t",
                     "min": 0,
                     "max": 6.283185307179586,
                     "samples": 360 },
      "xExpr": "t",
      // x_piston = r·cos(θ) + √(l² − r²·sin²(θ))
      // here r = 1, l = 3 → range [2, 4]
      "yExpr": "cos(t) + sqrt(9 - sin(t)*sin(t))"
    }
  },
  "layers": [{
    "mark": "line",
    "encoding": {
      "x": { "field": "x" },
      "y": { "field": "y" }
    }
  }]
}

No physics solver needed — the kinematics are closed-form. The non-sinusoidal shape comes from the sqrt, which encodes how the connecting rod tilts relative to the cylinder axis at different crank angles. View on GitHub.

Glyph compiler output SVG

Glyph-rendered slider-crank piston-position curve, byte-locked across CI

Byte-stable across Ubuntu / macOS / Windows × Node 20 / 22. Asymmetric around θ = π — the upper portion (cos > 0) climbs steeper than the lower (cos < 0) descends, because the sqrt term peaks at π/2 and 3π/2.

Your turn — prompts to try

Most mechanical linkages have closed-form kinematics. Name the mechanism and Claude can write the formula.

▸ Mechanism

"Draw me the Scotch yoke — same input/output as a slider-crank but with a slotted yoke instead of a connecting rod. Show the piston as a pure cosine. Side-by-side comparison with the Watt slider-crank."

▸ Engine cycle

"Show me a four-stroke Otto cycle on a P-V diagram. Intake at constant pressure, adiabatic compression, ignition at top dead centre, power stroke, exhaust. Label each leg."

▸ Locomotive

"Draw the driving wheels of Stephenson's Rocket — three coupled axles with connecting rods. Each wheel's crank pin offset by 90° from the next. Show the rod path over one revolution."

▸ Robotics

"Plot the end-effector trajectory of a two-link planar robot arm. Link lengths 2 and 1.5. Animate the joints sweeping through θ₁ ∈ [0, π] and θ₂ ∈ [−π/2, π/2]."