WHAT IS HAPPENING NOW
AMBER HIGHLIGHT = held surface
BLUE HIGHLIGHT = driving / lifting
GREEN HIGHLIGHT = impulse surface
RED HIGHLIGHT = reverse force
POWER CYCLE
The file vendor/three.min.js is missing. Copy it from a
sibling project, or re-download it from
https://unpkg.com/three@0.152.2/build/three.min.js and place it
in the vendor/ folder.
| Rotate view | left-drag |
| Pan | right-drag |
| Zoom | scroll wheel |
| Play / pause | spacebar |
| Restart | R |
| Escapement | 1 · 2 · 3 |
| Step 20 ms | . (period) |
| Chapters | ← → arrow keys |
A real pendulum — I θ̈ = −m g L sin θ −
c θ̇ + M, integrated at 2 kHz, with sin θ
intact so circular error is present rather than assumed. While two parts touch,
their configuration is solved from the contact geometry, and the
transmitted torque follows from the quasistatic force balance at the contact —
normal force plus Coulomb friction. With μ = 0 this reduces exactly to
the virtual-work rule M = T·dφ/dθ (verified to 10−10 by
the test suite); with μ > 0 the dead-beat's "dead" faces drag
μNρ across every arc of repose, and the gravity escapement pays a small
unlocking friction — the one honest path from train input to pendulum it has.
For figs. 288 and 289 the hanging mass is the input: gravity pulls the
cord, the cord turns the 12 mm drum and 36T wheel, and that wheel drives
the 12T pinion on the escape-wheel shaft. The model computes
T = m·g·r/3; weight fall and lost potential energy follow from
the resulting gear motion.
The gravity escapement's lifting pins, stop-teeth and arm weights are all derived from the drawn geometry: the pad a pin is shown striking is the pad in the contact equation, and the arm's moments come from the polygon on screen plus its counterpoise. The charts are measurements, not formulas: each point is a full run of the same integrator.
Mechanisms follow Henry T. Brown, 507 Mechanical Movements (19th ed., Brown & Seward, 1901; Dover reprint 2005): figure 288 recoil, 289 repose or dead-beat, 311 double three-legged gravity — the escapement Edmund Beckett Denison (Lord Grimthorpe) designed for the Great Clock at Westminster. Plate crops are reproduced in the chapters. Proportions are measured off the plates: the 288 anchor embraces five teeth close over the wheel, the 289 anchor is the long-arm form embracing thirteen, both wheels turn counter-clockwise as drawn, and the 311 arms lie between the two locking wheels with one set of lifting pins between them and the fly on the escape arbor — Brown's text, followed literally.