Reference record · 12 November 2026
What these engineering results establish
The Design lab adds nine independent teaching assemblies and seven editable calculations. They explain design decisions alongside the original 20-group movement and both saved courses. These are reference-informed reconstructions, with invented dimensions and operating inputs. No physical measurement dataset has been supplied.
Four kinds of evidence
| Kind | Implemented result | Limit |
|---|---|---|
| Calculated design geometry | Counts, signed ratios, pitch centres, chosen axial stacks and nominal gaps. | Known design inputs; not a measured ETA movement, a practical gear design or full contact analysis. |
| Rendered-mesh checks | Actual transformed axis-aligned bounds, current package envelopes and planar axial gap in the magnified bearing fixture. | AABB overlap is a candidate, not solid interference. A pierced jewel's bounding box includes its empty bore. Moving/exploded parts change the current envelope. |
| Tolerance example | Hard symmetric dimensional intervals and exact worst/best subtraction. | No measured distributions, yield probability, form/coaxiality, thermal effects or full GD&T. |
| Analytical teaching estimate | Beam, pure-bending strip, linear oscillator, friction limit and ideal barrel energy. | Illustrative independent inputs; none is calibrated to the displayed watch parts. |
Serviceable fixtures and their interfaces
The 17-part keyless fixture includes stem/crown, winding and sliding pinions, setting lever, yoke, yoke spring, jumper, two setting wheels, crown wheel, ratchet, click/spring, open supporting cover and two screws. The fixed plate leaves 16 parts available for removal. Its two-position selector releases one path before engaging the other; reverse winding is held by the click. Saved absolute winding/setting angles prevent previous crown turns jumping into another path on reload or undo.
ETA's 6498-1 technical communication, 6 May 2025 establishes the component identities and architectural relationships. Fixture outline, wheel profiles, covers, dimensions and leaf motion are reconstructed. The readout's 0/1.5 mm gaps mean displacement from a nominal selector stop, not minimum tooth clearance. The orthogonal face-tooth drive is illustrative; it has no conjugate-contact certification.
The 12-part spring fixture has an open drum, arbor, mainspring ribbon, cover/screw, leaf/clamp screw, balance, collet, stud and hairspring on a fixed plate. Installed anchors remain located; released shapes free their external constraints and can extend outside the housing. Click/yoke/jumper springs live in the keyless fixture. Their roles are storage, restoring motion, engagement, indexing and detent retention. All displayed spring deformation is prescribed. The beam and strip plots are separately calculated examples.
Parts lift clear and transfer at scale 1 to padded tray cells; installation reverses the path. Retainers and prerequisites are enforced. Each independent stored-input counter must be let down before opening its own fixture. These open fixtures use an upward removal path and snapping seats. They are not calibre-specific servicing instructions: a real stem, for example, withdraws through the movement edge.
Interface links select the original barrel/bridge, display, balance or motion-works connection. They do not add invisible gearing. Automatic winding, oscillator/hacking and calendar remain separate detailed assemblies to avoid suggesting an undocumented hybrid ETA. The automatic coupling internals are symbolic one-way elements; the bridle has a chosen storage threshold. The calendar advances a 31-position ring with a daily finger, jumper and quick-set; contact motion and its 18:00–06:00 interlock are prescribed teaching rules.
Architecture comparisons
Seconds: small seconds follows the off-centre fourth arbor, informed by ETA 6498-1. Direct central seconds relocates the transmitting fourth wheel and preceding arbors, informed by the ETA 2824-2 manufacturer communication. Indirect seconds adds a 75:10 branch from the third arbor, central pinion, take-up spring and bearing. US4684263A supplies primary discussion of indirect indication and spring braking; its patented magnetic device is not reproduced.
All three steady indications are one turn per minute. Optional indirect reversal play is a chosen angular deadband, not a physical backlash/friction solution or smoothness measurement. The illustrative design envelopes are 3.97 mm for small/direct and 4.32 mm for indirect, from the foundation bottom to the hand top. Small and direct differ in XY packaging; equal heights here imply nothing about the relative thinness of real calibres. Extra support screws, feet and complete wheel/pinion pairs are rendered.
Barrels: single, series and parallel use identical constant-torque sources and visible 1:1 transfer meshes. The series second drum, lid and fastener share a raised deck and its arbor reaches the lower support. Manufacturer architecture references are OMEGA 8912 (series) and F.P.Journe 1304 (parallel). Their actual reserve specifications do not calibrate these invented sources. Independent complication barrels such as Dual-Wing are outside this coupling model.
Supports: four individual cocks, two shared bridges and one three-quarter-style plate retain exactly the same four compound-wheel centres. Their separate feet, screws, jewel seats and dependency graph change access and simultaneous pivot alignment. A. Lange & Söhne's three-quarter-plate explanation informs the construction principle. No measured stiffness, shock resistance or exact Lange part is claimed.
Equations and independent checks
Each calculator exposes inputs, units, equation, source, assumptions, chosen screening range and exclusions beside its output. Invalid or out-of-model input suppresses results. Accepted software ranges do not certify a practical design. Geometry previews have a narrower safe display domain; outside it the view explicitly uses defaults while the calculator retains the entered values.
| Example | Model | Independent worked check |
|---|---|---|
| Gear pair | ω₂/ω₁ = −z₁/z₂; a=m(z₁+z₂)/2; ideal torque reciprocal. | 80:10, m=0.11 mm, 1 rpm → −8 rpm, 4.95 mm, torque ×0.125. |
| Clearance | D−d; radial half; worst gap = (D−tD)−(d+td). | 0.134±0.004 and 0.110±0.003 mm → nominal 0.024, minimum 0.017 mm. |
| Cantilever | I=bt³/12; k=3EI/L³; F=kδ; σ=6|F|L/(bt²). | 200 GPa, b=1, t=0.2, L=10, δ=0.1 mm → 0.4 N/mm, 0.04 N, 60 MPa. |
| Pure-bending strip | kθ=EI/L; M=kθΔθ; U=½kθΔθ². | 200 GPa, b=1, t=0.1, L=100 mm, Δθ=0.2 rad → 1.66667×10⁻⁴ N·m/rad, 3.33333 μJ. |
| Undriven oscillator | ωn=√(kθ/J), ωd=ωn√(1−ζ²); release-from-rest damped response. | kθ=3.94784176×10⁻⁹ N·m/rad, J=10⁻¹⁰ kg·m², ζ=0 → 1 Hz, −0.2 rad after 0.5 s from +0.2. |
| Static friction limit | Tlimit=μNr; compare |Tapplied|. | μ=0.2, N=1 N, r=0.5 mm → 0.0001 N·m capacity; 0.2 mN·m exceeds it. |
| Barrel energy | E=2πTn; Euse=Eηu; hours=Euse/(P×3600). | Two sources, each 0.2 mN·m ×6 turns, η=.75, u=.8, P=2 μW → 0.0150796 J ideal, 0.00904779 J usable, 1.25664 h. |
For identical ideal springs, series gives T and 2n; parallel gives 2T and n. Both store 2E and give the same calculated duration at the specified fixed power. An optional ideal downstream speed ratio changes torque and turns reciprocally and is explicitly not drawn. Loss and usable-window factors apply once to energy. Real torque curves, load, gearing, winding sequence and usable operating window are required to predict reserve.
Equation references: KHK gear geometry; MIT tolerance design; MIT beam appendix; Oregon State damped motion; OpenStax friction and rotational work. See the complete numerical derivations and ranges and fixture dimensions and sources.
What remains outside the model
There is no validated three-dimensional tooth contact, contact-force solution, coil contact, nonlinear elasticity, material/yield or fatigue dataset, lubrication model, friction calibration, measured balance inertia, impulse-energy feedback, rate/positional error prediction or timing-machine diagnostic. The separate oscillator's calculated mode is an undriven linear release, not a running watch. The main sampled two-dimensional escapement remains its earlier bounded demonstration.
Diagrams simplify or unfold the connections and omit axial layers/retainers. Component view hides other parts without disassembly; whole/subsystem/diagram transitions preserve saved selection and question context where the corresponding component exists. The nine design exercises record a prediction, require actual operation and save a supported explanation. Multiple choices can be defensible; their feedback states the compromise.
Independent Blender inspection
Actual browser meshes in winding, fully settled setting and spring-fixture states were imported into a new offline Blender 5.2.1 file, converting millimetres to metres. The crown's exported maximum X changes from 13.55 to 15.05 mm. Keyless snapshots contain 100 meshes each; spring snapshot 50. A report-only seam weld finds 172 boundary/nonmanifold edges in the keyless exports and zero in the spring export. These are render meshes with open seams, not watertight manufacturing solids. Renders inspect the construction and selector pose; they certify no contact or forces.
Browser, numerical, accessibility and performance evidence · Offline Blender inspection scene · Topology report