# Mechanics research — Inside the Machine

Bounded within-task research by `/root/mechanics_references`. No implementation files edited, no external writes, no child agents. Findings concern a schematic traditional Chevrolet small-block 90-degree cross-plane OHV V8; they are not an OEM CAD reconstruction or a validated combustion/structural simulation. References were checked with the web tool during this build. The original pilot may use these references as technical conventions, not as a claim to reproduce a creator's private prompt.

## Primary references

1. **General Motors Heritage Archive, 1961 Chevrolet Corvette vehicle information kit.**
   URL: https://www.gm.com/content/dam/company/no_search/heritage-archive-docs/vehicle-information-kits/chevrolet/1961-Chevrolet-Corvette.pdf
   - Printed *AMA Specifications—Passenger Car*, p. 1, General Specifications / Engine Type: **“90° V-8, OHV”**.
   - Printed AMA p. 9, Electrical—Ignition System / Timing: **“Left bank 1-3-5-7”**, **“Right bank 2-4-6-8”**; firing order **“1-8-4-3-6-5-7-2”**.
   - These are printed section page labels, not asserted PDF page indices. The PDF contains 59 scanned pages. The web search index exposed the specific OEM table text; the PDF opening confirmed the official URL, but the scanned PDF supplied no extracted line text.

2. **Chevrolet / GM Heritage Archive, 1965 Chevrolet Corvette vehicle information kit.**
   URL: https://news.chevrolet.com/content/dam/company/no_search/heritage-archive-docs/vehicle-information-kits/chevrolet/1965-Chevrolet-Corvette.pdf
   - Printed *Power Trains—7*, Principal Components / Cylinder Block, revised February 1965: **“Cylinder numbering arrangement (front to rear)”**, then **“Left bank: 1-3-5-7”**, **“Right bank: 2-4-6-8”**.
   - The section also presents the 327-cubic-inch V8 crankshaft with five main-bearing locations and connecting-rod bearing journals. Its numerical manufacturing dimensions were not used to derive the procedural display model.
   - This is a printed section page label, not an asserted PDF index. The PDF contains 99 scanned pages. The exact relevant OEM table text was retrieved through the web search index.

3. **Chevrolet Performance, ZZ6 Base Engine Long Block Specifications, part 19419198, revision 04FE21.**
   URL: https://www.chevrolet.com/content/dam/chevrolet/na/us/english/index/performance/resources/installation-guides/crate-engines/02-pdf/zz6-base-engine-19419198.pdf
   - Sheet 4 of 20 / PDF page 4, Engine Specifications: **“Firing Order 1-8-4-3-6-5-7-2”**. The same order appears on sheet 2.
   - Sheet 4 specifies a 350-cubic-inch engine, 4.00-inch bore, 3.48-inch stroke, hydraulic roller camshaft and 1.5:1 rocker ratio. These support a traditional small-block reference family, but the pilot should only claim dimensions it actually implements.
   - Sheet 3 specifies real ignition advance before TDC at a stated RPM; therefore an ignition flash at exact power TDC is an explicitly simplified educational convention, not a reproduction of real spark advance.

4. **NASA Glenn Research Center, Four Stroke Internal Combustion Engine, updated May 13, 2021.**
   URL: https://www.grc.nasa.gov/WWW/K-12/BGP/engopt.html
   - Sections describe intake, compression, power and exhaust, including the relation between piston motion, valves and gas exchange.
   - Near the end: **“the crankshaft makes two revolutions for every one revolution of the cams.”**
   - The illustrated historical Wright engine is not a Chevrolet V8. Use this reference for the general four-stroke/cam ratio only, not Chevrolet-specific layout, valve geometry, ignition hardware or calibrated pressure.

5. **NASA Glenn Research Center, Bore and Stroke, updated May 13, 2021.**
   URL: https://www.grc.nasa.gov/WWW/K-12/BGP/stroke.html
   - Opening explanation: **“The piston makes four strokes and the crankshaft makes two revolutions between combustion firings.”**
   - Supports TDC at zero, BDC at 180 degrees, stroke as the TDC-to-BDC travel, and one individual cylinder's 720-degree four-stroke cycle.

6. **FAA, Airframe and Powerplant Mechanics Powerplant Handbook, AC 65-12A.** Optional corroboration.
   URL: https://www.faa.gov/documentLibrary/media/Advisory_Circular/AC_65-12A.pdf
   - Printed p. 23, Camshaft; Figure 1-21: **“The camshaft always rotates at one-half the crankshaft speed.”**
   - Explains a cam lobe moving a tappet, push rod and rocker to open a valve. This is an aircraft-engine example used for the mechanism principle only.
   - A newer FAA-H-8083-32B chapter was also found at https://www.faa.gov/sites/faa.gov/files/03_amtp_ch1.pdf with the same principle around Figure 1-28. Direct opening failed because that file exceeded the web tool's size limit; it is not needed as evidence because NASA and the older FAA source already support the ratio.

## Coordinate conventions that make the proposed algebra valid

Let crankshaft axis be `z`, cylinder bank direction be `n=(sin(beta),cos(beta))` in the `xy` plane, with odd cylinders `beta=+45deg` and even cylinders `beta=-45deg`. Let theta zero be cylinder 1's ideal power TDC. Front-to-rear journal pairs are `(1,2), (3,4), (5,6), (7,8)`.

Define each journal center explicitly as:

```text
a = theta + phi
J = (r sin(a), r cos(a), z_i)
alpha = theta + phi - beta
s = r cos(alpha) + sqrt(L^2 - r^2 sin(alpha)^2)
P = (s sin(beta), s cos(beta), z_i)
```

Here `r` is crank throw / half stroke, `L` is rod pin-center length, `P` is the wrist-pin center and `J` the rod big-end center. The cylinder axis is assumed to pass through the crank axis in projection; there is no lateral wrist-pin or cylinder-axis offset. The positive square-root branch selects the piston farther from the crank axis. Require `L > r` for the usual nonsingular engine geometry.

**Transform direction is material:** `(sin a,cos a)` uses clockwise-positive angular motion in an x-right/y-up view. A conventional right-handed Three.js `rotation.z` is counterclockwise-positive in that plane. Therefore a crank group whose initial journals use `(r sin(phi),r cos(phi))` must use `rotation.z=-theta` to match these piston formulas. Alternatively calculate its positions directly from the same equations. A positive group rotation with these formulas makes the visible journals and rod calculations disagree.

**Axial staggering is material:** each rod's wrist pin and big end must have the same `z_i`, including its bank offset. Two side-by-side rods can share one journal's common x/y orbit while using different axial positions along the journal. If the implementation instead gives a single rod a nonzero `delta_z` between pin centers, the written 2D equation no longer preserves its 3D length: the root must include `-delta_z^2`, or the geometry must be aligned. Do not animate an angled rod from a journal midpoint to a staggered piston using the unmodified 2D solution.

The odd bank's `+x` assignment means it appears on the viewer's right when looking from the engine's front with x-right/y-up. Label left/right as vehicle/engine conventions; do not relabel banks based on current orbit-camera screen position. Define the positive z/front direction in the implementation because the research brief only says the crank lies along z.

## Firing phases and cross-plane check

The proposed front-to-rear crank phases `[45,135,315,225]deg` are internally consistent with the firing schedule and both banks. They give two opposed pairs on mutually perpendicular planes: 45/225 and 135/315. This is a valid derived cross-plane realization. These angular constants are derived from the stated coordinate system and TDC constraints, not quoted OEM manufacturing coordinates.

| Cylinder | Bank | Journal | phi | Ideal firing theta | `(theta+phi-beta) mod 360` at fire |
|---:|---|---:|---:|---:|---:|
| 1 | Left | 1 | 45 | 0 | 0 |
| 2 | Right | 1 | 45 | 630 | 0 |
| 3 | Left | 2 | 135 | 270 | 0 |
| 4 | Right | 2 | 135 | 180 | 0 |
| 5 | Left | 3 | 315 | 450 | 0 |
| 6 | Right | 3 | 315 | 360 | 0 |
| 7 | Left | 4 | 225 | 540 | 0 |
| 8 | Right | 4 | 225 | 90 | 0 |

All eight power events are 90 crank degrees apart over 720 degrees, in order 1-8-4-3-6-5-7-2. Piston geometry repeats at 360 degrees; valve/cycle state and each cylinder's power event repeat at 720 degrees. These periods must remain separate in code.

For a simple four-stroke teaching state, define `u=positiveModulo(theta-fireTheta[c],720)`:

- `0 <= u < 180`: power, piston moving toward crank.
- `180 <= u < 360`: exhaust, piston moving outward.
- `360 <= u < 540`: intake, piston moving toward crank.
- `540 <= u < 720`: compression, piston moving outward.

The valves are closed through the ideal power/compression ranges; exhaust/intake lift may be displayed in their named ranges with smooth boundary profiles. Real valve events have advance, delay, overlap and engine-specific lift profiles; any simple 180-degree event windows must be labelled schematic. The cam rotates `theta/2` with per-lobe phase offsets so all 16 valve events repeat once per cam revolution. A lobe model must visually contact its follower at the same phase that the valve opens; half-speed rotation alone does not prove this.

## Algebra and numerical checks completed

The rod vector satisfies `|P-J|^2=s^2-2sr cos(alpha)+r^2=L^2`; solving this quadratic yields the supplied slider-crank equation. TDC is `s=L+r` at alpha zero; BDC is `s=L-r` at alpha 180; therefore stroke is exactly `2r`.

A standalone JavaScript sweep ran in the tool runtime, independent of any product implementation, with illustrative constants `r=1.74`, `L=5.7`, axial pair spacing `4.4` and bank offsets `+/-0.47`. These constants were chosen to exercise geometry and are not all asserted OEM dimensions. It sampled all eight cylinders every 0.25 degrees from 0 through 720 inclusive (23,048 cases).

- Maximum rod center-length error: `3.552713678800501e-15` length units.
- Maximum 360-degree piston repeat error: `7.993605777301127e-15` length units.
- Maximum intended firing-TDC error: `0`.
- Maximum intended firing-plus-180-degree BDC error: `0`.
- Maximum piston bank-axis perpendicular residual: `8.881784197001252e-16` length units.

These results validate the stated mathematical equations and constants, not the eventual rendering code. The product must independently test its actual helpers/transforms.

## Minimum meaningful implementation checks

1. Assert all eight cylinders, two banks, four shared journals and the exact firing order; fire intervals must be 90 degrees modulo 720.
2. At each firing angle, the respective rendered/calculated wrist pin is at `L+r`; at plus 180 it is at `L-r`. Check actual object world coordinates, not only a duplicated helper formula.
3. Sweep the actual implementation through at least a full 720-degree cycle and measure rod length, piston axis residual, big-end alignment with the displayed crank journal and wrist-pin alignment with its piston. Include a noncardinal angle such as 37 degrees; cardinal angles alone can hide rotation-sign defects.
4. At theta plus 360, piston poses repeat but cycle state changes by two strokes. At plus 720, piston/valve/cycle states repeat and the cam has made one revolution.
5. Verify pause and angle scrubbing deterministically update every visible part and cylinder state; no independent free-running animation should remain.
6. Verify a selected cylinder's valve/rocker/pushrod/follower linkage and cam lobe stay coordinated. Smooth decorative motion that disagrees with contact geometry should be disclosed as schematic or corrected.

## Material limits to retain in the product/readme

- Kinematic teaching model; no thermodynamic combustion solve, pressure calibration, torque prediction, CFD, inertia/balance analysis, bearing-contact simulation or structural/thermal stress validation.
- Visual combustion colors and any plotted pressure are illustrative unless an independently specified model is implemented and identified.
- Geometric dimensions, block/head cutaway and valvetrain placement are procedural schematic design choices unless cited and matched individually.
- Ideal TDC ignition and simplified valve timing are not real calibration data.
- A clean render demonstrates appearance and animation continuity, not accurate physics. Numeric linkage and event checks support only their explicitly tested properties.


## Implemented dimensions and valvetrain

The actual pilot uses crank throw 0.72, rod pin-center length 2.65, nominal bore radius 0.67, journal pitch 1.62, and side-by-side rod axial offsets ±0.16, all normalized display units. These are not OEM manufacturing dimensions.

The rendered cam rotates at minus half the clockwise-positive crank angle in Three.js. Each lobe uses a sampled polar outline derived from the same ideal intake/exhaust lift window. A rigid pushrod of length 3.504 drives a 1:1 rocker with arm length 0.34; a numerical constraint solves its angle. Valve stems stay on fixed axes and use a sliding rocker-tip pad. Finite-radius tappet/lobe contact, lubrication and calibrated real cam geometry are not solved.

The linked 2D diagram projects the same crankpin into the selected cylinder’s axis/perpendicular basis. Its connecting rod and piston are derived from the shared 3D state.
