Research note / Cycle 019
A third point is not always independent
Four software cases show why a third reference cannot detect common motion when it shares the targets' support.
A difference that can be zero for two reasons
The Space Elevator Initiative's intended tether strip measurements depend on knowing where an endpoint is while KIS-61 and KB-2 remain in their established mounts. A path around the clamp reached selected positions with SE-M18, but the sacrificial support visibly flexed and was removed. Reed and Voss now examine the reference itself before making anything permanent.
On January 30 they execute four constructed three-channel cases. Each has a left target, right target and third witness, all given explicit numerical values. These are synthetic inputs in µm, not readings from a newly installed gauge or any physical fixture.
What the third point actually knows
In the independent-witness case the two targets both read 12 µm while the witness remains at 8 µm. The target difference is zero, but their mean is 4 µm above the witness. When the third channel shares their support and also reads 12 µm, both comparisons are zero even though a common shift was injected.
A one-sided constructed fault of 12 versus 8 µm gives a 4 µm target difference. The table deliberately keeps differential and common-mode failures apart: adding a third number is useful only if its reference path can remain separate from the error being sought.
The bracket is still a question
Dover Motion's Abbé-error discussion shows why a position reference separated from a point of interest can mislead. It does not supply the stiffness, angular calibration or provenance for a Meridian witness.
The next tangible task is to draw and resource an independent support path, then quantify its motion across the full bidirectional grid. No new bracket has been accepted; NQ-17 remains returned. The 25 µm budget, separate 6 µm return allowance and 1000 µm grid are unchanged. Strip loading remains withheld.
Results at a glance
| Constructed case | Left (µm) | Right (µm) | Witness (µm) | Target difference (µm) | Mean minus witness (µm) |
|---|---|---|---|---|---|
| no injected shift | 8 | 8 | 8 | 0 | 0 |
| independent witness | 12 | 12 | 8 | 0 | 4 |
| shared-support witness | 12 | 12 | 12 | 0 | 0 |
| one-sided fault | 12 | 8 | 8 | 4 | 2 |
External research and methods
- Abbé Error · Dover Motion · Motion Control Handbook, Abbé Error section (Undated online handbook; retrieved 2026-10-26). Abbé error introduction, offset-arm and encoder example..