Precise tools can be made without precise tools because some methods generate accuracy instead of copying it: three plates scraped against each other in rotation converge on true flatness, since no error can be consistent across all three pairings. A reference you can remake is worth more than one you merely own, because the owned one wears, so a workshop needs both a way to generate each reference and a way to notice when one has drifted.
Part of Precision Tool Making
How a workshop with no accurate instruments makes the first accurate ones, and how it knows when the accuracy has been lost.
You Cannot Check A Flat Surface Against Anything Flatter Until You Have Something Flatter
Every measurement is a comparison with a reference, and every reference was made by comparing it with an earlier one. That chain must start somewhere. If the only way to make a flat surface were to copy a flatter one, precision could never begin and every copy would be slightly worse than its master.
It did begin, because some references can be generated rather than copied. Two plates that fit each other can both be curved, one convex and one concave. Three plates that each fit the other two cannot: the only shape that agrees with itself in every pairing is a plane (Three-Plate Method). The plates are scraped in turn, A with B, A with C, B with C, and the errors that cannot be shared across all three pairs are the ones that get removed. No standard is consulted at any point.
Owning A Reference Is Not The Same As Being Able To Make One
A reference you only own has a weakness: it wears, it gets dropped, it rusts, and without a second reference you cannot tell. The three-plate set avoids this, because the three plates remain a self-verifying system. Any two can be checked against each other at any time to confirm neither has degraded, and if one has, a single scraping session restores both (same article).
A settlement holding one worn gauge block and no way of checking it is worse off than one that knows how to generate a flat. The first has a number it cannot trust. The second can remake its reference whenever it doubts it.
What Gets Generated And What Must Be Copied
| Quantity | How it is generated | How you would know it had drifted |
|---|---|---|
| Flatness | Three plates scraped in rotation | Plates no longer agree pairwise |
| Straightness | Three straight edges, or an edge checked against itself reversed | Reversed edge draws a different line |
| Angle | Dividing a circle and checking that the steps close at 360 degrees | The last step does not meet the first |
| Length | Copied from a reproducible physical reference | Reference re-made and compared |
| Thread pitch | Copied from a lead screw, corrected by lapping | Travel checked against gauge blocks |
Flatness, straightness and angle can be generated from nothing. Length cannot: it needs one physical reference to start from, and the most reproducible one this wiki offers is a pendulum. Standard Units (the settlement-planning one) gives a seconds pendulum of about 99.4 cm swinging a 2-second period as a way to recover a metre if the master bar is lost. The other article of that name, in the materials folder, is builders’ units and is not a traceability reference.
What You Need
- Three cast-iron or steel plates, a scraper and engineer’s blue (Hand Scraping)
- A pendulum string, a weight and a way of counting seconds
- A master length bar kept apart from the working copies
- The habit of writing down the date a reference was last checked
Method: Build The Chain In Order
Step 1: Generate flatness with three plates (Surface Plate Construction).
Step 2: Generate straightness from the flat plates (Straight Edges and Surface Plates).
Step 3: Generate angle by dividing a circle and checking it closes (Dividing and Indexing).
Step 4: Fix a length from a master bar checked against a pendulum, and make working copies.
Step 5: Build instruments that read against those references (Measuring Instruments from Scratch).
Step 6: Schedule the re-check of each reference against its generator.
Worked Example
The length of a pendulum with a 2-second period (1 second per swing) follows from L = g x T squared / (4 x pi squared). With g = 9.81 m/s squared and T = 2 s: L = 9.81 x 4 / (4 x 9.8696) = 39.24 / 39.478 = 0.994 m, which is the 99.4 cm in Standard Units.
How well can you set it? Time 100 swings against a heartbeat or sand timer and adjust the string until they take 200 seconds (Precision Measurement). A timing error of 1 second in 200 is 0.5% in period. Length varies as the square of the period, so the length error is twice that, 1%, about 10 mm on a metre. The pendulum therefore reproduces a metre to millimetres, not hundredths. That is enough to rebuild a shared scale, and it is why working copies are compared against one master bar rather than each re-derived from the pendulum.
The value of g depends slightly on where you are, so a pendulum metre carries that uncertainty too; Standard Units gives 0.6% as its accuracy.
Common Mistakes
- Trusting the one gauge you own. Without a second reference it cannot be checked.
- Treating the pendulum as a precision instrument. It sets the scale, to about a percent, and the master bar carries it from there.
- Skipping the re-check schedule. Drift is invisible until something fails to fit.
- Quoting a flatness figure without stating how it was verified. The existing articles disagree on how many cycles give how much flatness, so treat any such figure as unverified.
Safety
Scrapers, lapping dust and lathes
The tools in this tree include a sharp hardened scraper, abrasive compounds, a lathe and a grinding wheel. A grinding wheel that has been dropped or mounted wrongly bursts and the fragments leave at rim speed. Lapping compound and the dust from cast iron and abrasive are a respiratory hazard, not a nuisance; see Lapping for Ultra-Precision and Hand Scraping. Name the stop on every powered machine before using it.
What’s Next
- Learn next: The Precision Hierarchy - which tool enables which
- Combine with: Testing Flatness - how to tell whether a surface has drifted