In the machinery lab, first semester, we had to make two pieces out of a steel rectangle, that would fit each other, like a male and female, like that: _________ | | | | \ / \ / \_____/ Then we had to make a nut and a screw that would screw into each other, from a cube of steel (nut) and a bar (screw). You were free to use any tool you liked, and the professor and his assistant would show you how to hold them, use them right, etc. You'd have to ask special permission to use the electric reciprocating saw, because freshmen had regularly broken the blade
For the benefit of rcm, Virg mentioned the old student machinist's assignment of making a 1" cube flat, square, and parallel, by hand. He said they used a vernier caliper's jaws to gauge squareness.
I've mastered scraping flat, but wondered how you make things square. Really square. Like, how do they make and calibrate reference squares? How would you get, for example, a tenth per foot, from scratch?
My reference ideas: o a plumb bob hanging into a tub of water would make a 90 deg. angle to the water's surface. o a laser bounced off a first-surface mirror back to the source
It's a curiosity thing--I realize few machines need such precision.
Obtaining a square is easy. Take two EXACTLY equal length 'rods' or other suitable flat and true faced edge. Tie them together at one end, and separate the other end by exactly 1.4145926536 * the length used for the two faces. They will be precisely 90 apart.
Well yes, Jasen Betts implied that (in sed) when he said "Pythagoras". But is that how reference squares are really made?
I can imagine checking a standard with Pythagoras, but you can't just bolt three rulers together. There are gotchas. Like, you need three perfect straight edges, and you have to mate their reference surfaces exactly.
If you try to bolt three pieces of precision-length bar stock to make a perfect reference square, you can imagine the inaccuracies that would result.
Such an exercise is detailed in one of Guy Lautard's Bedside Readers. Both how to generate a reference square and how to check one. Neither one involved tubs of water(except for hardening) or mirrors. You DO have to have a true straight-edge first. For a rough check, with no other squares needed or available, you can take your straight straight- edge, put it on a piece of paper, park the square on top and draw a line the length of the perpendicular blade. Flip the square and repeat. The difference out of parallel is twice the offset of the end of the blade.
Also detailed was lapping a square and how to make a cylindrical square.
I think the caliper jaws would be more useful for parallelism, and perpendicular was determined by comparison with a toolmakers square.
First, make a surface plate or three.
Then scrape three rectangular bars into straightedges against the surface plates.
Then choose an end of each of the three straightedges to be the perpendicular faces.
Scrape the three ends into conformity with one another while the straightedge faces are also on the same surface plate. The process is very much like the process by which one generates the surface plates.
I think this and related methods were originally invented by opticians to make prisms, the difference being that they ground things together rather than spotting and scraping.
The following assumes that you have a surface plate of sufficient flatness. There are existing ways to make them starting with three of the same size, but I won't go into them here.
So -- start with a lathe and some steel perhaps about 4" diameter. Turn it to be a true cylinder -- measure the diameter at both ends and several other places near the center and make sure that they are all the same diameter (and use a toolpost grinder to get a really nice finish). Without moving it in the chuck, turn the end flat, recess all but about the outer 3/16", and then use the toolpost grinder to grind that outer rim truly flat. Part off the other end where it was held in a chuck as this is neither the right diameter. Ignoring the parting-off part, you have a cylindrical square. Set the ground rim end down on the surface plate, and you will have a reference which is as square as you were able to measure with the micrometers for the diameter of the workpiece. These are made commercially, but usually from hollow iron castings to minimize the weight. I have a couple of these of differing sizes and weights.
Brown & Sharpe used to offer one which had one end truly true, and the other a precise angle off, and a series of markings chemically etched into the cylinder to allow you to measure just how far off square you are -- measured in steps of 0.0002" up to 0.0012". The dimensions of this one are 6-1/4" high, 2-1/2" diameter, accuracy within 0.0001" and 6RMS surface finish. The part number was 599-558-6, and the price was $160.00 back in 07/1972, when the catalog which I have in hand was printed.
Once you have two opposite faces flat and parallel, make a fixture with an indicator point directly above a similar-shaped stop. Push the block up against the stop and read the indicator. Invert the block you're making and repeat. The difference between the indicator readings is twice the squareness error of the end of the block over the distance between the point and the stop.
It's cool that you can generally do arbitrary-precision measurements of dimensionless properties with pretty much just patience. For example, you can match resistors to any precision at any ratio with simple equipment. Ditto weight and distance ratios.
I thought in SED that some variation of rubbing three cubes' faces against each other on a surface plate might do the trick, but I didn't press it.
After some head-scratching, I think I get your method.
The bottom surfaces of bars I-III are first scraped flat. Then, sliding on a surface plate, faces a-c are rubbed against each other in rotation, making their profiles square with their bottom surfaces and the surface plate. (Fig. 1)
That is so far beyond even wrong that there are not words to tell you. Go make a 4-piece set of V-blocks with hand tools and maybe then you can understand.
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