There are many ways to do the Moore technique, you can even power scrape it. Though that one I'll save for another day. Also that would be cheating
. You gotta' suffer at least a little.
There are two main ways, both can be used for roughing and finishing. Though Moore had different ppi, percentage of contact, and depth of scrape mark for their machines. Their measuring machines are scraped very differently than the other machines. If scraped the normal way, it will cause it to be unusable till corrected. Also masters are scraped differently. I was also taught a way to get ways flatter than .00005" per ft. I messed a bit around with it got my 30" straight edge .00006" flat overall or 24 millionths per ft.
I'll stop blabbering on and I'll get straight to the technique. Also remember this technique does not need stoning after a pass if done correctly. Though you should follow up with a light stone till you get better with it. So you rotate the blade either from the center out or corner to the center vise versa. You can either rotate with the hand holding the handle or push down on the front near the blade. You push down with the palm of your hand while the hand holding the handle end is rotating in the palm of your hand. While you do this, you lock your arm on your side. Make sure you have a sharp blade and make sure your movement is consistent. The radius of your blade is 60 or 50 the smaller ones are a pain to use. Though with the 50 or 60 you can make any size half moon you want.
Lets go through one stroke... You start by putting your blade on the right corner. With the handle held in your right hand making a C shape so the handle will rest in the center of the palm of your hand. Your left is holding the front of the scraper as if your were doing normal push scraping. Your right arm is locked against your side. Now you push forward and while doing that you start rotating towards the center by pushing down on the left half of the scraper with the left hand. Then half way through the stroke you rotate backwards forming the other half of the half moon. Or you could do it the easy way by rotating the handle and applying pressure in the front. I would try to make large half moons and as you get better start making smaller and smaller half moons. The smaller amount you rotate the smaller the half moon.
You see Hbjj's photo, how the half moons have little tails or lines that extend at the ends of the marks? That's because of over rotation of the scraper. You can prevent this by using a small blade though that would be cheating
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I have a Moore master plate for no.3 tables. Earlier this year Moore sold their master plates or one of each set. They sold for less than a 1000$ each. I have seen a Moore no.4 umm that was used to prototype the first CD-ROM. I have also seen a custom Moore no.5 ucmm that had extended height and high load bearing packs on the ways. It had a cylindrical quill that could extend all the way down to touch the table. It was custom made for Oak Ridge Laboratories.
Professional instruments sounds like a cool place to get a tour of. They use a Moore No.4 to fly cut spindle housings. I would visit NIST just to see the Moore machines.
Normally I wouldn't share this info. I just don't like sharing things about their technique. It takes longer than push scraping, can't be used on dovetails, and it takes longer to learn. I was told once, that information is valuable no matter how useful or useless it seems. I contacted Moore to see if I could confirm what I know with them. They told me to go read the books, as it is a trade secret.
I scraped a little 6"x6" surface plate for a friend. I was doing the Moore technique. It was taking so long to rough it. I decided I would "scrape paint" till it has 5 or 10 ppi then do the rest in Moore's style. Which it proved to be a lot faster.
Hope this helps.