Checking a 45 degree square?

[loply]

Hi folks,

Some time ago I made myself a whole set of precision references for scraping/inspecting etc, including a very accurate master square.

I want to make a 45 degree reference from a slab of cast iron I have but I'm struggling to think of a way of checking it. I can think of a way of doing it if I make two or three, but that's 2x or 3x the work!

Anybody know an ingenious way to test for 45 degrees without a known standard to compare to, and without making 2x of them?

Cheers,
Rich

[loply]

I have a high precision level too, but no sine bar or sine plate.

[Fergus OMore]

Two 45's make a right angle, four make- a straight line whilst 8 get you back to where you started.

source Euclid.

[Arbalist]

Yes, bit tricky. Easy to make one but not so easy to check!  the only thing I can think of is to place it on a flat and scribe the outline, then flip and scribe it three times and see if it meets the starting point! If there's a gap it's under 45° and if it goes over the line it's over 45°...

Here's how I make mine.

[Lew_Merrick_PE]

Rich,

One of the tricks I use with great regularity is to drill and ream a set of dowel pin holes in a piece of (say) 1/4 X 6 inch material (usually either aluminum or steel).  My Trav-a-Dials (the forerunner of DRO's) allow me to do so ±.0005 inch, so my result will be quite accurate.  I then press in dowel pins and mill off the "outside" and end up with an angle plate of whatever (angular) size I need.

Thus, for a 45° plate, I would ream my holes at: (.375,.375), (5.250,0), & (5.250,5.250) from the corner of a 6 inch square piece.  I then insert (call it ø1/4 inch) dowel pins two at a time and mill my (call it .350 inch) offset edge around the periphery.  If I have done this as accurately as my machine is capable, then my resulting angle will be ±.0104° (0°0"2').  Would that be close enough for your purposes?

I usually make them in pairs.  The angle gets steel stamped on the "face" of the plate.    And they end up "living" in boxes where they can be found and reused.

[vtsteam]

Rich, along the lines of Fergus' suggestion, lay a straightedge on a metal plate and clamp it down. Lay a square on the plate butting on the straightedge.

Lay your new (but reasonably close) angle casting on the plate with its vertex at the square and straightedge juncture, and one edge along the straightedge. Scribe the other casting edge on the plate. Also mark the outer end point.

Flip over and shift the casting so it contacts the square's edge, and again shares a vertex with the two standards. Scribe a second line on the plate. Again mark the outer end point. (Since you flipped it, that should be the same distance out.)

If the two lines correspond, you're at 45 degrees.

If not, measure half the distance between the two endpoints, draw a line between the two, mark the point, and scribe a line from there to the vertex. That will be at true 45 degrees.

Clamp a second straightedge to the 45 degree line and scrape your casting to either straightedge as a reference surface, bearing against the other.

[Pete.]

Why exactly? Scraping references are usually less of an angle than the dovetail, and many (probably the greater proportion) are not 45 degrees.

[Fergus OMore]

All of this appeared in several references by Philf only in March this year.

Why the repetition at such a short interval, please?

Thank you Phil. I did read- well most of it.

Norman

[Arbalist]

Who's Philf? 

[Fergus OMore]

Philf?  Isn't he a Hero Member here with 500 odd posts

[philf]

Who's Philf? 

I'm philf but I don't remember anything about 45 degree squares!

Phil.

[Fergus OMore]

Correct me if I'm wrong but you listed the various books on machine tool restoration and measurement- one of which was Edward Connelly's treatise.
In Connelly, the details of the creation of 30, 45, 60 degree references were included using the 3 plate system which refers to both flat and angled work.

I recall fairly clearly what advice was there and used it many years ago.

I hope that this throws light on the matter

Regards

Norman

[philf]

Correct me if I'm wrong but you listed the various books on machine tool restoration and measurement- one of which was Edward Connelly's treatise.
In Connelly, the details of the creation of 30, 45, 60 degree references were included using the 3 plate system which refers to both flat and angled work.

I recall fairly clearly what advice was there and used it many years ago.

I hope that this throws light on the matter

Regards

Norman

Hi Norman,

Ah - now I understand - sorry.

Phil.

[Fergus OMore]

Phil,
       Amongst other things, I had to train my memory. Used something called Pelmanism and for my maths, I used Trachtenberg which was developed in a concentration camp- to keep the poor bloke sane.

As the years go galloping past, I'm glad- I think?

My regards- thank you for your most valuable contributions here.

Norman

[vtsteam]

Rich, your question is perfectly reasonable. It produced several interesting results. Glad you asked it.

[loply]

Hi guys,

Thanks for the replies.

In truth I don't have that much use for an incredibly accurate 45 degree square, but precision scraping has become something of a joy to me. I made by 12" master square which appears, as far as I can measure, to be within a few microns of 90 degrees 12 inches high, and I'd love a similarly accurate 45 just to complete the set. Within 10 microns would be nice and if I can get it within 5 I'd be chuffed for the rest of my days That kind of rules out any methods involving scribing though.

I'm aware that two 45s should make 90 which can be verified on a surface plate with an indicator easily but you'd need to make 3 to ensure you don't have a 44 and a 46... My next best idea is that I'd have to make a sine bar and set it at 45, then lay the 45 degree square in top and it should be flat... but then the accuracy is limited by the sine bar and the accuracy of all the gauges you used to prop it up. Maybe that's the best we can do though?

I like the idea about using the mill to drill holes in a triangle though. I feel like the general concept may have some mileage.

Will let you know how I get on,

Rich

[vtsteam]

Rich, there's a little confusion between distance and angle here.

Do you mean you want a 10 micron tolerance at the end of the new tool's leg, measured from a straightedge set at an absolute 45 degree angle to a baseline?

If so, and you give the length of the leg, the angular tolerance you want can be calculated.

You will obviously need some standard (no matter what method constructed) that is true to that angular tolerance.

Scribing can be extremely accurate if it is checked afterwards by reversal as mentioned earlier. If it isn't true after checking, whatever distance makes up the error can be halved and re-scribed, and then checked again. You can keep doing this until you are at the tolerance of a scribed line's thickness -- which at whatever distance out the leg extends is a tight angular tolerance indeed.

To get the last bit of tolerance possible, placing a straightedge on the scribed line, checking the workpiece against horizontal baseline straightedge. Layi another straightedge against the first angled straightedge and removie the first. This eliminates the visual aspect, and the thickness of the scribed line, and substitutes contact (which is the means of all scraping tests). Then the piece is placed against the second straightedge and checked for contact with the vertical 90 degree block edge.

When they both match side to side, by contact, it is as close as contact can measure. Which is as close as can be scraped by conventional methods.

[S. Heslop]

If it's triangular shaped couldn't you measure the lengths of the sides, and just make sure they match and the angle between them is 90 degrees?

[mexican jon]

I'm guessing that you can accurately check that you have 1 90 degree angle, therefore using pythagoras you can work out if the other angle you require is indeed 45 degrees. 

If it's triangular shaped couldn't you measure the lengths of the sides, and just make sure they match and the angle between them is 90 degrees?

Or you could just do what he said   

[Fergus OMore]

It's a bit early and the streets have to aired but surely Simon you have moved into describing and isosceles triangle which cannot have equal sides and 90 degrees somewhere.  If you split an isosceles triangle exactly down the middle you get back to the Euclidian solution of right angled triangles.

But enough 14 to 16 year old Matriculation antics, two practical thoughts emerge. The first is to cannibalise   a scrap machine tool to find the unworn sections and the second is to use things like Moglice, Devcon and Turcite in the construction of references.

These were not around when Connelly penned his epistle to the great unwashed.
My old mangle is running on Turcite!

Back to the coffee

Norman

[Bluechip]

 isosceles triangle which cannot have equal sides and 90 degrees somewhere. 

Back to the coffee

Norman

??? Surely a 45^o set square is just that  ......  two equal sides, ditto 45^o angles and 90^o at the apexy end ??

Enjoy your coffee, I'm back to fence painting ... 

Dave

[mexican jon]

 isosceles triangle which cannot have equal sides and 90 degrees somewhere. 

Back to the coffee

Norman

??? Surely a 45^o set square is just that  ......  two equal sides, ditto 45^o angles and 90^o at the apexy end ??

Enjoy your coffee, I'm back to fence painting ... 

Dave

What is needed here is a Isosceles Triangle    2 equal sides and 2 equal angles  and in this case 2 45 degrees and a 90 

[Fergus OMore]

Yes Dave- the coffee is not strong enough! Thank you.
I can't deduct 2 x 45=90 from 180 degrees.

I hope that I have not caused 'a fence' said he 'hedging' away. Lawn and ordure,
 that's me!

I ought to go back as a manure student

  arriba, arriba

Wor Norm

[awemawson]

Can one not precisely check or set angles by turning (and / or grinding) precisely sized disks and abutting them? Three such disks firmly in contact with each other can have straight edges tangentially touching two disks and forming an easily calculated precise angle between them?

[PekkaNF]

If it's triangular shaped couldn't you measure the lengths of the sides, and just make sure they match and the angle between them is 90 degrees?

There are some practical considerations on how sharp you can make the edges....therefore this is not very accurate.

Can one not precisely check or set angles by turning (and / or grinding) precisely sized disks and abutting them? Three such disks firmly in contact with each other can have straight edges tangentially touching two disks and forming an easily calculated precise angle between them?

Yesh, this is old "book" method and used to check squares etc. I would take some roller bearing parts or ball bearings or such. Surely there are three of them proper sized lurking somewhere? But you need a good square or four identical bearing rings to check the square first

Pekka