Some of you may be familiar with "Segmented Turning", a technique in which you glue wedges of wood together into rings then glue those rings together to make a vessel or platter. You can see some examples here: https://www.google.com/search?q=segmented+turning&rlz=1C1AVFA_enUS760US760&sxsrf=ALeKk03Np8enC6eccic2UrTNWdKgPcbirQ:1589782971560&source=lnms&tbm=isch&sa=X&ved=2ahUKEwiSqaiK47zpAhWWtp4KHZIACcgQ_AUoAnoECBEQBA&biw=1920&bih=843
As you can see, they can get quite complex.

Critical to the successful construction of the rings is absolutely precisely angled wedges. For example, if you wanted to make a ring with 7 segments, the half-angle, (the angle of ONE of the sides of the wedge), would be 360 (the number of degrees in a circle), divided by twice (2*) the number of segments (7) in the ring: 360/(2*7) = 25.714 degrees. The thousandth of a degree MIGHT not be critical, but I can assure you that the 100th of a degree is. Especially when the number of segments and the diameter of the ring get large.

There is a fellow 'out there' that created a jig to make the wedges, and offers for sale a series of angular templates - called "wedgies" - that facilitate cutting 'perfect' wedges for segmented turning constructions. You know me, I can't see paying for something that I can make. Furthermore, why own a bunch of machines to MAKE STUFF if you're not going to use them. However, cutting wedges of wood to a precision of 0.001-ish degrees ain't easy. That's why MANY people that want to get into segmented turning buy this fellow's "wedgies" - at $50 a pop for a 'set' of 5 (I think). There are about 5 sets you can buy. That's $250 JUST FOR THE TEMPLATES to cut the wedges!

Anyway, I set out to 1) make the jig to cut the wedges, and 2) make my own "wedgie" templates to use to set up the jig. Parts of the jig are pretty 'bog standard' woodworking jig precision. However, there are a couple of fences that have to be better than 0.001" parallel on two of their sides. THAT ain't 'bog standard' woodworking precision. In order to make those, I had to make yet another jig: A crosscut sled for my table saw. So... I had to make a jig to make a jig!

Here's a picture of the crosscut sled (with it's adjunct jig for cutting precise 45 degree miters):


With that sled, I can cut a four-sided piece of wood with sides 15" long in which the width of the square (the parallelism of the sides), is less than 0.001" out of square (parallel) over that 15". With that sled, I can cut the fences for this jig:

the wedge-cutting jig. Those two adjustable fences you see have to have sides that are parallel withing 0.001" over their 12" lengths. You'll see in a minute why that is so.

After constructing the two jigs, (two day's work), I tested the wedge-cutting jig by cutting wedges for a 7-segment ring, 3" in diameter. (A 6 or 8-segment ring would have been too easy. ) Wait a minute! I don't have the "wedgies" templates to get those fences set to precise angle to ensure NO gap in the fitment of the wedges creating the ring. Oh dear! What ever shall I do?

There's a device/tool used in machining called  a "sine bar". I won't go into it's theory here, but suffice it to say that it allows one to set up any angle from "zero" to about 60 degrees with extraordinary precision. The angle I needed for the 7-segment ring was 25. 714 degrees. However, the sine bar is not the only 'thing' you need to set up a 'workpiece'. The sine bar works based on Pythagoras's theorem of right triangles. Since I know the EXACT length of the sine bar, I can 'raise' the bar a specific amount and achieve ANY angle my little pea-pickin' heart desires. However, the precision of that 'elevation' AND a reference "0 angle", determines the precision of the angle. Here's a picture of the jig with the sine bar in place. It will help me explain the "wedgie" setup:


Annotated, you can see the sine bar, a "1-2-3" block, and "precision blocks". Not annotated because I assume everyone here recognizes a "square", is the "zero angle" reference line. In order to get that 25.714 degree angle, I have to raise one end of the 5" sine bar to a height of 2.169". Try measuring that on a wooden jig. Fortunately, I don't have to measure it. The "1-2-3 block" is precisely dimensioned to 1" x 2" x 3". Hence the name. Using the 2" dimension, I have the 2" I need. Next comes the precision blocks. The set I have goes from 0.050" through 0.500" in 0.001" increments. These blocks' calibration can be traced to the NIST. (https://www.nist.gov/) By putting the 0.050" and 0.119" blocks together, I get the 0.169" I need to add to the 2.000" of the "1-2-3 block" for a total of PRECISELY 2.169". With one leg of the square against the 'cutting edge' of the jig and the other perpendicular leg against the sine bar, I can set one 'round' of the sine bar against the fence and 'elevate' the other end by exactly 2.169" to achieve the angular relationship of 25.714 degrees of the fence to the cutting edge of the jig. Voila! No $50 set of templates required! Of course the template would have had the jig set up to the proper angular relationship in seconds, instead of the minute or so it took me to set up the sine bar. I can live with that. However, ultimately, I'll cut my own set of templates using my mill and some fairly stable material - aluminum or corian or ...? That aside, 'the proof is in the pudding'! I cut 7 wedges.



And the back side:

(There's a rubber band holding it together.)

That, my friends, is "good enough". Of course, 7 segments is not very many, and 3" in diameter is pretty small. Nevertheless, the fit is good enough to tell that using the sine bar will 'work' until I get around to making templates for EVERY number of segments from 6 to 53. (53 because it's a prime number, and I intend to use rings with prime number segments.  This is what j0e_bl0ggs would call "Making a rod for your own back.")

To tell you the truth, the primary reason for making this post was to demonstrate the use of the sine bar in a woodworking problem. For machine work, it's 'old hat', but I thought it was kinda novel for allowing me to get around buying a bunch of templates that I could 'make'.

Once again, I am reminded that selling an ATV, its trailer and paraphernalia, and using the proceeds to buy a metal-working lathe and mill, was one of the best things I have done in my life.

Paul

I guess I didn't really 'close the loop' on the reason for the required level of precision:

Whatever error is present in one segment is multiplied by the number of segments. So a 0.001" error in the cut of a wedge from  20-segment ring, (fairly common number for a ring), is 0.020". That's a "huge" gap when the glue-up comes and will be very visible in the final piece. Make the error 0.005", and the gap becomes a 10th of an inch.

Paul

Quote from: gitano;155015I guess I didn't really 'close the loop' on the reason for the required level of precision:

Whatever error is present in one segment is multiplied by the number of segments. So a 0.001" error in the cut of a wedge from  20-segment ring, (fairly common number for a ring), is 0.020". That's a "huge" gap when the glue-up comes and will be very visible in the final piece. Make the error 0.005", and the gap becomes a 10th of an inch.

 Paul

Which, to the nekked eye would be barely noticeable to even the most discerning.

However, chuck it up in a lathe and start spinning it at 800~1000 RPM and that 1/10th of an in translates into vibration and general ugliness, and the possibility of extreme hazard.  

Large(r) diameters make for high(er) peripheral speeds.
When large diameters are coupled with the inherent variations in wood densities, it's easy enough to get things out of balance.
Throw in dimensional variations and you've compounded the problem.


Goodonya for coming up with a way to bring more precision to the (typically) un-precise material we use so much, but often understand so little about.

Sine bars, 1-2-3 blocks  & precision gauge blocks come in handy for lots of things in the machinist trade  as well as  other things. A good granite surface plate is necessary in many circumstances. Especially    in the tool  making trade. I loaned a friend my precisiom gauge blocks & his shop burned up. I never was paid for the gauge blocks. When I retired, I gave my son most of my precision tools. I kept my set of Starett O to 6 inch micrometers. .......Paul, that's a beautiful job in wood. I never had much interest in woodworking. I suspect most people have no idea what  you're talking about. Not many people are toolmakers though. Thanks for sharing some light on intricate and precision woodworking. ......Paul H

Thanks, Paul and Jamie.270.

At the moment I'm working on a design for a segmented vessel. Funny how design is constrained by availability of tools. The jigs I made are just one example. When I get the design figured out, I'll let 'you' know and post some pictures of the layout before I start the construction. I'm toying with the idea of making all the rings have the same number of segments but alter their thickness and of course material. I'm thinking of using some aluminum and/or brass. That will require some extra 'thinking'. I am going to try to incorporate some bone. It may be black bear, moose, or bison, or all three. (Bones I have on hand.) Anyway, like I said, once I settle on a design, I'll post more of the 'processes' here.

Paul