# segmented circle jig expanded



## DanKrager (Apr 13, 2012)

After a lot of searching about tapered staves (like for buckets) and segmented rings for turning I began to realize that there is an overlooked common element that is very useful for cutting accuracy and simplicity of layout. Both types, staves and segments, are symmetric about a centerline. So if a jig is devised that registers the difficult to cut tapered stave based on a centerline, the same accuracy of segmented ring pieces can be transferred to tapered staves without complicated geometry calculations. The segmented ring jig developed by Jerry does not specifically register on centerlines, but if it did, the result would be the same. Here is a picture of what I'm thinking.









I have long realized that cutting tapers on all sides of a stick (think table leg or handle) is greatly simplified to one jig and one setup if the stick is held between centers. When a "center holding" jig is used, one can easily cut as few as 1 side or as many sides as your index will accommodate. Try cutting a tapered triangular piece on any other kind of jig. Here is a picture of one I built for cutting octagonal blanks for lathe tool handles. The bar that runs in the saw slot can be adjusted to create a wide range of tapers. (see slot at far end). 









Since jigs accumulate like rabbits, I thought long an hard how to combine the function of these two jigs into one unit simply for conserving space. But the blending eludes me. The closest I've come is to reuse the sled between the two setups.

DanK


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## DLK (Nov 26, 2014)

Without the keywords which only just noticed I would not have a clue to you are doing. 
I think you are designing jig to make tapered sleeves that will fit together to form a frustum but I don't understand how your jig is working. What is the shape of the blank you start with? What is the relationship between the first and second picture? I think you meant tapered trapezoidal piece and not triangular piece? I may need to see it in action or at least a diagram showing a piece being cut?


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## DanKrager (Apr 13, 2012)

Combo, in my shop the first picture jig is conceptual at this point, and my description is terse in attempt to be brief. And I assumed that the segmented ring wedge cutting jig (at the top) was pretty common knowledge among those interested in these jigs. You are right about different shapes of frustums, but I was using wood workers vocabulary knowing that our math vocabulary doesn't translate well. (wife and I are math majors) It's very easy to take shortcuts and describe things as if people could read my mind! LOL.

One of the interesting things about the concept of registering on centerlines is that the shape of the starting piece is irrelevant, as long as it is big enough to obtain the piece of interest. The very common symmetry about a centerline can keep jigs very basic, simple, accurate, and compact. Centerline registration is a change of thinking from the much more common edge registration of woodworking. If one is interested in next level accuracy where cumulative errors are eliminated, centerline registration is an important notion. Machinists know this.

The commonality between the first and second picture is that both jigs rely on centerline registration. In the top view of the first picture Jerry doesn't explicitly refer to centerline registration to produce the ring segments, but his method produces the same result because of the relationship between the centerline of the starting piece and its parallel edges; unique in this case. The second and third views of the same jig represent a natural extension of the jig's potential. The jig in the second picture exists and I used it for shaping solid wood pieces symmetrically about an axis on a table or band saw resulting in polygon cross sections with as few as three sides. "A triangular cross section of a tapered piece" would have been the most accurate wording, I suspect. Pictures of this jig in action cutting octagonal handle blanks from unmachined split hedge log pieces are buried somewhere on this site and in my website blog archive, but I can't find the originals on my computer.

Thank you for your interest and vocabulary comments. I'm interested in feedback and useful clarity. I was about to build Jerry's jig just to get segmented rings for turning, but in a sleepless fit, I realized the broader potential for tapered stave vessels made simple.

DanK


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## DLK (Nov 26, 2014)

Thanks. As it turns out I am not familiar with "segmented ring wedge cutting jigs" , but happened to be a professor of mathematics. (Combinatorial mathematics.) So your wording was confusing to me although it might be more familiar to the wood turners. You might recall I only have a vintage hobby spindle lathe and so I do not have the experience to know what you were talking about and hence needed more precision in the explanation. No worries. All is good. I'll poke around and see what I can see about these jigs. Incidentally centerline seems very natural to me.


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## ArtMann (Mar 1, 2016)

Don, I can assure you that you aren't the only one who can't make sense out of the drawings and text.


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## DanKrager (Apr 13, 2012)

OK, let's try this on with better pictures. Keep in mind my intent is to make one jig that will cut segmented circle wedges (see Jerrys site) as well as progressively larger pieces for staved vessels and tapered stave vessels without complicated angle calculations. One jig.

1. If the vessel is to be tapered, set the jig fences to the desired taper angle of the work piece. If the stave is to have an overall taper of 2°, then the angle between the fences is 1°. If the vessel is not to be tapered, there is no need for this jig.
2. Tilt the saw blade the appropriate number of degrees for the number of sides of the vessel. 
3. Mark a center line on the blank piece perpendicular to a straight cut on one end. Place the straight edge of the work piece against the fence snugly and check the center line with a large square to be sure it is perpendicular to the jig fence. Secure it with clamps and make the first cut.









4. Rotate the work piece end for end without flipping it other side up and place it against the other jig fence, snugging it up to a width stop set for total major width. Check with a large square to be sure the center line is indeed perpendicular to the jig fence. Secure with clamps and make the cut.









That's about as clear as I know how to make it. It may be a while before I can actually build this and take pictures of it in action. I do want to turn a segmented bowl for a show coming up soon, so there's motivation.
DanK


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## Loren (May 30, 2008)

The angle of the taper affects the angle of the
saw blade. Up to a few degrees it can be
ignored, but as the taper of the staves 
increases gaps will open in the glue joints.
If memory serves the more the taper, the
more the gap on the inside of the form, 
but I could have it backwards.

It's basic trigonometry really.

I used to make ashiko drums years ago using
tapered staves. I used a jig that ran against
my saw fence with a couple of toggle clamps
on it. It was probably about 34" long to 
cut 30" staves. It had a simple fence with
adjustment slots to adjust the taper of the
staves. Setting the blade angle was difficult
in those days because there were no electronic
gizmos to do it with. I used a jig with a dial
indicator on it. Results were acceptable and
to some extent I ignored the trigonometry of
tapered staves even though I understood it.
Glue filled the inside gaps adequately and the
forms were not made to have a presentable 
inside surface.


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## DanKrager (Apr 13, 2012)

You got it right Loren. The gaps open on the inside between the tapered staves. I made the jig and it cut a 24 segment ring perfectly. Next I cut some tapered staves for a six sided tapered vessel and found that the blade angle has to be about 28.5°. With a 30° setting of the blade the inside of the joint gap was estimated close to 1°. If I were going to be doing a lot of these vessels, I would use the compound angle calculator or use the free paper
template generator. There is a Droid app for a fee. 




































The tapered vessel is still in the clamps.

DanK


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## DanKrager (Apr 13, 2012)

Got the vessel out of the clamps this afternoon. Not bad for guessing. In the future, the calculators will be used to set up the jig and blade to the correct angles.










Next up, I'll try to use the calculators to determine the correct angles to use for a tapered stave "leg", something long and skinny. I'll need to put the clamp grooves in the jig because they are critical to accuracy.

DanK


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## wormil (Nov 19, 2011)

This is cool. Are you really saving any space combing the two?


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## DanKrager (Apr 13, 2012)

I don't really think I can combine the two jigs above. It was a passing consideration. Gas, you know!

But this does save a lot of special purpose jigs, two for every tapered assembly. And in principle it offers quicker precision. It might only be useful in a custom shop that does all sorts of constructions from time to time. In a hobby shop where a single use is planned, then disposables are the way to go.

DanK


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