Trircle Bowls

by rschoenm

24K14524

Intro: Trircle Bowls

Yes, you read that right: trircle! I’ll show you how to make uniquely shaped bowls on a bandsaw with a really simple jig. Using the technique you can make oval, triangular, rounded rectangle, and rounded five-sided bowls. As an added benefit, you get more than one bowl each time and they will perfectly nest to make a complete set. I’ll describe the technique by making a trircle bowl set; that is bowls with a roundish triangle shape.

The name of the actual shape shown here appears to be unsettled. I like the name “trircle”, it’s a tongue-twisting combination of triangle and circle. Here are a few other naming options being discussed by the graphic design and mathematics communities: tri-oval, trircle, egglipse, 3-lobed epitrochoid, trifocal ellipse, 3-ellipse

I will show a lot of pictures. Take a look at them, they are annotated throughout for additional information!

STEP 1: Fusion 360 Model of the Trircle

Before we go into the workshop, let’s model these bowls in Fusion 360.

Use the attached Fusion 360 file (triangular bowl parametric.f3d) to follow along for the trircle. I made the design parametric so you can change the shape and size of the bowl; and get the relevant measurements for making it in your shop.

If you want to go straight to cutting bowls skip to step 3 to make a bowl set from the attached pdf templates.

Load the Fusion 360 file in the ‘Design Workspace - Solid’, and go to ‘Modify’ > ‘Change Parameters’. You should see a screen like shown in the second image above.

The shape of the bowl is determined by the radii of the two different arcs forming the sides.

You can change these two parameters: the large_arc and the small_arc

The ‘diameter’ d of the bowl is then given by d = large_arc + small_arc

If the values of the large_arc and the small_arc are close to each other the bowl shape approaches a circle. A good range for a pleasant looking trircle is for the small_arc to be somewhere between 10% and 50% of the large_arc. The example we are making below has the values of large_arc = 5.5 inches and small_arc = 1.7 inches, resulting in a 7.2 inches ‘diameter’ bowl - measured at the bottom. The top of course is larger because of the angled sides!

You can change large_arc and small_arc in Fusion 360 and immediately see the resulting bowl shape. In the parameters window click on the ‘Expression’ for large_arc or small_arc to change its value. The values are assumed in inches. The animation in the next step shows a trircle going from 0.4 inches to 5.5 inches for the small_arc parameter.

STEP 2: More Model Parameters

Other parameters you can change are:

(1) the angle of the sides of the bowls

(2) the height of the bowl sides

(3) the wall thickness of the sides

Keep the parameters at reasonable values otherwise the results become unpredictable or break the model.


The last parameter is calculated:

triangle_side = (large_arc - small_arc)

You will need this measurement to lay out and cut your own bowl design as described below. In our example triangle_side has a value of 3.8 inches (5.5" - 1.7" = 3.8").


Once you have a design that you like write down the values for triangle_side, angle, height, and thickness. You can also do a screen capture of your design and parameters in Fusion 360. Now it’s time to actually make the bowls.

STEP 3: Make a Bowl Blank From Wood Segments

It is easiest and looks best to glue up three layers from six segments each as shown. Each segment is 6.5 inches long on the outside, 3.5 inches wide, with 30 degree miter cuts on both ends. Attached is a sketch (triangular bowl section) of the layout with dimensions. Six segments make up one layer ring. Glue three segment pieces together, then trim straight on the table saw for a perfect fit. Make three rings and be sure they lay flat; some planing/sanding might be required.

Make a bottom board that is about 12 inches by 12 inches square. Mark an equilateral triangle with a side-length of triangle_side from step 2 in the center of this board, and drill 1/8" holes A, B, and C through the board at the triangle corners. It is important that the spacing of the three holes is accurate and equidistant (e.g. 3.8 inches). The attached pdf file (triangular bowl sketch) will help in the layout.

Now glue up the layer rings to the bottom board, rotating each 30 degrees from the one below. This will overlap the seams for a stronger bond. Be sure that the three triangle holes are accessible for inserting the pivot pins later on. Trim the excess corners off the bottom board.

STEP 4: Trircle Cutting Jig - Very Simple!

You are ready to build a very simple cutting jig. Take a 12” by 15” MDF or plywood board (actual dimensions are not very critical) and draw a line across the center, from one side to the opposite side, not diagonal! Mark the hole locations A and B on the center line, 6 inches and 9.8 inches from the edge as indicated in the pdf drawing (jig dimensions). Drill 1/8” holes through the jig board at A and B. They need to be spaced exactly triangle_side inches (e.g. 3.8 inches) apart to exactly match the holes of the bowl blank from the previous step.

For cutting I am using a 1/4" wide bandsaw blade. Set your bandsaw table to 25 degrees (the angle from step 2 above, or whatever angle you designed for the side of the bowl - 10 to 30 degrees is good); and set the fence to about 2” from the blade. Make a single cut into the jig up to the center line. Clamp a stop block to the fence against the jig so that you can reliably repeat the cut to the centerline in the following steps.

STEP 5: Cut the Trircles


The video animation shows how the trircle cutting technique works.

Place the bowl blank on the jig so that you can insert two pins (8d nails work well) through holes A and B into the holes in the jig. You are ready to cut the perimeter of the first bowl.

Turn on the band saw and run the jig against the fence up to the stop block/centerline. This will make a tangential cut into the bowl blank. Turn off the bandsaw. Clamp the jig to the band saw table so it won’t move or slide off, or hold it in place. Then remove the pin from hole A (closest to the blade), turn on the band saw, and slowly rotate the bowl blank clockwise to continue the cut. You pivot around point B. Stop when hole C lines up with the open hole in the jig, i.e. at 60 degree rotation. You completed the first large arc cut. Turn off the band saw.

Insert a pin through hole C into the jig, remove the pin in hole B, and make the next 60 degree cut until hole A lines up with the open hole in the jig. As you pivot around point C you make your first small arc cut.

Then repeat the same procedure making 60 degree large/small cuts until you made it all the way around. Turn off the band saw and unclamp the jig. Carefully back the jig out from the blade and discard the outer waste piece.

The technique works by cutting consecutive arcs at 60 degrees each. A large diameter arc is followed by a small diameter arc, large diameter arc, small diameter arc, etc. The transition from large to small to large is perfectly smooth.

Again, check out the "Cutting a Trircle Animation" at: https://youtu.be/-F7vzGYhPi4

Move the fence to the left by about 1/2” (12 mm). This determines the wall thickness of the bowl. Then repeat the same procedure as above. When you are done you will have the first trircle shaped wall-ring. There is a tangential split (entry cut) at the start of the ring that you will have to glue back together. I have found that with careful cutting/glueing the split is nearly invisible in your final bowl.

Continue cutting wall-rings until you run out of wood towards the center, or until the blade gets too close to the pivot points and can't cut the small arc. The last picture above shows the bottom of the bowl blank where I was unable to cut the very small radius around the pivot.

The resulting bowls will nest nicely into each other. Depending on your glued-up blank and angle you may get from two to four nested bowls.

STEP 6: Alternative Glue-up

I prepared a different bowl blank that may be easier to make; but not as good looking. It is also a little more difficult to cut the wall-rings cleanly as the bandsaw blade tends to follow the long-grain. Pictures only!

STEP 7: Finish the Trircle Bowls

After gluing the split in each wall-ring together you need to sand the inside faces smooth to your liking. Do this before attaching a bottom. Then prepare some boards, 1/4” to 1/2” thick for the bottoms. Cut them a little larger than the bowl bottoms. Glue four small spacers to the bottom around the outside of the bowl like shown. This will keep the wall-ring from sliding around when you glue it to the bottom. Carefully glue the wall-rings to the bottom, and trim flush after everything is dry. Sand the outsides, and apply food safe finish of your choice. 

STEP 8: Wait, There Is More!

You don’t have to stop at trircle bowls. The same approach can be used for oval, rounded square/rectangle, five-sided pentagon shaped bowls, and even higher polynominal shapes.

Ovals: use four pivot points, and e.g. 38 degree and (180 - 38) = 142 degree arcs (angles vary with design)

Trircle: use three pivot points as shown in this Instructable, and 60 degree arcs

Rounded rectangle: use four pivot points and three different arcs

Pentagon: use five pivot points and 36 degree arcs

Fusion 360 model renderings are shown, but I should mention that I haven’t made these in my shop yet. If you do please share with the Instructable community! I can share my parametric Fusion 360 files for these designs if there is interest.

Of course you can also 3d print the bowls from the Fusion 360 mesh files! I’m showing one small trircle bowl, just for fun!

And the last picture is a ceramic bowl made with the help of a wooden trircle mold.

20 Comments

ChrisWx 1 year ago

That's a pretty advanced band saw technique. If you aren't experienced with using a band saw with a jig, doing stop cuts, cutting continuous curves, or cutting on an angle, you may want to practice on a smaller, less expensive glue-up. Hints: Do Not Rush the cut (good rule for every band saw cut!). Use a thin blade - a wide re-saw blade is going to bind, and even a 1/2" blade may be too much for the tighter inner curves. The author looks to be using a 1/4" blade - perfect for those kinds of curves. And if your band saw hasn't been tuned up in a while, you're going to be disappointed with the quality of any (vertically) long cut, but especially with something like this. Bad blade tension, worn, loose or badly adjusted guide blocks, will cause your blade to go places you don't want it to.

rschoenm 1 year ago

Thanks, you are making very valid points. I started out a few years ago by making round bowls ( https://www.instructables.com/How-to-Make-Wooden-Bowls-Using-Your-Bandsaw/ ), then angled round bowls ( https://www.instructables.com/How-to-Make-an-Angled-Segmented-Bowl-with-Your-Ban/ ), and finally these 'Trircle' bowls. Use glue-ups from inexpensive pine/fir boards for practice. Use a 1/4" or smaller sharp blade. Set your guide blocks/bearings as low as possible for the cut. Proceed cutting slowly but steadily. The end result is fun and satisfying.

cjwmarin 1 year ago

Hermosos. Que gran trabajo.

bippy8 1 year ago

Congrats. Amazing bowl. I might try it .

rschoenm 1 year ago

Thank you! If you make a set of bowls, please share with the Instructable community!

Dwargh 1 year ago

Awesome technique! :-D

rschoenm 1 year ago

Dankeschön 👍 Eine Kombination von Mathematik, Ingenieurwesen, und Holzarbeit. Macht immer Spass!

Dwargh 1 year ago

Well, this is what this work looks like!
So schaut die Arbeit auch aus! ;)

LeslieGeee 2 years ago

Your bowls are beautiful and your name for them is a tongue twister (take the 2nd R out) but once you get past the initial pronunciation it's fine. The only problem with the name which I like is that this technique can be any shape which the name doesn't match. Because my brain has to solve problems I think the name "Fusion Ware" might be a good one because it may cover everything about this items construction. You are fusing pieces of wood together in order to make beautiful products. Plus the name tips the hat to the program used to make the bowls. The "Ware" gives you the latitude to make ANY shape whether a bowl or plate or dough bowl or even a pitcher without having to worry about does the name suit the shape. If the word Tricle is still wanted you can make the name "Tricle Fusion Ware". :)

rschoenm 2 years ago

Lots of play on words :-) , I like it!
So we should name the technique "Fusion Ware Ircle Bowls". No sharp corners allowed! You can make oval, egg-shaped, trircle, squircle, rectircle, pentircle, and polygircle Fusion Ware! Other suggestions welcome :-)
Thanks for your comment!

ArthurJ5 2 years ago

I’m going to try this. I’ll tell everyone I did it on my lathe. =D

Edit, I had a thought that with six pieces in a ring you could use either two or three contrasting woods, also you could make layers of different thicknesses. Another idea is to make two bowls one tall and the other short and use the short one upside down for a base. I’m really excited to go make some sawdust now, thanks for the inspiration!

Dmotoguy 2 years ago

As a full-time woodworker who has a CNC but not a bandsaw (someday I hope), I'm always impressed by your creativity and talent, whether it be in software or wood. At first glance I thought you had misspelled the name of these (because it's so awkward to pronounce) and that perhaps they were closer to a Reuleaux triangle, so your explanation was a good idea. Thanks for sharing it and as always, nice job!

rschoenm 2 years ago

Thanks! I thought Reuleaux triangle at first, but its different as the trircle has no sharp corners. I suppose if you set the parameter small_arc in the Fusion 360 model equal to zero you would get a Reuleaux triangle. It does break the model as is at small_arc = 0, but you can see an almost Reuleaux triangle at small_arc = 0.01 inches, see attached image.
Thanks again for you kind comment.

Nick70587 2 years ago

These look fantastic. Good work. I'm partial to egglipse my self.

rschoenm 2 years ago

Thx. Maybe we'll take a vote on the name in a little while :-)