Cutting Polygons

[Jacob Snow]

I am making drinking mugs from slats by taking 360 dividing by the number of sides, then beveling the edges of boards at half that angle then gluing them together and attaching a handle. I am trying to find an accurate way to cut the bottom for the mug (aka how do i get a uniform 10, 8,7 , 6, etc...) sided shape. anyone have an thoughts?

[Mark Patoka]

Are you trying to fit the bottom inside the mug so you wouldn't see it or just attached it to the bottom? If it's to the bottom I would trace the final shape onto the piece and and cut it close using a scroll or jigsaw. Then attach it to the bottom and using a flush cutting router bit or sander to flush it all up.

[Dave Novak]

Hopefully not too far off the OP's question, but just an expansion - I've forgotten the formula for calculating the length of the sides. For example, if I want to make an octogon table top that is 6 foot in diameter, how do I calculate how long (wide?) each of the 8 sides will be?

[Roy Harding]

Dave:

You're looking to calculate chords. There's a great discussion (complete with formula's) available here:
http://www.woodweb.com/knowledge_base/Calculating_RadiansChords.html

[Scott Rychnovsky]

Jacob,

I would suggest picking one polygon and then changing the size. That way you can make a jig to cut just that angle and not have to mess with changing the angle for every figure. (If you need to use different numbers of sizes then the project is doable, but it is more complex.)

Octagons are easy. The sides are all 45 degrees from the adjacent side. You could cut it on a miter saw or set up a special jig on a table saw (or band saw) with a shooting board.

Here is a way to do it with a shooting board. Mount a 1/16" inch nail facing up on the shooting board to use as a pivot. It should be 1/2 the short diameter from the saw edge. (Adjust this distance to make different sizes.) Drill a 1/16" inch hole in your work piece and place it on the pivot. Now the piece will spin around a fixed distance from the saw edge. This arrangement fixes the size of the octagon (or other polygon). All you need to do now is to control the angle of each face.

To cut a polygon, start by holding (or clamping) the work piece in one position on the pivot and make a cut with the table saw. This gives you a flat edge to work with. Now turn off the saw and rotate the work piece towards you. Use a 45 degree angle ( a drafting triangle works great) and set the first cut face at exactly 45 degrees from the saw blade. Hold it or clamp it an make the second cut. Now you have two sides cut at 45 degrees apart. You can continue around the figure until you have all eight sides cut.*

To make a different size polygon, use a different angle between the faces. It is too late tonight for me to work through the geometry for a general solution for the angle to give the different polygons. (A triangle is 120, square is 90, and hexagon is 60, an octagon is 45 and I forget the others.) (OK, now I remember. The angle between adjacent sides in just 360/n, where "n" is the number of sides. Go crazy and make a 13-sided figure.)

*Once you have two adjacent sides cut for an octagon, you can finish up easily because all the other sides are either parallel (use a fence) or perpendicular (use a shooting board). If your jig is set up well it is easiest to just proceed around the figure.

Have fun with your project.

Scott

[Mike McCann]

here is a nice octagon calculator. You chnge one valus it will change them all.

http://www.members.cox.net/ultimate_poker_table_top/Octagon%20Layout%20Calculator.html

[Lee Schierer]

I would glue up the polygon sides of the mugs with how ever many sides they need. Then glue the tubes to a square piece of the base material. Chuck up a flush trim bit with the bearing on the end of the bit in my router table and route the bottoms to the perfect size and shape of the tubes. This method will use a bit more wood, but will be much faster than trying to cut exact sized bases to glue on.

[Alan Schwabacher]

If your polygons have enough sides, or the slats are thick enough, you can make the bottoms round, and set them into a rabbet cut into the bottom of the slats using a template and a top bearing bit. A circle is faster to cut accurately than a polygon.

If you do want polygons, Scott Rychnovsky's approach is general. (Hi Scott! It's nice having a distinctive name, isn't it?) The reason you don't see too many polygonal structures with funny numbers of sizes is that precision is tough with general methods. There are special tricks for specific shapes. Here's one for octagons:

First, make a crosscut sled with a fence absolutely square to the miter slot. Google "5 cut method" for a way to calibrate it to extraordinary precision. A stop block on the fence is all you need to cut squares of precise and accurate dimension. To convert these to octagons, you need to clip the corners. You want to place the square so the diagonal line from corner to corner of the square is parallel to the sled kerf, spaced away from the cut line by half the length of the side of the square. Position it by carefully measuring from corners to kerf, and screw two blocks to the sled that fit against the centers of two sides. Make sure the blocks don't get in the way of cutting the squares in the first place. Now put the squares against the blocks and cut off the corners.

Make two octagons, and check that the edges are all identical. You are unlikely to be able to position the blocks well enough by measuring directly, but a rabbet plane, sandpaper, or glued on paper should adjust the block position to the point where deviations from dimension are unmeasurable.

[Scott Rychnovsky]

Hi Alan,

Is that you, THE Alan Schwabacher?

How is life? Send me an e-mail.

Scott

[Dave MacArthur]

Don't cut a polygon to perfectly fit inside. Rout or drill out the bottom of your mug into a circular rabbet, which is easily done with a router template placed on top of your mug. Now place a circular bottom into the mug. MUCH easier, MUCH better/tighter fit.

[Jacob Snow]

How do i rabet out a circle on the bottom of the mug. I a real beginner when it comes to using the router and router jigs...

[Jacob Snow]

Bump for some advice :)

[Greg Hines, MD]

I would rabbet it out with a hand held router, after you have glued it up. You will need some kind of fixture to hold the workpiece for milling. Maybe use a round template held to center the workpiece, and then a straight bit and rub collar to form the rabbet.

Doc

[Jacob Snow]

So i am still struggling trying to figure out how to rabet a circle in the bottom. Does anyone have and example jig or some pictures so i could see how to do it?

[Greg Sznajdruk]

These two tools may be of some interest to you.



http://www.leevalley.com/wood/page.aspx?c=1&p=32521&cat=1,240,41064 (http://www.leevalley.com/wood/page.aspx?c=1&p=32521&cat=1,240,41064)

http://www.leevalley.com/wood/page.aspx?c=1&p=45160&cat=1,46168,46174 (http://www.leevalley.com/wood/page.aspx?c=1&p=45160&cat=1,46168,46174)

Greg

[Dennis Lopeman]

If your polygons have enough sides, or the slats are thick enough, you can make the bottoms round, and set them into a rabbet cut into the bottom of the slats using a template and a top bearing bit. A circle is faster to cut accurately than a polygon.


AWWWW - that is what I was going to suggest.

My approach to many things is: "How do I get the same or better results by doing things the simple way??"

The rabbit cut should work if the pieces are thick enough, and if there's lots of "sides"...

[Dennis Lopeman]

So i am still struggling trying to figure out how to rabet a circle in the bottom. Does anyone have and example jig or some pictures so i could see how to do it?


Uuuuhhhhhm.... have you already glued the sides together???? I think you would have cut the rabbits BEFORE you glued... and then glue and join the pieces, aligning all your rabbits...

Kinda like getting all your ducks in a row, but with rabbits instead!! LOL :) :)

[Brodie Brickey]

How big is the cup? If the diameter at the bottom is 2 3/8" or smaller, consider a forstner to create a rabbited shelf and insert a circular plug.

Check out this article by Malcolm Tibbets. In it he plugs the bottom of a mug. Mind you, he does use a lathe. See picture steps 3-6.

http://www.smoothturning.com/shop/gallery/TravelMug.pdf