I need to cut lots of identical parallelograms from stock that’s about 3/8″ thick. Each one will be about 2″ point-to-point and about 1″ wide. The parallelograms will be combined to make hexagons. The hexagons will be combined into a larger field. (see attached pic) In order for it all to work, all of the parallelograms must be exactly the same size. Just to add complication, each edge will also need to be slightly beveled because I plan to lay them up in an arch. Does anyone have any tips or jigs they’ve developed to provide this kind of repeatable accuracy?
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Love Math
What is the end goal for this thing? Looking at your picture, it would seem that the point-to-point width of each parallelogram would need to be a multiple of the radius of the circle - so are you working with a definite radius for your arc or are you letting the parallelogram width determine the final size of said circle? So long as you stay in the 2D world and don't plan on making it into a sphere, the math and angles are fairly straightforward. The best tip I can give you is plan out your operations correctly and mill all the stock you need at the same time - by doing each task at the same time on all pieces the machine setup should stay consistent and yield good results. Most of these operations can be accomplished at the table saw with a good miter gage w/fence and stop blocks.
However, I do not see how you would "bevel" the edges to lay them in an arch - from your picture it looks like you want a set field of hexagons contained by a given arc or circle, a 2D plane, versus that set being contained in a sphere which would introduce compound angles on each side of the polygon in 3D. If you can clarify that bit I can answer your question a little more precisely.
I hope that helps.
-Ian
My goal is for the pieces to become a banjo resonator. The back of a resonator has a relatively slight arc. I plan to lay it up in a form. The result will be a faceted arc which I will turn to make smooth.
OK so you will not have to build that arc into the resonator if you plan on turning it to shape, and thats a good thing (less figuring).
I would be concerned about the setup holding together while turning, even if it was restrained in a form. The problem is that glueing the polygons together is essentially going to create a lot of butt-joints which is not the most mechanically sound way of joining pieces together.... I have a lot of faith in polyurethane glues (which I would reccomend for strength and flexibility) but the centrifugal force and torque that will be applied to this while turning could be destructive, even at low speeds. This will become more of an issue the more material you remove to radius the back. You may want to spline the joints between the polygons and their pieces to give some long-grain to long-grain contact for the glue to have maximum strength - that is as simple as running the contacting faces through a slot cutter on the router table and fitting a spline in the groove.
I would also make a full-scale drawing of the resonator and its component pieces before cutting anything - that way you know how many of what type of piece you need as well as total stock requirements.
-Ian
I can think of two ways to do this that avoid the horrendous beveling issue.
1. As suggested by cedargroves, glue up a turning blank thick enough to be turned the shaoe you want. End-grain glue joints don't have as much strength as edge-grain glue joints, but they can still have plenty, especially with hot hide glue. I've read 80%. For additional safety, glue the whole thing to a sacrificial board/check. You can cut it loose after you're done.
2. You could create your desired pattern as a marquetry sheet, and apply it to a solid wood resenator.
If you have good turning skills, try #1. If not, I think #2 would be the easier path.
Good luck,
Chuck
Foot powered saw.
Not so long ago there was a video about a man who was doing exactly what you are talking about on a table saw powered by a peddle mechanism similar to a bicycle I just googled foot powered table saw and came to the clip. it is fascinating to see him cut the pieces one after another on this saw that used no electricity. They show some jigs he uses. I remember seeing another clip which showed more of the cutting, but who knows where that is. I think it is a man named Robin Tucker and a Company called Wood Mosaic.
The pieces he assembled of geometric patterns was also quite impressive. So there is a place to start.
Peter
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