Project by JoshLawson |
posted 03-12-2010 01:35 AM |
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27 comments |

I made this router jig to shape a slight curve into the seats on a set of bar stools I recently made. I new the rough shape I wanted the curve to be based on the size and thickness of the seat.

Ok, so I’m guessing some of you have already glanced below and begun panicking about the equations below. Yes. I am an engineer (and quite a nerd) and yes, I did solve simultaneous equations to design this jig. Could you make this jig without it? Sure, but it would take some trial and error.

The seat width was 15” wide by 1” thick. I wanted the curve to cut into the seat by about 3/8” and for the curve to meet up with the edges of the pieces (so as not to waste any material). This set up my equations to determine the desired radius.

The equations are as follows:

D = R – cos(theta)R

W = 2sin(theta)R

where

W = width = 15 ”

D = depth = .375

R = Radius (unknown)

theta = angle (unknown)

If anyone is still with me after opening this harmless “project” only to find trigonometry embedded… You can theoretically simultaneously solve these equations, but most often calculators (even the nicest graphing calculators) will balk at the trig functions in the equations. So the simplest method is to solve for D and substitute in different values of theta (0 to 90 degrees) until you get a close enough answer for R. I happen to have access to The Mathworks software at my workplace which made this much easier.

D = W/(2sin(theta)) – cos(theta)W/(2sin(theta))

You’ll find that the equation evaluates to true around 5.75 degrees. Substitute that back into the original equations and solve for R and you get: R = 75” (if you want to be very precise you can add some distance for the offsets due to your router setup).

Now, done with the boring stuff all you have to do is go about making a giant trammel, tracing out the arc on a piece of MDF, and assemble the jig.

The router mount is pretty simple, just some 1/18×1” angle aluminum coupled with some 1/4” x 1” aluminum flat stock on the ends. I made a simple square piece of MDF to replace the router base plate and mounted that to the angle aluminum.

When using this setup you’ll need to be very careful, taking shallow cuts, since this is essentially free routing.

Post Script:

After reading the comments below, someone mentioned a simpler way to do this – without the messy trigonometry. That got me thinking… So I looked into some alternate solutions. If you use the Pythagorean theorem and derive the neccessary equations in terms of the variables in the Pythagorean theorem you can simplify it to a** much **simplier equation.

R = (D^2 + W^2/4)/2D

Easy!

Thanks Ger21 for the tip!

-- Josh Lawson - Ankeny, Iowa

## 27 comments so far

Earlb

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48 posts in 2019 days

#1 posted 03-12-2010 01:44 AM

do the math and you get what you need instead of what you hope is correct. nice looking jig there.

-- It is all in your perspective.

Beginningwoodworker

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13347 posts in 2673 days

#2 posted 03-12-2010 01:45 AM

Nice looking jig.

Maveric777

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2692 posts in 2077 days

#3 posted 03-12-2010 02:27 AM

All the math makes my head hurt. Cool jig none the less…..lol

-- Dan ~ Texarkana, Tx.

Jeison

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947 posts in 2108 days

#4 posted 03-12-2010 03:24 AM

Math = Perfection

Trial & Error = More Sawdust + Profanities.

Therefore, logically, Trial & Error > Math

:D

also cool jig :)

-- - Jei, Rockford IL - When in doubt, spray it with WD-40 and wrap it with duct tape. The details will attend to themselves.

Bob Areddy

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177 posts in 2402 days

#5 posted 03-12-2010 03:37 AM

Josh, I did something similar when making some curved backs for a chair. I’d like to make a suggestion, though. Instead of mounting the router base to the aluminum, I would let it move side to side, and then bolt two pieces of mdf (or some other square stock) to the angle aluminum on the outside of the wood frame. This will insure that the aluminum runs perpendicular at all times to the jig instead of getting skewed.

-- --Bob http://www.areddy.net/wood

DocK16

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1162 posts in 3087 days

#6 posted 03-12-2010 03:57 AM

You lost me at D= but I get the idea. Nice bench underneith.

-- Common sense is so rare anymore when you do see it, it looks like pure genius.

AaronK

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1411 posts in 2464 days

#7 posted 03-12-2010 03:58 AM

iterative calculations can be fun, but http://mathworld.wolfram.com/CircularSegment.html shows how to get at the same answer without it… you do need to be able to take inverse trig functions though. also, i calculated exactly double your angle: 11.45º. so i think your angle is 1/2 of what it should be if you were tracing an arc with a trammel… so how did that work out? anyway, i have to admit that i wouldnt have bothered with the math and wouldve done it with the cursing and sawdust!

Ger21

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690 posts in 2131 days

#8 posted 03-12-2010 04:01 AM

At work we make a lot of curved window casings. We use a very simple formula to find the radius, that only uses your 15” and .375”, and no trig. Don’t know off hand what it is, but I’ll check tomorrow and post it.

Usually, I’ll just draw it in a CAD program in 5 seconds and it’ll tell you the radius. :-)

Just googled and found it.

http://mathforum.org/library/drmath/view/55037.html

-- Gerry, http://g-forcecnc.com/jointcam.html

donjoe

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1360 posts in 2031 days

#9 posted 03-12-2010 04:15 AM

Excellent jig. Well thought out and executed with good workmanship.

-- Donnie-- listen to the wood.

JoshLawson

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63 posts in 2004 days

#10 posted 03-12-2010 04:58 AM

Bob – the MDF pieces to keep the jig from getting skewed is unnecessary, if the aluminum frame gets skewed at all it lifts the router bit, so you can never cut too deep by skewing. It seems to me it would just get in the way

AaronK – I did calculate the half angle, if you look at the second equation – W = 2sin(theta)R – I multiply the horizontal by two.

CAD programs are already nice, but if you just have some determination, paper, and a calculator you can do it the fun way.

-- Josh Lawson - Ankeny, Iowa

OutPutter

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1199 posts in 2990 days

#11 posted 03-12-2010 07:30 AM

Hi Josh. Interesting approach to solving the problem of describing an arc that meets the conditions of being 3/8” deep and intersecting the ends of your board at the top. I would have driven a nail in the edge of the board at 3/8” and half way between each end. Then taken a flexible straight edge and hooked it below the nail and bent the two ends up until it intersected each end of the board. Draw the arc. No math, no headache, no trial and error. Now, tell me why it wouldn’t have worked because I doubt I’m smarter than you.

Best,

-- Jim

AaronK

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1411 posts in 2464 days

#12 posted 03-12-2010 02:03 PM

sometimes you just want exact. i can understand his approach :-)

JoshLawson

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63 posts in 2004 days

#13 posted 03-12-2010 02:22 PM

Outputter – You described the same method I use for the majority of my arcs, it’s only when I want a very precise arc that I bother with all the math. (Don’t forget I am a bit of nerd, so some part of me enjoys whipping out my giant calculator I paid all that money for in college). I’ve also had some mixed results using the flexible straight edge method, I have trouble getting the arc to be truly a simple curve instead of a complex curve (non constant radius) I seem to get more of a parabola than an arc.

-- Josh Lawson - Ankeny, Iowa

Riehlez

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24 posts in 2044 days

#14 posted 03-12-2010 04:05 PM

you did it dude! goodJob! this is one jig that cant bring my self around to building, but alwaya can use it.

bobthebuilder647

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128 posts in 2252 days

#15 posted 03-13-2010 01:46 AM

Nicely done.

-- Rick, Pa. Courage is what it takes to stand up and speak; courage is also what it takes to sit down and listen.

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