|Project by JoshLawson||posted 03-12-2010 01:35 AM||8345 views||64 times favorited||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
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.
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
Thanks Ger21 for the tip!
-- Josh Lawson - Ankeny, Iowa