Router Curve Math!

[Chris H]

Good Morning, 

 

I need some help with setting up a router jig to cut a curve for a table top.  The curve is very subtle, but needs to be exact on all the boards, so I am planning to use a "Compass" type jig on my router to cut the template, and then just flush trim bits with a guide to cut all the pieces. 

 

Unfortunately my geometry is failing me at the moment, and has for a few days.  So I am hoping someone can give me a quick refresher course here on how to calculate the length of the arm (radius) that I need on my compass jig to get this arc.

 

 

The table top spans 22" long, and the boards all deflect (not sure that's the right word) 1/4", and are symmetrical.  So the middle of the center board is 5", while the ends are 4.5".

 

As always, thanks in advance for your help!

[Tpt life]

I did this all the time engineering surrounds for garage doors, windows and the like. If you want the theory I can walk you through it. If you just want the solution this web solver is set right up for you. All you need to know is the width of the arc and the rise in its center.

http://www.mathopenref.com/arcradius.html

Where radius = (height squared + 1/2width squared) divided by 2 times the height.

[Chris H]

That is perfect!  Thank you so very much.  

 

Unfortunately, I expected a large radius, but >20' maybe prohibitive.  I may have to rethink my approach.

[Tpt life]

I used a driveway and a spike to layout a template. This leaves you with a free hand cut and sanding but lets you rout what you need based on the template.

There is the more complicated elliptical shape also. These shapes utilize two focii. Take some cardboard and poke two nails in it. Tie some string in a loop. Put your pencil in the string and loop it around both nails. Draw a "circle" keeping the string taught. You wind up with shapes that are ovals with semi curcular ends but gently arcing to almost flat centers. There may be online calculators to help with this also but I have never used one.

This also would likely require freehand cutting a template since I cannot see using a loop with a router. The only benefit would be the potential to find a pleasing arc without needing 20 feet of space.

[Tpt life]

The same site talks ellipse.

http://www.mathopenref.com/constellipsefoci.html

[wdwerker]

I have had good success with a thin strip of wood and a string. Cut a notch on the ends of the stick and tie the string tight to bow the stick. Use the bow to draw your line and then flip the bow end for end to check the symmetry . A longer slightly thicker stick will give a more gentle curve.

I made a 12 ft arm for a router radius jig years ago. I also made an ellipse accessory for it. A square base with 2 dovetailed grooves routed in an "X" from corner to corner. Two dovetailed blocks slide in the groves with a pin that pivots in the 12 ft arm. The second pivot makes the arm trace a long axis and a shorter axis which results in a ellipse. We cut a 5ft by 12ft oval conference table with it. It took a couple of days to build and fine tune the jig.

[Tpt life]

Wdwerker, I am struggling to visualize the ellipse jig. Would you be willing to post a picture?

[CessnaPilotBarry]

I'm a big fan of a drawing bow myself...  

 

They're easily made as long or short as you need, with a strip and string, but here's a commercial version:  http://www.leevalley.com/en/wood/page.aspx?cat=1,42936,50298&p=44631

[Chris H]

Given the subtlety of the curve my customer wants, I think I may opt for making a drawing bow, create a template using the spindle sander, and then route the final product.  

 

You guys rock!  I love all the different approaches.  

[dwacker]

These are real easy, I do this on a regular bases for millwork between two set of upper cabinets. Make the jig to make a jig.  No drawing or sanding just make the jig and make a hardboard template on the router table. You can cut the kerf on a router table easily. Sorry for the bad hand writing my hands are not working well today.

 

 

 

 

 

[Darren66]

I recently made the following jig (patent pending  ), picture attached, to cut a shallow curve in the end rail of my king size bed. Worked quite well. I used my CAD software to calculate the height from the chord of the arc to the arc at 150mm/6" intervals to check the curve was curved as I was worried about symmetry and ending up with flat sections. Wanted a curve not an ellipse. Cut most of waste out with jig saw. Routed with template bit. Tiny amount of finishing with spokeshave. Radius of circle would have been 5m/almost 16' 5". A slightly thinner piece of wood with bolts at more frequent intervals might have resulted in an even smoother curve. Curve can be seen in my project journal entry.

[wdwerker]

Google oval cutting jig. Rockler sells one version. Imagine the center cross shape 4 ft square and the arm 12 ft long.

[Tpt life]

PB and Darren,

Looks like innie vs. outie:-) I thank you for similar and simple suggestions that are new to me.

WD, I found the jig at Rockler, thanks.

[dwacker]

Here ya go less than 5 minutes. Just a tablesaw and bandsaw. Perfect every time.

[Vic]

Very cool, PB!

[Darren66]

PB that's great. Sadly I don't have a band saw :-( no doubt though if you do a better option than the router.

[Chris H]

PB wins, only because there is no sanding, which imo is always a WIN!

So simple, and logical, I love it.

 

I plan to use the Table saw for the template, and then a trim bit on the router to cut the final pieces.  I have a band saw, but it's a HIC cheapo, so the cut quality is garbage.  

 

Thanks again everyone, this has been incredibly helpful.

[dwacker]

PB wins, only because there is no sanding, which imo is always a WIN!

So simple, and logical, I love it.

 

I plan to use the Table saw for the template, and then a trim bit on the router to cut the final pieces.  I have a band saw, but it's a HIC cheapo, so the cut quality is garbage.  

 

Thanks again everyone, this has been incredibly helpful.

 

On the template your just using the band saw to square the kerf made by the tablesaw blade. Id transfer the template to MDF with a flush trim and use it to make your mirror cuts. Meaning cut two pieces at once dont use the template on each board. Use the router and bushing, split the two pieces apart on band saw and use the router cut as the guide for your flush trim.

[Daniel Kuehl]

Here's my math from an arc I calculated a while ago. I didn't know about that website....but if you wanted to go at it old school - Here's what it looks like...