Compound radius fretboard shaping jig

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Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Compound radius fretboard shaping jig

Post by Dennis Duross »

I hesitate to post this, as I'm not sure how clear it's going to be, but here goes.

The basic idea is: a router sits in a carriage and rides on two rails down the length of the board. The rails rest on arc templates with different radii, so as you move from string path to string path, the compound radius is cut.

The "fixed" part of the jig consists of a base (0.5" thick mdf x 10" x 36"), a platform (2.5" w x 2.75" h x 17" l) to stick the fretboard to, and two "stops" to attach the radius templates to.

The stop on the left (near the nut end of the board) is 5" from the platform, and is fixed to the board.

The stop on the right is moveable depending on the scale. In this case, it's clamped down at 24.75".
photo(1).JPG
photo(1).JPG (32.97 KiB) Viewed 14446 times
Here's the moveable stop at the bridge location.
photo.JPG
photo.JPG (36 KiB) Viewed 14446 times
Here are what I call the setup arcs. Two identical templates used to set the height and location of the rails. I'm cutting a 7.25 radius at the nut, and the rails will ride on an arc 1" above the fretboard, so they need to be an 8.25" radius.
photo(2).JPG
photo(2).JPG (29.93 KiB) Viewed 14446 times
I clamp the setup templates to the platform.
photo(3).JPG
photo(3).JPG (33.96 KiB) Viewed 14446 times
Oops, forgot the spacers, which hold the rails a fixed width apart.
photo(4).JPG
photo(4).JPG (32.47 KiB) Viewed 14446 times
More tomorrow.

It really does work, despite what it looks like so far.
John Sonksen
Posts: 356
Joined: Sun May 20, 2012 12:16 pm
Location: Portland, OR

Re: Compound radius fretboard shaping jig

Post by John Sonksen »

I had this exact same idea a little while ago but I wasn't sure if the router would actually follow the contour of the individual radius guides or just end up doing a radius that was somewhere in between them and consistent down the whole length. I intended to put bearings or rollers on the ends of the tubes to ride on the radius guides but in my mind at least it poses a problem. The tubes should be parallel so the router can follow a linear guide instead of a tapered one, and if that's the case the wheels would need to be located in such a way so the wheels can roll freely on both ends simultaneously, which may involve having some kind of hinge mount so the wheels can find their shared neutral point for rolling. I pretty much gave up on it and have decided when I have the time to make a rig similar to the grizzly compound radius jig for their edge sander but using a router in a table instead of a belt sander.

I kind of hope I'm wrong though and was overthinking it! Best of luck, I hope it works!
Jason Rodgers
Posts: 1554
Joined: Fri Jan 06, 2012 4:05 pm
Location: Portland, OR

Re: Compound radius fretboard shaping jig

Post by Jason Rodgers »

I'm having difficultly following. Can you post some more shots with the jig in use?
-Ruining perfectly good wood, one day at a time.
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Here's one of the spacers (on the nut end) aligned to the center line (pencil lines) and clamped to the fixed stop.
photo(5).JPG
photo(5).JPG (32.02 KiB) Viewed 14441 times
At the bridge end I've just set the spacer in front of the stop. The rails get dropped into the slots in the spacers, and they rest on the setup arcs.
photo(6).JPG
photo(6).JPG (27.66 KiB) Viewed 14441 times
Here are the "cutting" arcs. Different radii. They get clamped to the stops.
photo(7).JPG
photo(7).JPG (31.85 KiB) Viewed 14441 times
Before I attach the cutting arcs I put some weight on the rails. The rails are resting on the setup arcs, and are kept a fixed width apart by the spacers. Next I'll slide the cutting templates between the spacers and stops, pulling them up tight against the rails (which is why I added the weight to the rails).
photo(8).JPG
photo(8).JPG (32.62 KiB) Viewed 14441 times
Here's the bridge arc pulled up tight against the rails and clamped temporarily.
photo(9).JPG
photo(9).JPG (32.93 KiB) Viewed 14441 times
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Then I clamp it up for keeps and clamp the spacer to the stop (not shown).
photo(10).JPG
photo(10).JPG (33.08 KiB) Viewed 14442 times
Same deal on the other end. Pull the cutting template up tight against the rails, clamp it to the stop, and clamp the spacer to the stop.
photo(11).JPG
photo(11).JPG (34.86 KiB) Viewed 14442 times
Now everything is locked in place, so I can remove the setup arcs. Now the rails are resting on the cutting arcs.
photo(12).JPG
photo(12).JPG (35.9 KiB) Viewed 14442 times
Now I double-stick the fretboard to the platform. Here I'm just using an mdf piece that I've already radiused, just for illustration.
photo(13).JPG
photo(13).JPG (33.67 KiB) Viewed 14442 times
This is the router carriage. Just a piece of 0.25" thick mdf, 5.25" x 5.25" with a couple of pieces of 1 x 2 glued on, and three knock-down bolts (which ride on the rails).
photo(14).JPG
photo(14).JPG (36.71 KiB) Viewed 14442 times
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Now you set the depth of the router bit, and align the spacers to the first string path. Clamp the spacers to the stops and cut the path. Move from path to path until they're all cut.
photo(15).JPG
photo(15).JPG (26.92 KiB) Viewed 14442 times
Wow. Unfocused. Here's the outermost path, which starts out (at the nut end) at a pretty good tilt.
photo(16).JPG
photo(16).JPG (32.91 KiB) Viewed 14442 times
So that's the easy part. Set it up relative to the radius you want at the nut, attach cutting arcs, use the string paths. Done.

But you also have to be sure that the cutting arcs are the correct radius. Or what's the point?

And that part I really do have to save for tomorrow.
Jason Rodgers
Posts: 1554
Joined: Fri Jan 06, 2012 4:05 pm
Location: Portland, OR

Re: Compound radius fretboard shaping jig

Post by Jason Rodgers »

Ok, I get it now. I thought the tubes were attached to the sled and the whole thing moved together. That would require some long tubes! I like how your main cuts are along the length of the board. Do you go back with crosswise passes to blend the facets?
-Ruining perfectly good wood, one day at a time.
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Jason: No, you don't cut crosswise. You can't because the spacers are clamped to the end stops. There IS a slight faceting of the board, but that can either be sanded out, or you can make an additional set of passes between string paths to fix that.

I thought that maybe a drawing or two might help visualize, so I'll try to post a few today before I explain how to get the correct radii for the cutting templates.

Here's an end view of some of the components:
01.gif
Bill Raymond
Posts: 367
Joined: Fri Jan 06, 2012 5:37 pm
Location: Red Bluff California

Re: Compound radius fretboard shaping jig

Post by Bill Raymond »

If you put your spacers on wheels and had them run in a track that could be clamped so as to keep the spacers where you wanted them you could rout from side to side as well as end to end.
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Here's another view from the end with some dimensions. Unfortunately the drawing shows a 9" radius, but that's the only difference between it and the photos.
02.gif
02.gif (8.77 KiB) Viewed 14366 times
And here's the carriage width.
03.gif
03.gif (5.72 KiB) Viewed 14366 times
And some spacer dimensions.
04.gif
04.gif (6.98 KiB) Viewed 14365 times
On the last few drawings I included the cell references from a spreadsheet I use, but not sure I can upload an Excel file.
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

This may be a good point to start over...

The basic idea is: a router sits in a carriage and rides on two rails above the fretboard. The rails rest on arc templates with different radii, so as you move from string path to string path, the compound radius is cut.

Here are the base components (all made from 0.5" thick mdf):
-base
-platform
-2 stops: one fixed (nut stop) and one that's moveable, depending on the scale (bridge stop)
setup 01.gif
And here's a side view:
setup 02.gif
setup 02.gif (2.68 KiB) Viewed 14311 times
You need to construct a simple carriage for the router to sit in (held in place with double-stick tape). Just a 0.25" thick piece of mdf, a couple of pieces of 1 x 2 (hardwood), and three knock-down bolts (1.75" long):
setup 03.gif
setup 03.gif (4.66 KiB) Viewed 14311 times
You need a couple of templates to setup the rails. Since I'm going to cut a 9" radius at the nut, and because my setup templates will suspend the rails 1" above the face of the fretboard, the setup templates need a 10" radius. Because the combined height of the platform (2.75") and the fretboard (0.25") = 3", the setup templates need to be 4" high:
setup 04.gif
setup 04.gif (4.27 KiB) Viewed 14311 times
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Next, you need 2 spacers, which hold the rails a fixed width apart. The critical dimensions below are the spacer width and the slot width. The undercuts (below the slots) just keep the spacers from running into the clamps that hold the cutting templates to the stops. They should be 0.5" thick:
setup 05.gif
setup 05.gif (7.15 KiB) Viewed 14308 times
The rails are just 2 lengths of 0.85" dia pipe, 36" long:
setup 06.gif
setup 06.gif (1.84 KiB) Viewed 14308 times
And finally, you need the cutting templates (whose radii will be determined later). Note that they are 0.5" shorter than the setup templates:
setup 07.gif
setup 07.gif (7.93 KiB) Viewed 14308 times
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Now we need to take these components and do the initial setup. Clamp the setup templates (with a long bar clamp) to the platform:
setup 08.gif
setup 08.gif (2.62 KiB) Viewed 14304 times
Use two spring clamps to tack a spacer to the nut stop (the white square is supposed to represent the point of attachment for the spring clamps in the following drawings). Just place the other spacer about an inch in front of the bridge stop. If your spacers are 0.5" thick it should stand up on its own without tipping over.
setup 09.gif
setup 09.gif (7.35 KiB) Viewed 14304 times
Now you can drop the rails into the spacer slots:
setup 10.gif
setup 10.gif (3.52 KiB) Viewed 14304 times
Next, apply some weights to the rails. I use two 10 lb weights. The reason for this is that you need to slip the cutting template between the spacer and bridge stop, and pull it up tight against the bottoms of the rails with one hand, and clamp it to the stop (spring clamps) with the other. You don't want the rails to move around while you're doing this.
setup 11.gif
setup 11.gif (2.82 KiB) Viewed 14304 times
I removed the rails from the inset at right (below) for clarity:
setup 12.gif
setup 12.gif (8.58 KiB) Viewed 14304 times
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Now that the template is tacked to the bridge stop with spring clamps (and you have both hands free), use bar clamps to securely attach the template to the bridge stop. (Bar clamp attachment points are depicted with gold squares in the following drawings):
setup 13.gif
setup 13.gif (8.17 KiB) Viewed 14303 times
Remove the spring clamps:
setup 14.gif
setup 14.gif (7.07 KiB) Viewed 14303 times
Now you can slide the spacer up against the stop and spring clamp it in place.
setup 15.gif
setup 15.gif (7.94 KiB) Viewed 14303 times
Attach the cutting template for the nut stop side of the jig using the same process used above for attaching the bridge stop template.

Once both cutting templates have been secured, the setup templates can be removed. Now the rails are resting on the cutting templates.

At this point, the cutting templates are attached and the spacers are aligned and clamped to the center line of the base, so you can double-stick the fretboard to the platform.

Place the carriage on the rails and adjust the router bit depth so that it just touches the face of the fretboard at the nut end. Then move the carriage to the other end of the fretboard and check the bit depth.
setup 16.gif
setup 16.gif (4.33 KiB) Viewed 14303 times
Ideally, the bit will just touch the face of the fretboard at both ends. In practice, I've found that the bridge end of the fretboard is slightly higher (like 0.01" or so), which is most easily remedied by taping a shim to the top edge of the bridge stop template. This will raise the rails enough to equalize the cutting depth of the bit.
setup 17.gif
setup 17.gif (3.01 KiB) Viewed 14303 times
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Here I want to take a moment to show how the cutting templates affect the positioning of the rails from string path to string path. Note that the spacers and the jig base are marked with center lines, and string path are also marked on the base.

First in the center position:
setup 18.gif
setup 18.gif (5.25 KiB) Viewed 14303 times
Notice how the rails are affected as the spacers are moved to the bass E string path:
setup 19.gif
setup 19.gif (5.41 KiB) Viewed 14303 times
This is why there are just three knock down bolts in the carriage. Four bolts would never all make contact with the rails given how the height of the rails varies from one end to the other. Note: It is especially important to apply downward pressure on the trailing of the two bolts, to keep the carriage from tipping forward as it's pushed along the rails.

Note also that because the bridge stop cutting template has a greater (flatter) radius, it sits closer to the base than the nut stop cutting template does. It is important to make these templates 0.5" shorter than the setup templates.

You can also see that the spacer cutouts allow the spacer to be moved beyond the outermost string paths without being interfered with by the clamps holding the cutting templates to the stops.
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Okay, now comes the best part, figuring out the cutting template radii.

Bear in mind that a spreadsheet can be set up to do the grunt work that follows, which makes changing and updating scales, nut widths, fretboard radii, etc, all quick and easy.

To determine the cutting template radii, you first need to know the width of the fb at the nut (1.7") and at the 14th fret (2.125"), and the distance from the nut to 14th fret, which since I've got a 24.75" scale = 13.725".
radius 01.gif
radius 01.gif (3.35 KiB) Viewed 14298 times
The goal is to determine the width of the fb if it was extended to the nut stop on the one end, and to the bridge on the other.

So here's the math for the nut stop end:

fb width at nut stop = (((w14 - wNut) / distance to 14) x distance to nut stop) + wNut
= (((2.125 - 1.7) / 13.725) x -5.0) + 1.7
= ((0.425 / 13.725) x -5.0) + 1.7
= (0.031 x -5.0) + 1.7
= -0.1550 + 1.7
= 1.545 at nut stop

Do the same thing to determine the width of the fb at the bridge:

fb width at bridge = (((w14 - wNut) / distance to 14) x distance to bridge) + wNut
= (((2.125 - 1.7) / 13.725) x 24.75) + 1.7
= ((0.425 / 13.725) x 24.75) + 1.7
= (0.031 x 24.75) + 1.7
= 0.766 + 1.7
= 2.466 at bridge
radius 02.gif
radius 02.gif (1.82 KiB) Viewed 14298 times
The next thing we need to know is the sagitta (or "sag") of the 9" radius arc at the nut. The dictionary definition of sag = "the distance from the midpoint of an arc to the midpoint of its chord".
radius 03.gif
radius 03.gif (2.35 KiB) Viewed 14298 times
Math time:

sag = radius - sqrt(radius^2 - (chord/2)^2)
= 9 - sqrt(9^2 - (1.7/2)^2)
= 9 - sqrt(81 - (0.85)^2)
= 9 - sqrt(81 - 0.723)
= 9 - sqrt(80.277)
= 9 - 8.96
= 0.04

So the sag = 0.04

Now to find the radius of the fretboard at the nut stop position:

radius at the nut stop = (sag^2 + (width at nut stop/2)^2) / (2 x sag)
= (0.04^2 + (1.545/2)^2) / (2 x 0.04)
= (0.0016 + (0.773)^2) / (0.08)
= (0.0016 + 0.597) / (0.08)
= (0.599) / (0.08)
= 7.439” radius on the fb at the nut stop

Same math to find the radius of the fretboard at the bridge position:

radius at the bridge = (sag^2 + (width at bridge/2)^2) / (2 x sag)
= (0.04^2 + (2.466/2)^2) / (2 x 0.04)
= (0.0016 + (1.233)^2) / (0.08)
= (0.0016 + 1.521) / (0.08)
= (1.522) / (0.08)
= 18.921” radius on the fb at the bridge

Getting sleepy. More tomorrow.
Bob Francis
Posts: 582
Joined: Wed Jan 11, 2012 6:28 pm

Re: Compound radius fretboard shaping jig

Post by Bob Francis »

Thanks!
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Okay now for the last bit.

Getting the correct radii for the cutting templates had me stumped for awhile. Initially I thought that if I could find the fb radii at the nut stop and bridge, I could just add 1" to that, like I had with the setup templates.

That didn't work.

What I finally realized was that with respect to the cutting templates, a portion of that 1" setup offset is a fixed value, and adding that fixed value to the fb radius will help you solve for the template radius.

Here's an end view of the setup. I've shaded the area in question:
fixed 01.gif
fixed 01.gif (5.59 KiB) Viewed 14276 times
The setup template suspends the rails 1" above the face of the fb. The width of the rails (from center to center) is 6.15":
fixed 02.gif
fixed 02.gif (2.59 KiB) Viewed 14276 times
The fixed value is going to be the difference between the 1" offset height and the sag:
fixed 03.gif
fixed 03.gif (1.51 KiB) Viewed 14276 times
Back to the blackboard:

sag = radius - sqrt(radius^2 - (chord/2)^2)
= 10 - sqrt(10^2 - (6.15/2)^2)
= 10 - sqrt(100 - (3.075)^2)
= 10 - sqrt(100 - 9.456)
= 10 - sqrt(90.544)
= 10 - 9.515
= 0.485

So the sag = 0.485

And the fixed value is 1" - 0.485"
= 0.515"

NOW we can find the radii of the cutting templates.

First the nut stop template:
fixed 04.gif
fixed 04.gif (8 KiB) Viewed 14276 times
You just add the fb radius and the fixed value = the triangle's altitude (7.954), and we know the base is one-half of the chord (6.15/2) = 3.075.

a^2 + b^2 = c^2
7.954^2 + 3.075^2 = c^2
63.271 + 9.456 = c^2
72.727 = c^2
sqrt(72.727) = 8.528

8.528

Who knew?

8.528 is the radius of the nut stop cutting template.

Do the same for the bridge cutting template.
fixed 05.gif
fixed 05.gif (7.92 KiB) Viewed 14276 times
Again, you just add the fb radius and the fixed value = the triangle's altitude (19.437), and the base is still = 3.075.

a^2 + b^2 = c^2
19.437^2 + 3.075^2 = c^2
377.796 + 9.456 = c^2
387.252 = c^2
sqrt(387.252) = 19.679

19.679 is the radius of the bridge cutting template.

SEE? It's not that hard.

Actually, it's infinitely easier if you have all this in a spreadsheet.

Forum rules don't allow uploading Excel files, but I'd be happy to email the file to anyone who's interested.

(crickets)

Well, if you change your mind, send me a PM.
Dennis Duross
Posts: 132
Joined: Sun Jan 08, 2012 12:46 am

Re: Compound radius fretboard shaping jig

Post by Dennis Duross »

Something I just noticed:

The drawing: setup 15.gif

The setup templates should still be in place in this drawing, as the nut stop cutting template has not been attached yet.

AFTER both sets of cutting templates are attached, THEN the setup templates can be removed.
David King
Posts: 2690
Joined: Sat Jan 07, 2012 10:01 pm
Location: Portland, OR
Contact:

Re: Compound radius fretboard shaping jig

Post by David King »

Great illustrations and explanation Dennis. Thanks for taking the time to explain it all (and showing us your math work!)
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