Curtate cycloid plate carving tutorial

[Dave Cohen]

Last night and this morning, I carved a mandocello top plate using a variation of curtate cycloid arching from my article in American Lutherie #96(Winter, 2008). The two photos in this first post show the joined plate and the plate bandsawed slightly oversize, with the contour lines drawn on the top. The contours and elevations were calculated in Excel, as per the AL article, with modifications at the heel end of the plate for the oval sound hole.

http://www.Cohenmando.com/

[amowry]

Thanks Dave, that's very cool. After reading your article in '08 I redrew my octave mandolin and guitar arching using curtate cycloids as a starting point, and it was a definite improvement.

[Dave Cohen]

In the first photo in this post, I have drilled all of the holes along the outermost contour lines. I set the drill press depth stop to 0.22" using a homemade gauge block. In the second photo, all the rest of the holes have been drilled. After drilling the holes for the outer contour lines, the depth stop was reset for the next contour line in, then all of the holes were drilled for that line. The process was then repeated for each of the contour lines.

http://www.Cohenmando.com/

[Dave Cohen]

The first photo in this post shows the waste between the holes removed by a gouge and then a fingerplane. The second photo is of the plate after the remaining waste has been removed by a scraper to just eliminate the drill marks. The third photo shows a side view of the longitudinal arch.

http://www.Cohenmando.com/

[Dave Cohen]

Total carving time for the outside arch was a little under four hours.

The first photo in this post shows a wood "finger" mounted on the drill press table. There is a threaded rod in the wood finger, and it is mounted with a fender washer and a wingnut under the table. The depth stop was set with another gauge block so that the bit stopped 0.27" above the top of the wood finger. The next photo shows all of the holes drilled in the underside of the plate. The plate was set on the wood finger, and all of the holes were drilled in a short time. The third photo shows the waste removed from between the holes to just eliminate the drill marks. As before, that was done first with a goiuge, then a finger plane, and finally with a scraper. As of the last picture, the arch portion of the plate was a constant 0.27" thick. The plate is ready for graduation and for shaping the "ramp" for the fretboard extension.

Forgot to mention that I carved a bit of the recurve on the outside of the plate before drilling the underside. There is no need to completely carve the recurve; just enough that the thickness is consistently thinner than 0.27". That insures that holes will not be made around the outside of the plate where they shouldn't be. I also rough-carved the scroll before drilling the underside. Once the recurve is a bit deeper, the perimeter around the arch portion of the plate will be planed (with a block plane) to a constant 0.22" thick.

While this is not as fast as using the pantograph, it is not bad at all. Further, in order to make a pantograph template, one has to go through this procedure. If you are using a CNC, you should be able to use the machine code to avoid having to draw everything. Seems to me that you should be able to feed the thing the equations using discrete intervals. The curtate cycloid arching as per the AL article allows a lot of flexibility w/ regard to arch height, width of recurve area, etc.

http://www.Cohenmando.com/

[Dave Cohen]

Thank you, Andrew. Didn't answer until now, as I was "on a mission" to post all of the photos. I thought this might be helpful to someone thinking about carving their first plate(s). Someone without a CNC router should be able to use the curtate cycloid arching to achieve as consistent an arch as any computer can achieve. So, in what way did the cc arching improve your OM and guitar plates?

http://www.Cohenmando.com/

[amowry]

Thanks Dave, and sorry to interrupt your stream of photos. I would say I mainly like the aesthetics of the arching. Up to that point I had used somewhat arbitrary arching that wasn't necessarily consistent from one cross-section to the next. I will say that while I started with curtate cycloids, I altered them in the recurve area to give me more exaggerated recurve. Maybe that defeats the purpose?

[StuartGold]

Very cool...... I'm just starting to carve the top for my first oval. Any chance that you could post an image or chart of the numbers that you are using?

[Dave Cohen]

Andrew, I don't think you are defeating the purpose. I alter the cc arch in the recurve area also. I don't think there is anything special about the cc arch w/ regard to instrument sound. In fact, it is pretty close to what is commonly done. My point in the article was that using the cc arching gives one consistency, alows flexibility, and above all gives one control over the arching process.

http://www.Cohenmando.com/

[Graham McDonald]

Great stuff, Dave. Curtate cycloid arching is such a useful tool when carving, as as you point out simple and repeatable.

More power to yer arm

cheers

g

[tom.gibson]

Very cool...... I'm just starting to carve the top for my first oval. Any chance that you could post an image or chart of the numbers that you are using?

There is a very user-friendly CC generator here which might help you:

http://liutaiomottola.com/formulae/curtate.htm

First set out the longitudinal arch. (On an oval hole this requires some fudging of the curve from the apex to the neck because of the fingerboard ramp, as Dave Cohen points out.) Once you have a series of heights along the longitudinal arch you can generate the arches which cut across the top at each of these points. When you've marked the heights along the cross arches it's just a matter of 'joining the dots' to get your contours.

[Pete Jenner]

This is very good Dave - a must bookmark thread.

BTW is there a mandocello build competition going on between you and the Sunburst Kid? Just askin'.

[Stephen Perry]

Very similar to how I work on violins, in some ways. However, I am only generating cross arches and the ends of the top. The top on a violin I make with a long center section, a cylinder in gross form, and a longitudinal back arch that is more full towards the ends. The mandolin is different, of course, but some of the best I've played seemed to somewhat reflect at least this top arching approach, moving away from strict bullseye approach. Any thoughts?

I have the wood post on a plate, by the way, that I clamp down. I hadn't considered just making a plug for the center hole! I also use a stack of feeler gauges to set thickness. I have a nice calibrated tapered wedge for depth setting somewhere, probably sitting next to all the other stuff I can't find! I'll have to make another. This moving shops thing (twice) has dissociated a number of important things from me.

[Dave Cohen]

Pete, no competition at all between Butch Cohen & Sunburst Kid. As luthiers go, we are neighbors, after all. I have had this mandocello commission since October, & just now getting started in a serious way. This plate happens to be a mandocello plate, but for the purpose of this thread, it could have beenany mandolin family instrument. I am not planning on sharing the whole build, as John will be doing.

Stuart, the parameters for a mandolin cycloid are in a table in the Al article, as well as instructions for generating your own parameters. I make templates for the contour lines from aluminum flashing or some such. For an oval hole instrment, you will have to modify the templates for the heel end of the body. I'll see if I can post a photo of some oval hole templates.

Tom, if you are generating the longitudinal arch, then using it to generate lateral arches, you are in effect using Cartesian coordinates. That is the hard way when it comes to the drilling. You will have to hunt for all of the holes of the same depth, which can be confusing. If you use the cylindrical polar coordinates, as in the article, you generate the contour lines. Each contour line is a single depth setting. You will be able to drill all of the holes on a contour line without having to stop and re-set the depth stop. Then you can re-set for the next contour line and drill without re-setting until you are done with that line. Learning to use the polar coordinate may be a bit daunting if you are not familiar with it, but it is worth it for the labor and time saved.

I had to default to Cartesian cordinates for the archtop guitar body. I have since figured out how to use polar coordinates for that, but it is complicated, involving Jacobean transformations to invert the functions. Best to keep it simple.

http://www.Cohenmando.com/

[Dave Cohen]

Attached is a photo of the templates for the oval hole 'cello top plate cycloid. They progress from outer contours at the top to innermost contour at the bottom. You can see from the templates how the contours are modified such that the "ramp" for the fretboard extension is left untouched.

http://www.Cohenmando.com/

[tom.gibson]

Tom, if you are generating the longitudinal arch, then using it to generate lateral arches, you are in effect using Cartesian coordinates. That is the hard way when it comes to the drilling. You will have to hunt for all of the holes of the same depth, which can be confusing. If you use the cylindrical polar coordinates, as in the article, you generate the contour lines. Each contour line is a single depth setting. You will be able to drill all of the holes on a contour line without having to stop and re-set the depth stop. Then you can re-set for the next contour line and drill without re-setting until you are done with that line. Learning to use the polar coordinate may be a bit daunting if you are not familiar with it, but it is worth it for the labor and time saved.

You can achieve contour lines for easy depth drilling using the method I suggested. If you generate enough points on the lateral arches (say 20 or so) you can find heights which are very close (within a quarter of a mm or so) to the height settings you have chosen for your contours (say 12mm, 9mm, 6mm and so on). Mark these points on your map and then join them to get the contours. No doubt this is a lot clumsier than using polar coordinates, and not as accurate, but it's probably also less daunting (at least to me!)

[Dave Cohen]

As I said, I used the Cartesian coordinates for archtop guitar plates. Accuracy is not the problem; you can be plenty accurate with Cartesian coordinates. The problem is finding all your elevations so that you don't have to keep re-setting the depth stop to catch all the ones you missed. When you have a large plate (e.g., 17" archtop guitar body) with elevations marked every inch (both X and Y), you will have in the neighborhood of 300 elevations marked on your plate. Then, once you set your depth stop for a given elevation, you have to find all the marks at that elevation out of the 300 or so marks. Good luck with that. I can tell you that I missed several when doing the archtop guitar plates, meaning that I had to go back and re=set the stop for the ones that I missed, several times. Every time you re-set for a point that you previously missed, you are potentially introducing error. By contrast, if you have, say, eight contour lines, you can be sure that you are setting for each elevation only once, and you drill all of the holes on that line to its' specified elevation. I've done it both ways. It is a lot easier and faster with contour lines.

Now, if you have a CNC router, Cartesian coordinates are fine. The computer is a dumb brute when it comes to repetition. It will dutifully go back and forth, repeating elevations at great speed without complaining. That, plus the stepper motors are designed to deal well with Cartesian cordinates anyway.

http://www.Cohenmando.com

[Dave Cohen]

A minor update. I have since cut the soundhole, and carved the "ramp" for the fretboard extension.

The soundhole is a simple ellipse. I calculated the parameters for the ellipse, drew it on the computer, and printed it to size. Used the printed ellipse as a template for a polycarbonate template, and made the template. Traced the ellipse on the top plate by positioning the template, then wasted the interior of the soundhole with a Forstner bit to minimize the amount that would need to be removed with the router. Finally, the template is mounted in a tray for holding the plate. The plate is positioned accordng to the plans, and the soundhole is cut to final size and shape with a pattern bit.

Once the soundhole is cut and the fretboard dimensions are known, the ramp can be finished. In the last pictures, the ramp was flat (i.e., the angle was 0 degrees) and ovesize. I use a 3 degree angle for oval hole instruments. I used the tangent of 3 degrees to find the height by which the heel end of the ramp would be dropped. I subtracted that height from the overall height of the flat ramp, and marked it on the heel end of the plate. From there, I just used a block plane to plane to the marks for the 3 degree ramp. Finally, I marked the positions of the edges of the fretboard extension on top of the ramp, and carved the rise to the top of the ramp using finger planes, and a gouge where the finger planes would not reach. Two views shown.

http://www.Cohenmando.com

[Keith Newell]

So this is a fancy name for another cad/cam system. This is common in so many systems and not groundbreaking. Get Spaceclaim and your worries of part or fixturing are over.

[Keith Newell]

That is 2x the time for a off the shelf Cad cam and experienced programmer. There is so much more out there right now

[Larry Simonson]

Well, I am about 30% done with carving the maple back and even with my router jigs and rim thicknessing router bit my 73 year old fingers are complaining. I think next one, if there is one, I might engage a CNC shop to rough the plates out leaving the final tweeking for me.

[Dave Cohen]

That is 2x the time for a off the shelf Cad cam and experienced programmer. There is so much more out there right now

What??? No CAD/CAM was involved in any of this. That plate was carved entirely by hand. What I did in my American Lutherie article and in this thread was to describe the geometry of the plate. Once you have the geometry of the plate, you can choose to execute entirely by hand, partly with the aid of machinery, or entirely w/ CNC or some other form of automation. That is entirely up to you. But no amount of computation or interfaced machinery or 3D printing will give you the geometry in thefirst place. You have to have the geometry of thr object before you can digitize it and do what you are describing.

http://www.Cohenmando.com/

[Pete Jenner]

Dave, do you use the same CC data for your backs? If not, do you vary the arch height (of the backs) according to the properties of the particular piece of wood you are working with? Do different arch heights, back and top, affect the trampoline mode\s ?

[Dave Cohen]

Dave, do you use the same CC data for your backs? If not, do you vary the arch height (of the backs) according to the properties of the particular piece of wood you are working with? Do different arch heights, back and top, affect the trampoline mode\s ?

I use a curtate cycloid spreadsheet for back plates, but it is not the same spreadsheet as the one for the top plate. For backs, the contour lines are modified in the heel area differently than they are for top plates. I have the back plate for this 'cello marked, ready for drilling and carving. I'll see if I can take a photo of the back plate that will highlight the difference. No guarantees.

http://www.Cohenmando.com/

[Dave Cohen]

Here is a photo of the back plate, with curtate cycloid contours drawn on it in pencil. I bumped up the contrast and dropped the brightness way down in order to emphasize the pencil lines. The height of the apex of the arch will be about the same as that of the top plate. You can see how the contour lines were modified/distorted in the heel area. Part of that comes directly from the outline of the plate itself. The only "freehand" part is in the immediate vicinity of the heelblock.

Everything affects the trampoline modes to some extent, but the shape of the back plate trampoline modes is dominated by the outline of the back plate. The modes of this back plate will look substantially like those of most mandothingy back plates. Frequencies are affected by arch height, but also by Young's moduli. That is, you could f'rinstance raise frequencies with a high arch, but lower them even more by carving thin enough. This plate will be typical of mandocello back plates.

http://www.Cohenmando.com/