Arching Templates

[MikeC]

If you have a point defined by the height of the long arch and another point defined by the inflection point then a simple circular arc connecting them seems to fit the cross arches from the Titian poster.  Then all you need to add is the scoop.   Having said that, using cross arches on my current build I kind of screwed things up in the C bout      Noob mistake!    

[David Beard]

1 hour ago, MikeC said:

If you have a point defined by the height of the long arch and another point defined by the inflection point then a simple circular arc connecting them seems to fit the cross arches from the Titian poster.  Then all you need to add is the scoop.   Having said that, using cross arches on my current build I kind of screwed things up in the C bout      Noob mistake!    

No.  There are some tops in earlier Amati work that do have arching based on circles.  In these examples, the curvature is constant through the center, but of a large radius. Then, as you move away from the center, the curvature abruptly shifts to a shorter radius, still circular.

But with Strad and most Cremona work, the curvature is continuously changing to a tighter radius as you move from the center, gently and smoothly.  Moreover, the rate the curvature changes at begins from nothing and gently accelerates as you move from the center.

[MikeC]

1 hour ago, David Beard said:

No.  There are some tops in earlier Amati work that do have arching based on circles.  In these examples, the curvature is constant through the center, but of a large radius. Then, as you move away from the center, the curvature abruptly shifts to a shorter radius, still circular.

But with Strad and most Cremona work, the curvature is continuously changing to a tighter radius as you move from the center, gently and smoothly.  Moreover, the rate the curvature changes at begins from nothing and gently accelerates as you move from the center.

Would you agree that observation is true for the Titian Strad?   Since that's the only one I have templates for, it's the only one I can check with drawing tools.  

[David Beard]

9 minutes ago, MikeC said:

Would you agree that observation is true for the Titian Strad?   Since that's the only one I have templates for, it's the only one I can check with drawing tools.  

Generally I would expect it to be.

You do have to watch for distortions from the post.

[Dennis J]

9 hours ago, David Burgess said:

You're a tough nut to crack, Mr. J.

While a formulaic method may eventually emerge to reproduce the best of the 16th through 18th century Cremonese violins, what I would suggest in the meantime is improving your visual assessment skills. Some of us were immediately able to see that your method is a little off, if your goal is reproducing the archings of such instruments.

I thought about what I have presented here about three years ago simply as a way to plan and make arching guides. I've never been concerned about reproducing the arching shape of early makers' violins.

However, I have examined many scans or arching profile examples that have shown up on Maestronet or elsewhere. And, given the age of some of these instruments, I have been amazed at how precise they are and how closely they comply with spiral geometry. Putting french curves up to a computer screen and seeing an exact match is pretty convincing to me.

 

[MikeC]

Dennis what do you mean by spiral geometry?   Did I miss a post on that somewhere? 

[Dennis J]

39 minutes ago, MikeC said:

Dennis what do you mean by spiral geometry?   Did I miss a post on that somewhere? 

Probably not a good way to describe it. I'm alluding to french curves which are spiral forms, just like scroll geometry. I'm no expert on the subject but early makers would have been familiar with it. They knew how to draw accurate ellipses as well. It has occurred to me that they could have used various ellipses to draw the upper convex section of the wider arching, as could anyone with a CAD program.

[HoGo]

4 hours ago, Dennis J said:

Probably not a good way to describe it. I'm alluding to french curves which are spiral forms, just like scroll geometry. I'm no expert on the subject but early makers would have been familiar with it. They knew how to draw accurate ellipses as well. It has occurred to me that they could have used various ellipses to draw the upper convex section of the wider arching, as could anyone with a CAD program.

Ellipses are often approximated by four circles which is more than "close enough" for violin making. Having two circles meeting smoothly can always be viewed as a part of ellipse...

Spirals can be also constructed "close enough" using parts of circles...

ANY curve can be approximated by small parts of circles (or even straight lines) to any level of accuracy. Thats what CNC machines actually do regardless of whatever type of curve your CAD drawing contains.

[bungling_amateur]

One of the bees in my bonnet with all this kind of thing is how hardly anyone ever mentions tolerances, or error margins, or uncertainties. This being the real world, nothing is ever going to be an "exact match", it's not physically possible, and so then it is just a matter of qualifying and quantifying how close you want to get.

How small do our tolerances have to be before we can distinguish between the different theoretical geometrical constructs discussed here? And how close to the "design" are we getting with our tools? Is the tool accuracy bigger or smaller than the difference between the theoretical models? This can be quantified e.g. ±0.1mm or ±2%

[David Beard]

Any kind of gentle curve you can think up from circle arc to parabola, spirial, elipse, catenary, cycloid, bent stick, wet cloth, etc is going to able to match arches to good tolerances if you cherry pick and muck about to make things fit.

What matters more is how predictive the approach is.  Can you reduce the fitting to definitely predictable and limited choices.  Or is there an aspect of just tinkering about to follow an example.

And how well does this work across many (preferably all) classical examples.

[Dennis J]

I don't think about tolerances. I just use digital calipers to take arc measurements from the plan to calculate the height of the inflection point at each arch position. Even then I treat that height mark as a guide. I probably get close to .2 mm accuracy. And by using dividers I can transfer the horizontal position of the inflection points from the plan to the aluminium blanks accurately. So, even with inevitable inaccuracies in the drawn plan I don't think accuracy is much of an issue.

Although the arching templates I have made are very accurate I think the biggest benefit is that they can be relied on to work together because the height of each inflection point is located along an arc as it should be. That is an absolutely necessary requirement.

And that particular aspect of arching is definitely in evidence in early makers' work.

So, in my opinion, very high levels of accuracy are achievable with the right methodology.

[sospiri]

5 hours ago, Dennis J said:

 in my opinion, very high levels of accuracy are achievable with the right methodology.

Such as carving by eye and experience, which is how they did it back in the day methinks.

[Shunyata]

I appreciate the learning that comes from this kind of work.  Understanding the geometry helps with the carving.  

Ultimately, however, I don't carve that accurately and a small change in temperature or humidity will change the arching anyway.  Add to that deformation of the box after installing the bass bar, sound post, stringing up, etc.

[Dennis J]

11 hours ago, sospiri said:

Such as carving by eye and experience, which is how they did it back in the day methinks.

This is a circular argument but I'll try anyway.

Let us assume for a moment that early makers knew how to make arching templates the same way I have outlined and were as skilled as you say.

Why would they then not use those templates to check their arching in its final stages.

Those templates, being as accurate as they are, could have been used with scrapers to refine the arching even after the plates were glued to the ribs. That would have resulted in what we now see of their work.

That approach is the opposite to what contemporary makers seem to do now. Generic or copied templates are used to do most of the work and the maker then refines the shape by eye.

 

Edited October 17, 2020 by Dennis J
Addition

[sospiri]

6 hours ago, Dennis J said:

This is a circular argument but I'll try anyway.

Let us assume for a moment that early makers knew how to make arching templates the same way I have outlined and were as skilled as you say.

Why would they then not use those templates to check their arching in its final stages.

Those templates, being as accurate as they are, could have been used with scrapers to refine the arching even after the plates were glued to the ribs. That would have resulted in what we now see of their work.

That approach is the opposite to what contemporary makers seem to do now. Generic or copied templates are used to do most of the work and the maker then refines the shape by eye.

 

Why would they need templates if they could carve by eye? For the final scraping the bumps and dips would be really tiny and very easy to smooth out. They weren't looking for absooute perfection and it doesn't exist anyway. They didn't have time to over analyze everything the way people do these days. And the amount of work they did mean they had superior skills anyway.

 

[Dennis J]

No, I didn't say the final scraping. I said the final stages of their arching. Big difference. It's all about controlling the shape. That is what the arching templates I've shown are for.

I'm not sure that people over analyse anything these days. They just soak up what is fed to them.

[sospiri]

2 minutes ago, Dennis J said:

No, I didn't say the final scraping. I said the final stages of their arching. Big difference. It's all about controlling the shape. That is what the arching templates I've shown are for.

I'm not sure that people over analyse anything these days. They just soak up what is fed to them.

My point was that their carving was accurate enough to only need a tiny bit of scraping. Did i not make that clear? They worked quickly and with great skill, they knew what shape they wanted. I don't understand the need to rely on templates for the arching if you know what you want it to look like? People over analyze to the nth degree here, but in those days they didn't have that luxury.

[Dennis J]

You are getting close to saying they made violins like cheap ones made in China today. There is no doubt those workers are highly skilled. Or, for that matter, cottage industry ones made in Europe during the 1800s.

 

[sospiri]

3 minutes ago, Dennis J said:

You are getting close to saying they made violins like cheap ones made in China today. There is no doubt those workers are highly skilled. Or, for that matter, cottage industry ones made in Europe during the 1800s.

 

Yes I am.

Dennis is this instrument going to be a Nicolo Amati influence?

[Dennis J]

 As far as I can tell early Cremonese makers made violins based on original patterns and geometry, and that their work was very precise. That's not to say they didn't vary what they did. The geometry they used was proportional and flexible, just like the arching plan I've presented here. The outline pattern shown here, which I drew up, is close to one of Andrea Amati's violins, not Nicolo's. 

 

[sospiri]

I really don't care for the speculative geometry. Shapes evolve for practical and aesthetic reasons. I am more interested in structural ideas than abstract ideas.

[Marty Kasprzyk]

On 10/16/2020 at 3:46 AM, David Beard said:

Any kind of gentle curve you can think up from circle arc to parabola, spirial, elipse, catenary, cycloid, bent stick, wet cloth, etc is going to able to match arches to good tolerances if you cherry pick and muck about to make things fit.

What matters more is how predictive the approach is.  Can you reduce the fitting to definitely predictable and limited choices.  Or is there an aspect of just tinkering about to follow an example.

And how well does this work across many (preferably all) classical examples.

Buckled column shapes can be added to your list that look a lot like violin arches.  If you do a Google search for "Euler buckling modes" or look at "Buckling columns" in Wikipedia you will find many engineering illustrations and references.

An important variable in determine the buckle shape is how the ends of an axially loaded vertical column are held: fixed with no rotational or lateral motion, no rotation but with lateral motion, free to move in any direction, etc.  Various violin arch shapes can be easily mimicked by changing the angles of the column's attachment.

Attached is a photo of simple fixture to demonstrate the arch shapes of a thin wooden strip when it is end is progressively loaded at various attachment angles.  Also attached are some photos of tracings of these buckled shapes which shows how the curves inflection points can change and how the "bulge" changes with arches all of the same height.

[Greg Sigworth]

 

On 10/16/2020 at 5:21 AM, Dennis J said:

Although the arching templates I have made are very accurate I think the biggest benefit is that they can be relied on to work together because the height of each inflection point is located along an arc as it should be. That is an absolutely necessary requirement.

And that particular aspect of arching is definitely in evidence in early makers' work.

Thank you all for sharing ideas. Question: would the arc connecting the inflection points be at the same height from the plane of the plates as one moves around the violin or would it differ? I assume the same height would be a good choice, but possibly not true in reality.

[Dennis J]

4 hours ago, Greg Sigworth said:

 

Thank you all for sharing ideas. Question: would the arc connecting the inflection points be at the same height from the plane of the plates as one moves around the violin or would it differ? I assume the same height would be a good choice, but possibly not true in reality.

No. The arc in the layout serves two purposes. As a flat arc at a nominal (4.5 mm) edge height on the horizontal axis determining the inflection points' distances from the edge of the plate. And, tilted at 6 degrees (for the top arching) determining the height above the nominal edge height at each cross-arch position of each inflection point. So the waist cross-arch position (at the narrowest part of the Cs) has the highest inflection point. And at each end of the arcs, at the uppermost and lowest cross-arch positions the elevation is zero, or at plate edge height. The fact is that the inflection point for both the upper and lower bout and right around the top and bottom of the plate the inflection point is at edge height, or at the beginning of the scoop.

 

[Dennis J]

Something that I'd like to point out is that when using french curves to draw an arch I place them at the top centre of the intended arch with the part of the curve with the longer radius at that point, and the part with the shorter length of radius at the inflection point.

This means that when the other side of the arch is completed there is a smooth connection between the two. With no peaking.

And in the scoop the part of the french curve with the shortest radius is next to the edge of the plate.