Sunday, February 17, 2019

The Curate Cycloid

I use a curate cycloid for most of my cross arches.  Some models are slight variations of it.  This guitar arch is very wide.  To get the rise off the top that I want, the cycloid can't be the full width.  I'm doing it in the Guadagnini style, so I'm bringing the arch low point to 7-12 mm from the outside edge,  and that will be perfectly flat.  There will be no dip.  The arch will just rise.

4 mm thick at the edge.  This is for the back.

The most important point to know in carving a cycloid is the inflection point.  This is where it changes from concave at the end, to convex across the middle.  This point is at a different place on every cycloid.

If the arch is narrow and tall, the inflection point will be pushed out more to the edge. It will also be lower relative to the height of the arch. If the arch is low and wide, the inflection point will get closer to the midpoint in height, and will be further in from the edge.

This will show you how it works:



70 is the angle of rotation.  You will need to check every degree and see the difference in angles.  If the point is before the inflection, the angle is continually increasing.  After the inflection the angle between the points decreases.  You have to use all the numbers to the right of the point.  The angle changes are very slight, and rounding off will mess you up.  Here's what this one looked like.  I write down some things, and the difference between the lengths in width I put in the memory:






You can see that the angle doesn't change that much, and each degree of rotation makes very slight movement.  Armed with that information it is easy to draw a cycloid:




I can readily see where the arch needs to come down, and about how much.  I also see that the middle is still far too thick, since the outside arch in the middle is where I want it.   I wanted it high.  Guadagnini was not Strad, and he certainly wasn't del Gesu.  It is just about 29 mm from the bottom.  I mark up the outside of the back, and then can trim it down some.




The area in the middle is how much the cycloid is extended in the middle.  It just blends in with the rest.  The numbers show the thicknesses.  It is still very thick.  I didn't know what I needed.  The inside needs to go up about 2 mm on the long arch.  I made a gauge for measuring.  I found a cheap TTC dial gage that measures in TENTHS  of a mm.  It was on sale for a crazy low price.  Maybe it's overkill; but it works great, and is just deep enough for the arch top.




It comes in handy for fine finishing.  Especially on the back where the thickness can vary by 100% or more from the edge to the middle.  The belly is not as difficult as far as thicknessing goes.  It doesn't have a ton of travel, and maxes out at 11 mm.  No problem; anything that thick would be useless for sound anyway.  I was thinking more in the way of 3 mm to 7.5 mm.   We'll see.

I roughed some off the outside, and wanted to see what digging the inside arches deeper would do.  It is working out nicely.  The long arch is a straight catenary, and the diagonals are straight catenaries now too!

Next time we'll go over catenary curves.  It is the essence of the instrument.




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