Compound curve help.

Hi, I have a problem, I don’t quite understand what’s happening and I was hoping that someone with more experience could tell what’s happening and why.
I was approached by a customer to design and make a curved entrance table along these lines. I came up with this design using recycled Kauri.

I decided to make each leg with a skin on each side and a void in the center, I made a template curved in the appropriate shape, cut them all out on the bandsaw then routed them smooth. The first problem I had was that as I glued each layer the “skin” actually twisted, that was a very upsetting and expensive learning curb. I appropriated some more Kauri and began again this time being very careful and sure that as I added each layer it stayed square and true on a flat table with a square, I noticed that this was very difficult to do and I began to realize that perhaps the curve was compounding or complicating the job. The next issue was cutting the sides of the “Leg” in the “V” shape, I once again made a template from bendy ply, then lay the template over “outer skins” and using a straight copy router bit with the bearing at the top, routed the two outer skins out.

BUT, when I lay them on a flat table, the join is not flat or square, I’ve run a square over it is definitely square, I am completely baffled and unsure of what to do and where to go from here. Failure is NOT a option. I feel like I am breaking some sort of law, but for the life of me I don’t understand what’s happening. Can someone with experience with compound curves explain exactly what is happening and why and how to fix it. Thank you.

My suspicion is that it's because the legs taper from one end to the other, rather than having the same cross section throughout; essentially you're making a curved pyramid and that's going to f--- with your head to no end.

In a normal square pyramid, the sides are at 90 degrees to each other when measured relative to a line drawn from the tip to the centre of the base, but NOT when you measure square to the face as shown by angle DA. For a straight pyramid this can be calculated fairly easily

https://1.bp.blogspot.com/_OGu0H7TFU...00/pyramid.jpg

̶W̶h̶a̶t̶ ̶y̶o̶u̶ ̶h̶a̶v̶e̶ ̶i̶s̶ ̶a̶n̶ ̶a̶n̶g̶l̶e̶ ̶D̶A̶ ̶t̶h̶a̶t̶ ̶i̶s̶ ̶c̶o̶n̶s̶t̶a̶n̶t̶l̶y̶ ̶c̶h̶a̶n̶g̶i̶n̶g̶ ̶a̶s̶ ̶i̶t̶ ̶g̶o̶e̶s̶ ̶a̶r̶o̶u̶n̶d̶ ̶t̶h̶e̶ ̶c̶u̶r̶v̶e̶ ̶o̶f̶ ̶t̶h̶e̶ ̶l̶e̶g̶.̶

The other problem is that when you unfold curved objects, lines that are "straight" in 3D are not straight in 2D. As you can see here, all of the lines are straight around the sphere, but if you were to flatten out the triangle, all 3 sides would be curved

https://upload.wikimedia.org/wikiped...9rique.svg.png

Here's the wiki page, you will not like the math https://en.wikipedia.org/wiki/Spherical_trigonometry

If the legs were solid it'd be no issue; just make however many pieces you need to the shape and stack them together (as I suspect the one in the photo is done). Unfortunately, your decision to make it hollow has shot you in both feet. Short of a 5-axis CNC, the only way I see to do it is to fit each join by hand with a spokeshave :no:

Thank you for your reply, I just KNEW I was breaking mathematical rules. Yes I've made all 4, 2 inners and 2 outers but I have an idea. If I can get my hands on some large drum sander belts I think I could essentially sand them flat on a table by clamping wood to the side "At level" then just move it back and forth, hopefully flattening and straightening the join. The inner skin is going to be even harder to deal with I think, If I do this again I'll be going at it in and a completely different way.... I know there is no substitute for experience but boy sometimes it hurts...

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Originally Posted by Kiwi75

I just KNEW I was breaking mathematical rules.

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Well...trying to :p

Hope you can find a solution relatively easily. Sometimes the learning curve is more like a cliff :doh:

Quote:

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Originally Posted by elanjacobs

My suspicion is that it's because the legs taper from one end to the other, rather than having the same cross section throughout; essentially you're making a curved pyramid and that's going to f--- with your head to no end.

The other problem is that when you unfold curved objects, lines that are "straight" in 3D are not straight in 2D. As you can see here, all of the lines are straight around the sphere, but if you were to flatten out the triangle, all 3 sides would be curved

If the legs were solid it'd be no issue; just make however many pieces you need to the shape and stack them together (as I suspect the one in the photo is done). Unfortunately, your decision to make it hollow has shot you in both feet. Short of a 5-axis CNC, the only way I see to do it is to fit each join by hand with a spokeshave :no:

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Without drawing the design to scale, I think the desired result can be achieved using brick construction and then applying veneer to surface of the blank. If you used balsa as the substrate you could build solid light weight legs

That would be an ideal method starting from scratch, but I believe the OP is trying to salvage the timber he's already got.

Ian, I would do something similar using veneer for sure next time, Paulownia would be ideal I'm thinking.
After a day's playing around I think I have got it back on track. The sides are on both outer skins, now to shape and attach the inners, I'm expecting more push back but feel for-armed now.
Thanks for you opinion guys.
Much appreciated.

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Originally Posted by elanjacobs

That would be an ideal method starting from scratch, but I believe the OP is trying to salvage the timber he's already got.

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I'm thinking that, for a commission, time is money -- or in this case rebuilding from scratch might represent a lower total investment of time compared to salvaging the timber already used.
I doubt that the OP's client is willing to pay for the learnings a project like this involves.

Restarting from scratch is not an option as I've already had to start again already, I have to make this work.
I feel confident that I've got it sorted, Not a great feeling knowing that this job is almost a right off financially but it does come with the bonus of the client being very wealthy and she wants to use this piece to show off to her other wealthy friends in order to get me more work, she seems to have taken a personal interest in me and my work (I've made stuff for her already) I have to take the loss on the nose and take the lessons learned as positives and and just keep moving forward.

"Life is suffering" Budda