# Inversions cutting board tutorial



## jadams (Sep 12, 2011)

*Inversions cutting board tutorial*

In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.

Here's the original project I posted: http://lumberjocks.com/projects/53452

Hint: When you look at the board, long ways going left to right, every row is a different size, but every group of 2 rows are all the same size!

Solution: First you rip strips like you would for a regular end grain board, but in a progression of widths from largest to smallest in pairs (one light one dark). The height of the strips needs to be the largest width + the smallest width + at least 1/8 inch. I made a really simple thin strip jig for the table saw, indexed the side for 3/4 and 1/8 strip sizes, then with a very sharp pencil free handed in the number of "steps" I wanted there to be to add up to the final board width that I wanted. So I'd set the jig, cut a light and dark strip, then bump the jig to the next size and repeat. Each pair of strips need to be *exactly* the same width, or else the whole thing won't be symmetric down the middle and nothing will line up when you swap them back and forth. I ran them all through the planer in pairs.









The ripped strips all merged together. Ideally these would all be the same height.

After lining up your two progressions of strips so they merge together biggest to smallest and smallest to biggest, glue them all together, cross cut them into rows and flip them end grain up. It works out easier/better later if you end up with an odd number of rows here. That finishes progression #1, and you could stop here and invert every other row and have a pretty board…









Crosscut and end grain flipped up, then every other row flipped long ways. *You don't want to actually flip them long ways if you're going on to the next round of cuts. Leave them all going dark to light!*

But, if you flip/invert every other row now, that leaves every row the same size! So what we can do now is cut each of these rows, end grain up, into two rows each, in a progression again (say 3/4 to 1/8 again but with a different number of steps), then alternate swapping those. This uses up that 1/8 inch that we added in for the height earlier, leaving just enough so the widths and heights line up square in the corners after the second round of cuts.

*UPDATE:* Here's some extra explanation on this step. After cross cutting all your rows you should have all your rows going dark to light, left to right, with the end grain up. *Like the picture above, except all dark to light in one direction.* What we're going to do is cut every row in half, left to right, in a progression, making each row into two rows. By varying the size of these rows we're able to make a pattern going the other direction. This is really the central "new" idea vs. other end grain cutting board designs.

If you remember from before we said our smallest size would be 1/8" and the largest 3/4", then we added those plus 1/8" for the height. The height of those strips is now the width of these rows. So for your first row, you would cut 1/8" strip from the "inside", lose around 1/8" from sawing, ending up with a 3/4" remainder piece! Then flip the 1/8" piece. On the second row you'd cut a bit more than 1/8" from the inside, lose 1/8 inch from the cut, and end up with a bit less than 3/4. Flip the bit larger than 1/8" piece. Keep going, sizing your cuts so when you get to the last far row your cut size will be 3/4", leaving a 1/8" remainder piece. If you give it a little thought you can actually do two rows (say cut 1/8 off the inside of the first and last row) per saw setup. Just keep track of your grain direction.*END UPDATE*

If you have an odd number of rows that means the middle row gets cut right down the center. I actually used a band saw and a drum sander for this round of cuts. These thinner strips from the second round of cutting can be brittle at the glue joints.

Then just glue it all up and do your finishing.









An extra row appeared in mine. How did that get there….

-Joe


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## rrdesigns (Sep 4, 2009)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


Wow. I wish I had paid more attention in geometry. Thanks for sharing. Now to try and figure it all out without creating a psychedelic mess.


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## John_G (Jan 12, 2011)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


ummmm yeah…. still confused about the size of the strips…. could u give us a breakdown for this board for example…..

I get the largest and smallest strip all add up to the sme amount…..
1-1/2" + 1/8" = 1-5/8" 
next strip
1-3/8 + 1/4 = 1-5/8" 
next strip
1-1/4 + 3/8" = 1-5/8" 
next strip
1-1/8" + 1/2" = 1-5/8"

.....and so on until i get to….

1/8" + 1-1/2" = 1-5/8"

That makes sense, but why do u state to add 1/8" atleast….????


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## jadams (Sep 12, 2011)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


You have to account for the material loss from the second round of cutting. If you only make them 1-5/8" high, there wont be enough material to cut the row into 1/8" and 1-1/2" (etc) strips plus have room for the saw kerf+any sanding or planing. So in your case you would want your first strips to be 1-1/2" x 1-6/8" + 1/8" x 1-6/8", etc. Anything beyond the 1/8 just gives you extra wiggle room with your second round of cuts.


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## rance (Sep 30, 2009)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


Nice board, but must be some magic involved. Getting from pic2 to pic3 is not clear to me. I'm a guy, I only look at the pichures.  I'm sure it will come to me when I'm in the middle of the process. Or I'll do it in SketchUp first. Thank you for sharing.


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## jadams (Sep 12, 2011)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


Haha, no problem. The second picture is just after cross cutting and flipping the end grain up, then every other row flipped long ways. You don't want to actually flip them long ways if you're going on to the second round of cuts.


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## roer (Jul 13, 2009)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


How does your thin strip jig for the table saw look like ?


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## topherstrux (Jul 25, 2011)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


How many bf of material did you use?


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## Gonecrazy (Jun 23, 2011)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


WOW … this took me few mins to figure out but i got it … once it hits you all in the bad of the head you will also feel the duh moment …. so ill try to help with that moment … since the second round of cuts is what is most confusing we will start there ….. with the end grain facing up on all the pieces as a finished board take 2 sections (one from each side of the board on the outside) and cut say a 1/4 " strip … lay them back in place then flip the 1/4" strip end for end …. then move the the next set moving towards the center but this time say cut a 3/8" strip off then rince and repeat ….

P.S. Jadams ya might want to add a forth pic of the way the board should be set to get to the forth pic …. pic 3 was just a sample that you could do and just leave it that way …


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## jadams (Sep 12, 2011)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


Roer: I just used a roughly 1"x1"x6" piece of white oak with a slit cut along 3/4's of its length. Through the slit I put a bolt and a washer that I has ground down until it would fit in the miter slot of my table saw. A nut on top let me tighten and loosen the whole thing. Very rough, but it did the job, just be careful it doesn't bind. Rockler sells a much nicer one here: http://www.rockler.com/product.cfm?page=18056

topherstrux: I'm not sure exactly, I'd guess around 3-4. I'd have to go back to my plans and crunch a few numbers.

Gonecrazy: Thanks for helping explain it all! You're almost there, except that you don't flip both 1/4 pieces, you always flip the "second" piece. So for the first one you would flip the 1/4 inch piece, and on the last one you would flip the remainder, not the 1/4 inch piece.

(On the last piece you're not really cutting off the 1/4 inch, you're cutting off the largest size, since it's the last row, which should leave that 1/4 inch. It's the same thing in the end, just up to how you choose to wrap your head around it. I actually set it up and cut it how you explained, working from the outside rows in. Fewer cuts to setup that way.)

I would post another picture if I had one, but those are the only pictures I took during the build process. I wasn't planning on doing any kind of write up when I started unfortunately.

edit: I updated the original blog post with some extra explanation. Thanks.


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## roer (Jul 13, 2009)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


Thank you for the explanation, but how do you ensure accuracy - the incremental change in the width of the rows is very small


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## jadams (Sep 12, 2011)

jadams said:


> *Inversions cutting board tutorial*
> 
> In response to some questions about how this pattern is made… I'm not sure if this is the only method, but here's how I did it.
> 
> ...


roer, you're telling me. When I first started figuring this out I came up with some formulas that would generate a table of numbers with all the widths of the strips. That was all well and accurate, but what good is it when the numbers are all 1.2134/128's apart? It's a huge pain to measure and cut that accurately. What I realized was that it's more important for the first and last pieces to be near their start and end sizes, and for the pieces in between to just be progressively smaller (ending at the right end size), but it doesn't matter if it's not an absolutely perfect linear progression. What does matter, especially if you do it this way, is that you use the same saw setup to cut both a dark and light strip. That way, even though it's not a 1/1000" perfect progression, it'll still be symmetrical when you flip.

Here's my exact method:
1. Setup the jig for the smallest size (1/8 for me), mark the jig where it was over the miter slot.
2. Do the same for the largest size (3/4 for me).
3. Free hand mark the jig between those two marks with the number of steps that you want. Try to get it as perfect as you can, but don't stress too much. I marked mine for 15 rows.

My table saw is terrible, so I've adapted by using my jointer and planer more.
4. Reset the jig for the first cut.
5. With a fresh jointed edge against the thin strip jig, cut the pair of strips. One from the light lumber and one from the dark. 
6. Rejoint the edge of the lumber to clean up from the cut
7. Reset the jig a hair to the next size.
8. Jump back to 5 and repeat for all sizes.
....
9. I then ran each pair of strips through the planer to clean them up, taking off between 1/128-1/64", but making sure no strips came close to becoming smaller than the next size down. My planer goes down to 1/8" depth, so that was the lower limit for my strip size.

My second round of cuts had a much larger step size (fewer number of steps), so I just used a ruler for that and just cut along the line on the band saw. The relative size setup would work there too, though.


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