Finding My Way with a Compass
This morning I was excited to spend the day in the shop. My twelve tiny boxes were patiently waiting to be given bottoms. In the previous tiny box building, I had done a rather poor job on this aspect. Having lots of box bottoms to cut gave me many opportunities to get better at it.
The other advantage of needing so many bottoms is the desire to come up with a plan to not only improve but to be able to duplicate the results. The first step was to ‘do the math’. I approached it differently than the last time. Starting with a blank piece of typing paper and a compass, I drew a line and then used the compass to measure the distance of the inside of one of my boxes. From starting point A on the line I drew an arc across the line. This became point B. I then drew the arc all the way past 90 degrees. Next the point of the compass is place on point B and an arc drawn past 90 degrees.
Now I needed to draw a perfectly perpendicular line from both of my points. The beauty of using a compass is that one is able to construct perfect angles. I needed to create two additional points along the original line and it was easiest to make them the same distance as my original line from point A to point B. So now I have four points along the line.
To get the first perpendicular line, I place the point of the compass on the point to the left of point A. I then extend the compass degrees to beyond point A, by a good bit. Next I draw an arc above point A. After this, I simply put the point of the compass on point B and draw another arch above point A, passing through the arc I just drew. When I draw a line from point A to the intersection of the two arcs (using a straight edge), the results is a perfectly perpendicular line. By repeating these steps with point B, a second perpendicular line is created.
The precision of my drawn box makes me happy. I place one of the boxes down on top of the piece of paper and it is dead on. It is important to know how deep the groove is, so I measure and found them to be 4 mm. I then measured and drew an additional box around the box I had just derived using my compass. These are my notes. Having this map really helped with my next step.
I want to do six of the boxes with walnut tops and bottoms, but having a few extra bottoms is probably a good idea. My little map let me figure out exactly how big a piece of walnut to cut. The piece is rough cut, so I planed it flat with my 5 and 4 1/2 and used Jeff to resaw the piece to the thickness I wanted. Lastly I took it to the router table and used the ‘map’ I had created to calculate how to run the piece across the 3/8 ” down spiral Freud bit.
I would estimate that it took about as long to cut six bottoms as it had previously taken to cut one. Each of the bottoms cut today were much better than the previous two, so there was much joy in my secret bunker in Martelle. I celebrated the success by using the key hole bit purchased yesterday, to cut holes in my rare earth magnet tool holding thingy, which I had built earlier this year. When it was hung on the wall, there was another wave of satisfaction.
All in all, I would have to give today a 34 on a scale of 1 to 37.
"I then measured and drew an additional box around the box I had just derived using my compass."
I hope you used your compass (and straight-edge) for that too! Doing otherwise would seem to be a Euclidian crime! Your straight-edge was not ever mentioned. People unfamiliar with the construction (not derivation) you performed probably want to know about points C and D too--and a picture is worth a thousand words! : )
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LikeBill,
You are absolutely correct, so I made the corrections you suggested. Thanks so much. I do need to add a picture of my drawn box, that is a good idea.
Brian
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LikeAccording to a math genius I know that IS pretty good!
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Like"I then measured and drew an additional box around the box I had just derived using my compass."
I hope you used your compass (and straight-edge) for that too! Doing otherwise would seem to be a Euclidian crime! Your straight-edge was not ever mentioned. People unfamiliar with the construction (not derivation) you performed probably want to know about points C and D too--and a picture is worth a thousand words! : )
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- disagree
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LikeBill,
You are absolutely correct, so I made the corrections you suggested. Thanks so much. I do need to add a picture of my drawn box, that is a good idea.
Brian
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- disagree
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Like