Introduction: Circular Slide Rule
After seeing Phil B's Making Your Own Slide Rule, I went on a huge slide rule kick. I did a lot of research on them, and when I did, I discovered that there are circular variations. One of the nice things about circular slide rules is that you'll never run into the "run the cursor off the end of the slide rule" problems, since there is no "end" to a circular slide rule. Plus, circles are nice. Ok! Let's get slidin'!
Step 1: Design the Slide Rule
The first thing you'll need to do is design the rule. There are places on the internet that have templates for circular rules, but I wanted to design my own. It turned out that in the process, I learned a lot about how slide rules worked. Anyways, I wrote a C code to produce a .svg file of the front and back faces, along with the interior pieces that hold the rule together while letting it slide around. The code is below, and the result is in "slide_stator.svg". The cursor is in "cursor.svg". I designed these files so that the rule could be cut out of acrylic with a laser cutter. I don't have my own laser cutter, so I had the guys over at ponoko.com do the cutting for me.
Anyways, some notes on the design:
On one side (let's call this "side 1"):
* A log scale (inner)
* A C/D scale (sliding)
* A sine scale, in radians (outer)
On the other side (side 2):
* A K scale (inner)
* An A/B scale (sliding)
* A cosine scale, in radians (outer)
UPDATE: At someone else's suggestion, I'm also attaching .pdf versions of the templates, so people can just use card stock. Note that when you look at the files, the lines are very very thin. This is because the Ponoko folks need to have the templates in a certain format.
Anyways, some notes on the design:
On one side (let's call this "side 1"):
* A log scale (inner)
* A C/D scale (sliding)
* A sine scale, in radians (outer)
On the other side (side 2):
* A K scale (inner)
* An A/B scale (sliding)
* A cosine scale, in radians (outer)
UPDATE: At someone else's suggestion, I'm also attaching .pdf versions of the templates, so people can just use card stock. Note that when you look at the files, the lines are very very thin. This is because the Ponoko folks need to have the templates in a certain format.
Step 2: Tools and Materials
For the assembly, you won't need much:
* Tweezers
* White acrylic paint
* Superglue
* Lubricating oil
* A steady hand
* Tweezers
* White acrylic paint
* Superglue
* Lubricating oil
* A steady hand
Step 3: Prepare Pieces
After getting my pieces in the mail, I had to unpeel all the protective backing from all the pieces. I went with 3mm black acrylic for the slide, and 3mm clear acrylic for the cursor. You might want to use the tweezers to peel the small pieces. After unpeeling everything, take note of which side is which. They're marked in the pictures (side 1 has the C/D scale, side 2 has the A/B scale). Also, note the blank circular pieces. These are the pieces that get sandwiched between the two faces of the rule, allowing it to slide.
Step 4: Paint the Numbers and Tics
(I actually did this part after I assembled the slide, but you'll definitely want to do this BEFORE assembly.)
The scoring marks weren't bright enough to be able to see the tic marks and numbers easily, so I decided to use white acrylic paint to make them stand out. Luckily, you don't need to hand paint each individual line: just glob a whole bunch of paint over the tics and numbers, and then wipe off the excess with paper towels or rags. Do the same for the cursor pieces with the fancy-pants design on them. The acrylic is so smooth that the paint doesn't stick to the un-scored parts, and only stays in the grooves. Awesome!
The scoring marks weren't bright enough to be able to see the tic marks and numbers easily, so I decided to use white acrylic paint to make them stand out. Luckily, you don't need to hand paint each individual line: just glob a whole bunch of paint over the tics and numbers, and then wipe off the excess with paper towels or rags. Do the same for the cursor pieces with the fancy-pants design on them. The acrylic is so smooth that the paint doesn't stick to the un-scored parts, and only stays in the grooves. Awesome!
Step 5: Assemble the Slide
Ok, here's where you're going to need the steady hand. It's really important that everytihng gets positioned just about perfectly here, otherwise the slide won't be able to slide, and/or you won't be able to read the scales on side 2 correctly.
First, take the larger of the sandwich pieces, and carefully superglue it to the outer ring of side 2 (the one with the A/B scale). It's very important that the rings are flush ALL the way around. Then take the inner ring of side 2, and superglue it to the inner ring of the sandwich pieces, making sure the interior is flush.
Now you'll superglue the inner ring of side 1 to the other side of the inner sandwich ring. However, you need to make sure that the two sides are properly aligned. Take a sheet of paper and draw a straight line with a ruler across it. Fold down this line, and tape it to the inner ring of side 2, making sure to bisect it with the marked line. Now, find the side of the bisected circle that has the index on both the A/B scale, AND the K scale. This will be where two 1's line up. Put a little arrow on the guideline here, so you know which way the index should go on the other side. Now flip the whole thing over, unfolding the paper at the same time.
Use the guideline to superglue the inner ring of side 1 in the correct position. Make sure the 1 (the index) points towards the little arrow, and also that the interior circle is flush all the way around. Did you get it? Phew! But wait, there's more!
Do the same process of creating a guideline on the outer ring of side 2. Place the inner rings (all three that are now glued together) in the middle of the face down outer rings, making sure that side 2 FACES DOWN. Now, take the outer ring of side one, and superglue it to the outer sandwich ring ONLY. Since it's superglue, you only need a tiny bit; if you use too much here, there's a chance that it will seep out onto the inner rings, which would make it so it doesn't slide at all. Bottom line: use superglue sparingly here.
If you did everything correctly, you should be able to slide the inner rings freely. Mine were a little sticky, but after the oil (next step), they were moving pretty smoothly.
First, take the larger of the sandwich pieces, and carefully superglue it to the outer ring of side 2 (the one with the A/B scale). It's very important that the rings are flush ALL the way around. Then take the inner ring of side 2, and superglue it to the inner ring of the sandwich pieces, making sure the interior is flush.
Now you'll superglue the inner ring of side 1 to the other side of the inner sandwich ring. However, you need to make sure that the two sides are properly aligned. Take a sheet of paper and draw a straight line with a ruler across it. Fold down this line, and tape it to the inner ring of side 2, making sure to bisect it with the marked line. Now, find the side of the bisected circle that has the index on both the A/B scale, AND the K scale. This will be where two 1's line up. Put a little arrow on the guideline here, so you know which way the index should go on the other side. Now flip the whole thing over, unfolding the paper at the same time.
Use the guideline to superglue the inner ring of side 1 in the correct position. Make sure the 1 (the index) points towards the little arrow, and also that the interior circle is flush all the way around. Did you get it? Phew! But wait, there's more!
Do the same process of creating a guideline on the outer ring of side 2. Place the inner rings (all three that are now glued together) in the middle of the face down outer rings, making sure that side 2 FACES DOWN. Now, take the outer ring of side one, and superglue it to the outer sandwich ring ONLY. Since it's superglue, you only need a tiny bit; if you use too much here, there's a chance that it will seep out onto the inner rings, which would make it so it doesn't slide at all. Bottom line: use superglue sparingly here.
If you did everything correctly, you should be able to slide the inner rings freely. Mine were a little sticky, but after the oil (next step), they were moving pretty smoothly.
Step 6: Assemble the Cursor
Before assembling the cursor, you'll want to oil the slide. I used stone sharpening oil since it was the only thing I had on hand, but it ended up working very nicely. I'm pretty sure you could use any oil lubricant, as long as it doesn't affect acrylic.
Anyways, take the three innermost circular pieces left over from the slide pieces, and superglue them in a stack directly over the circle pattern on one of the cursor pieces. If everything is still lined up correctly, you should be able to push the three stacked pieces through the middle of the slide pieces. CAREFULLY glue the three clear endcap pieces onto the end of the cursor as shown in the picture.
Finally, superglue the final cursor piece onto the top of the three-circle-stack and the endcaps. Woot! It's done!
Anyways, take the three innermost circular pieces left over from the slide pieces, and superglue them in a stack directly over the circle pattern on one of the cursor pieces. If everything is still lined up correctly, you should be able to push the three stacked pieces through the middle of the slide pieces. CAREFULLY glue the three clear endcap pieces onto the end of the cursor as shown in the picture.
Finally, superglue the final cursor piece onto the top of the three-circle-stack and the endcaps. Woot! It's done!
Step 7: Use It!
So as not to leave you hanging, here's a few examples of what this slide can do. Suppose you want to calculate 2.08 * 4.30:
* Position the inner index of the C/D scale on 2.08 of the outer C/D scale.
* Move the cursor to 4.30 on the inner C/D scale.
* The answer is on the cursor on the outer C/D scale. In this case, it looks to be about 8.94.
To calculate sines, you use the cursor and the sine scale. For example, if you wanted to know sin(0.89):
* Place the cursor on 0.89 on the sine scale.
* Read the answer on the outer C/D scale. In this case, it looks to be about 0.777.
Now, if you've been paying attention, you'll notice that the scales on side 2 go counterclockwise, whereas the scales on side 1 go clockwise. This is so that reading a number on side 1 corresponds to an answer on side 2. To calculate squares and cubes, you need to use the second side. For example, to find 9^2 and 9^3:
* Align the indices on the C/D scale (line up the 1's).
* Place the cursor on 9 on the C/D scale.
* Flip the rule over. 9^2 is on the A/B scale, and 9^3 is on the K scale.
Ok! I hope you've enjoyed this! I had a lot of fun making this one. As always, comments and constructive criticism are welcome.
P.S. - If you didn't catch my *cough cough* note back in step 1, I'm entering this into the Epilog challenge. I can only assume that if you've read this far, you're at least mildly interested in this, which warrants a vote in my book. So please vote for me! Thanks!
* Position the inner index of the C/D scale on 2.08 of the outer C/D scale.
* Move the cursor to 4.30 on the inner C/D scale.
* The answer is on the cursor on the outer C/D scale. In this case, it looks to be about 8.94.
To calculate sines, you use the cursor and the sine scale. For example, if you wanted to know sin(0.89):
* Place the cursor on 0.89 on the sine scale.
* Read the answer on the outer C/D scale. In this case, it looks to be about 0.777.
Now, if you've been paying attention, you'll notice that the scales on side 2 go counterclockwise, whereas the scales on side 1 go clockwise. This is so that reading a number on side 1 corresponds to an answer on side 2. To calculate squares and cubes, you need to use the second side. For example, to find 9^2 and 9^3:
* Align the indices on the C/D scale (line up the 1's).
* Place the cursor on 9 on the C/D scale.
* Flip the rule over. 9^2 is on the A/B scale, and 9^3 is on the K scale.
Ok! I hope you've enjoyed this! I had a lot of fun making this one. As always, comments and constructive criticism are welcome.
P.S. - If you didn't catch my *cough cough* note back in step 1, I'm entering this into the Epilog challenge. I can only assume that if you've read this far, you're at least mildly interested in this, which warrants a vote in my book. So please vote for me! Thanks!
