Hi r/spirograph! It really is me.
A simple way to make a engaging interesting looking design is to use multiple simple designs. This one is made by using one design from each of three different gears.
Selecting which gears to pair together can be a challenge when there are so many options to choose from. In this design the three component simple designs from the three different gears have 8, 16, and 16 petals. But the gears weren't selected with that knowledge in advance. How then do you make a design like this without lots of planning and testing; which is a fine way to go about it too but I want to show that it isn't the only way.
I selected a 160 ring and a 120/96 hoop which I had out from another design that I was working on. I decided that the 160 would be stationary with the 120/96 inside it and free to move. That gave me an internal ring on the hoop of 96. I wanted a relatively simple design so I picked gears with a large common multiple that they shared with the 96. I selected 24, 48, 72 (1/4, 1/2, and 3/4 of 96 respectively). Another way to look at that is that I picked gears that shared lots of common factors with the 96 ring and with each other.
Aligning all the pieces at the 6'oclock position with the darts I started with the 24 1A, then 48 1B, and finally 72 2A.
If this short time lapse is too fast you can adjust the play back speed to slow it down to 0.25x speed.
The pieces used in this design are:
160 ring (Plentiful Gear Set or Full&Plentiful Hoops Gear Set)
120/96 hoop (Full&Plentiful Hoops Gear Set)
72 gear (Compact Gear Set)
48 gear (Compact Gear Set)
24 gear (Compact Gear Set)
Today I'll be discussing the process of making this piece:
The pieces I used to make it are:
160 ring (Plentiful Gear Set or Full&Plentiful Hoops Gear Set)
120/96 hoop (Full&Plentiful Hoops Gear Set)
48 gear (Compact Gear Set)
I used the 210/160 hoop from the Full&Plentiful Hoops Gear Set and I held it still in the large oblong from the Nested Oblong gear set which is not necessary but made keeping everything still easier.
How was it made?
Start by aligning the gears like this:
Hold the 120/96 hoop stationary and use the pen hole 1A. This will make an oval. The angle of the oval is determined by the rotation of the 48 gear. If the 1A hole was aligned at the bottom with the darts in the other pieces then the oval would be going radially into the center. By rotating the 48 gear by 12 teeth it makes the oval on a diagonal. One iteration of this looks like this:
To make the rest of the design you step the 120/96 hoop 2 steps clockwise around the 160 hoop. Keep the 48 gear in the same spot in the hoop. This means that you move the 48 gear and the hoop together and that column A of medium pen holes always stays lined up with the triangular darts on the 120/96 hoop.
With each two tooth step and repetition of the design you change pen holes going up and down the small pen hole A column. 1A to 2A to 3A to 4A to 5A to 4A and so on up and down.
Yesterday I posted the Art Recipe 2 but there was a mistake in the recipe I'd posted. The first take away from this is that I should make actual notes while making the art rather than type it up after an evening of creative experimentation.
Down to the detective work to find out where I'd gone wrong. I knew I had the gears right because I had a photo of the setup that I'd used. And I had a photo that I'd take on the first half of the design where it is easier to see the patterns.
I was pretty sure that it wasn't many steps that I was doing with the hoop and with the gear and while I thought I know which direction I was moving each gear I could no longer be sure.
To begin my investigation I set about testing a few simple combinations.
Each test helped me get a better intuitive feel for how the different combinations of movements changed the design.
Also, I quickly came up with a simple notation for myself at the top of each page after realizing that I was going to loose track of what I was doing almost immediately if I didn't.
After doing a few of these I started to think more critically and try and work out what I could deduce because even if I was only searching in the space of three steps or less that was 36 different combinations to test and that was going to take far too long; especially if I could be clever and make it easier.
My first realization was that I could look at the reference picture to see how many times I had iterated the base 9 pointed design. This would tell me how many times I was shifting the hoop to the right. Every two steps of the bottom of the hoop is like translating it one step right in terms of hoop position.
Picking one of the fans created by shifting and rotating the design I counted 24 instances of it. Combined with the fact that I knew that the design had been concluded somewhere in the 20s on the oblong this helped me conclude that it must have been made with 2 step increments on one side of the hoop. That nailed down the parameter as 2(right).
Next I looked at the designs that I'd made and the one I was trying to copy and saw that on the same fan of petals that I counted when I stepped the gear to the right it did not make that counter clockwise progressing swoop. From there I determined that I would explore the left stepping solution space. Instead of trying the few combinations at hand now I was able to make one more deduction.
If I step the hoop two steps right and the gear 1 steps left it is very similar (but not identical) to translating the hoops top and bottom both 1 right. The movements almost cancel each other out as I'd seen in hoop 2 right and gear 1 left. I'd also tried hoop 1 right and gear 1 left and I figured that would make something similar to hoop 2 right and gear 2 left and that wasn't the shape I was looking for either so I opted to try hoop 2 right gear 3 left which worked out.
Other things to note take away from this is that the translation of the center of each 9 pointed design is shifted to the right with each iteration but because of the 3 left steps of the gear the pattern itself rotates to the left making the characteristic fan shape that was counted.
Made with the Nested Oblong Gear Set and the Full Page Gear Set.
Using the large oblong (334), the 210/180 hoop, and 140 gear.
Center the 210/180 hoop at the 0 mark in the oblong ring.
align hole 3A with the bottom (closer to you) of the hoop in the oblong.
Complete the simple design with the 3A in the 140. Repeat this design many times. Between each repetition make these two moves:
1) step the bottom of the hoop two teeth to the right
2) step the 140 gear three steps to the left (clockwise)
This design was taken out to about the 27 mark on the right hand side of the oblong rack. This completes the first half of the design which looks like this:
To make the completed design reset the gears to the starting but with the 140 aligned to the top of the oblong at the zero point.
Do the simple design and this time the steps between each repetition are:
1) step the top of the hoop two teeth to the left
2) step the 140 gear three step to the right (clockwise)
completing this set of simple designs and translations completes it to look like the top picture.
Note: This recipe has been corrected about 24 hours after being initially posted. Step 2 used to indicted that the 140 gear should be moved 1 step instead of three. Thank-you to Angie Woollard for pointing out the mistake.
Made with the compact gear set.
Using the 96 ring, the 72 gear (with 36 ring in it), and the 24 gear in that.
The 24 in the 36 makes a 3 pointer design.
Start with the 72 gear at 6 o’clock in the 96. Position the 72 so that the 36 is at 6 o’clock.
Align the 24 gear so that the 1B pen hole is one gear tooth off of the 6 o’clock position.
Hold the 72 gear still and make one copy of the 24 in 36 design.
Shift the 72 6 teeth in one direction and repeat the design.
With each set of steps the 1B pen hole and 36 cutout should remain as close to the edge of the 96 ring as possible.
Repeating this design 16 times will complete the design.
Note: the photos of this gear set are of a V3 fluorescent blue gear set so it doesn't perfectly represent the improved appearance of the V4 compact gear set.
Lots of big Wild Gears news today!
1) New Gear Set Announcement: Nested Oblong Gear Set
2) Improved Gear Set Lettering
3) Improved Doughnut Pieces
4) Faster Order Delivery
5) Full/Plentiful Hoops Gear Set
6) Version 3 overstock sale
7) Request For Feedback
1) The Nested Oblong Gear Set:
This exciting new gear set is designed to explore complex compound designs. New straight gear segments allows for the creations of parallel rack gears. Using a hoop in the rack system gives precise control over positioning and re-positioning pieces. This gear set has an unparalleled number of ways to adjust and control the shape and position of your designs. These new degrees of freedom make creating new compound designs that were previously impossible. It is hard to describe but easy to show this gear set in action. Please take 90 seconds and check out this video on YouTube. (seriously, check out this video. It is beautiful)
In the video a hoop is being used in the large oblong. In the hoop is a gear with an off-center cutout and in the cutout is a small gear. Repeating the simple design that the system makes while moving the hoop and the starting point of the small gear creates a piece of art with a sensation of movement and depth.
For more excellent pictures of Wild Gears art made with the Nested Oblong Gear Set you can check out the work of my collaborator on this gear set, Jeddy Grant, at:
YouTube: @Jeddy Grant
the r/spirograph subreddit is also a great place to see and post beautiful art.
The Nested Oblong Gear Set is not a stand alone gear set. It is designed to be used with other Wild Gears Gear Sets for best effect. It is strongly recommended that you have the Full Page Gear Set as the 210/180 hoop is very useful to have.
2) Improved Gear Set Lettering:
Gear Sets now have frosted engraved letters! They are very legible now. This change is the most obvious impact of Wild Gears now being produced in house. New material selection and more laser cutter control allow for new exciting changes; like the improved lettering. The lettering has been re-done on all the gear sets. A variety of other small improvements are also being made to tweak the designs, such as adjusting pen hole placement where it has made pieces fragile.
These two photos show the contrast between the new lettering (the frosted white bold lettering) and the hairline lettering.
3) Improved Doughnut Pieces:
The plastic doughnuts that make parallel lines possible are wonderful and used to be very hard to tell the sizes apart; they are sized in 1 mm increments. Now the doughnut pieces are colour coded! Each size increment on the medium sized ones (6mm diameter) have there own colour code. For the larger doughnut pieces (9 mm diameter) they repeat the colour code twice. The colours are:
The smallest hole used to be 1 mm but that has been widened to 1.5 mm to accommodate a wider range of fine tip pens. Additionally all the 1mm holes on the encyclopedic gear set have been increased to 1.5 mm to improve usability.
All new gear sets will have these new colourful doughnut pieces included as default.
Additional cards of doughnut pieces will be available for replacement or supplementation of doughnut piece supply
4) Faster Order Delivery:
Most orders will now be shipped they day they are placed. Doing in house manufacturing means that a stock of inventory can be maintained. Previously orders took 5 days to make before they shipped. Large orders or during particularly busy times orders may take 2-3 days to ship.
5) Full&Plentiful Hoops Gear Set:
In the Full & Plentiful Hoops Gear Set the large shapes of the Full Page and Plentiful Gear Sets have been packed onto one gear set sheet as sets of hoops. This is designed to make them more portable and easy to handle, as well as giving some new hoop combinations.
This gear set cuts the large sheet into 4 smaller frames making it much easier to handle each part. The 210/160 hoop also gives more possibilities for using the large oblong in the Nested Oblong Gear Set.
6) Version 3 overstock sale:
There are some remaining gear sets from v3 that are for sale for half off or better. Quantities are limited. There are also a couple of v.4 gear sets that have minor imperfections listed too. Act now before they run out.
7) Request for feedback and suggestions:
If you have any parts that have broken or other things about Wild Gears that haven't worked well for you, I'd like to hear about it. Send your emails to firstname.lastname@example.org. I'd also like to hear about what you really love about Wild Gears.
If you have an idea for a new theme or idea that you'd like to explore that needs gears that don't exist yet I'd love to chat with you about your idea and dream. If I have the time I'll sometimes design new gear sets based on requests and suggestions.
Thank-you for your enthusiasm for Wild Gears and for taking the time to read this email,
Sometimes acrylic breaks. It can be fragile when bent and accidents happen. If you get a break in your Wild Gears it can be repaired. This method works best if the broken piece has a break in it rather than being broken into multiple pieces.
The glue to use is acrylic cement, or superglue should work well too.
Use a toothpick or pin to apply a small amount of the glue to the broken face. Then align the break into the flat position you want the glue to cure it. Wipe off any extra glue. Some tape can help hold the pieces together nicely.
Read the glue container to learn how long it should take for the glue to set.
Be careful not to glue your piece to whatever surface you are working on, like your table, or to yourself.
This fix should make the piece usable again but there will be a visible mark where it was broken and glued.
Good luck in your mending!
Today'll be a quick post about what all the different numbers on the gears mean.
Most gears have two sets of numbers and non-circular gears have three sets.
The biggest number is the tooth count of the gear. This is a measure of the circumference and is helpful to know when making design choices. Most gears also list the prime factors of the tooth count. Prime factors help predict how many lobes/petals/points a design will have. In the picture above the tooth count of the gear is 135 and the prime factors are 3^3*5 (3*3*3*5). Some small gears have the tooth count as their only number due to space constraints. Prime factors will still be listed where the number is engraved beside the ring. Some gears have a prime number of teeth and therefor don't have any factors to list.
The numbers on the non-circular gears will be written as 'big number / small number' ( 120/24 for example). These numbers tell you about the different parts of the non-circular gears. These gears are constructed from arc-segments of different sized circular gears. A triangular gear that was 120/24 means that the flat 'sides' are made from part of a 120 tooth gear and the corners are made from part of an 24tooth gear. This is important to know because the resulting triangle gear will not work properly in a ring that is smaller than 120 teeth and the triangle ring will only work with gears that have fewer than 24 teeth (bigger ones will get stuck in the corners).
There is also hoops which have an inside and outside tooth count.
In the picture above the outside of the hoop has 210 teeth and the inside has 180 teeth. The prime factors of each are listed beside. On some hoops the tooth counts will be listed separated by a slash (210/180) due to limited space.
Additional note: Pen hole numbering
Pen holes come in 4 sizes: small, medium, large, and extra small. Small pen holes are on every gear and have a diameter of 3 mm, medium pen holes are on most gears and have a diameter of 6 mm, large pen holes are on some gears and have a diameter of 9 mm, and extra small pen holes are rarely seen on very specific gears and have a diameter of 1 mm. Each line of pen holes is numbered starting at 1 at the edge of the gear and counting up until the line ends. Lines of the same size are marked with A, then B, and so on. Line A starts closer to the edge of the gear than line B. The distance between A1, B1, and A2 are the same; this allows placing more equally spaced pen holes on the gear than one line could hold.
Non-circular gears also have 'side' and 'corner' pen holes to distinguish between.
Using the little cylinders ('doughnuts') that go into the medium and large holes can yield a wide variety of results. This post is a starting point for developing further techniques.
Gear Sets come with a range of sizes of the doughnut pieces with each one provided with some duplicates; recognizing how easy they are to lose. The multitude of them can make it hard to determine how many sizes there are and what size any one piece is.
When I start using the doughnut pieces I'll line them up by size, removing ones that I can recognize to be of the same size. To calibrate the doughnuts take a simple ring-gear combination (72:36 for example) and start with the doughnut with the biggest hole and make the design. Switch colours; ideally to a lighter one, black to red is very good for this. Using the lighter colour and the next doughnut piece in the line repeat the design. If it is the same size then the red line will not show up as it is directly on top of the black line. If it is a very little bit different the red line will show up very close to the black line. Depending on the pen type there may be no white space between the two lines. If the size difference between the pieces is larger there will be a blank pinstripe gap between the two lines. This process can be repeated to calibrate the sizes between all the doughnut pieces in the line; sorting them by size and removing any duplicates as well as informing the relative step sizes between them. Note: Using different brands of pens will yield different line positing too. For this calibration step use two pens of the same brand, or stick to just one pen.
In this photo I have finished the calibration step and selected 4 different sized doughnut pieces. I have them lined up so that I don't get confused. I've selected colours to go with each step and you can see that black and red are aligned with a 5th blank step that corresponds to using the medium pen hole without a doughnut piece.
The picture below was made using 72:48 1B (+4Hoops), (12 CCW) 2B (+4Hoops) where 1B used Black, Blue, Dark Blue, Purple, and Red and 2B used Red, Orange, Yellow, Light Green, Dark Green.
Notice that the pen lines and colours are each distinct but have not white space between them. Because these pen colours overlap just a bit the stronger colours dominate and the central lines look narrower.
Depending on pen line weight it is possible to use this effect to make a narrow pinstripe of colour down the middle of a black line by sandwiching a line (I like red or gold for this effect) between two heavy black lines.
More space can be made for each individual line and colour by choosing doughnut pieces that provide more space, like in this next example.
These are the core techniques of how to determine the spacing provided by the doughnut pieces and some different ways to begin using them. By experimenting with spacing, colour, and line weight you can create incredibly diverse and powerful variations on a design.
The tightly packed parallel lines made by the doughnut pieces also appear different at different distances. Quite some time ago I made a design that was composed of a tightly packed set of these lines that played to tartan inspired colours and and spacing. Much to my surprise, at a distance it looked more like a beige design but it caught the eye in a hard to describe sort of way. When approaching the piece I would cross a some critical distance and all the individual colours in ti would snap into focus and it would suddenly appear colourful. I'll try and find this piece and share it in a future post, but I have no idea how to capture this feeling of it photographically.
Thank-you for reading.