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Do not read this in order. Go look at all the pictures, then come back and read the words, then go look at the pictures. Repeat as needed. Hoops, like the 210/180 from the Full Page gear set, have an interesting property. There are only some points on the hoop where there teeth on the inside and on the outside of the hoop line up. Lets call this an alignment point. On the 210/180 there is an alignment point every 7 outer teeth, or 6 inner teeth. This is because on a 210 gear each tooth is 1.714... degrees and on the 180 gear each tooth is 2 degrees. 7*1.714... = 12, and 6*2=12 If you look at each side of the hoop and cancel the common prime factors that will tell you the periodicity of the alignment points. When you put the 210/180 hoop in the 210 ring in the frame you can impact the orientation of the 180 by where you place the alignment point. I'll explain. Think of the 3 o'clock position on the 210 frame as our default starting position. It has a dot marking it. For many gear sets that position in the ring has a dart making it easy to find. With the Alignment Point at the default starting position the 180 side of the 210/180 hoop is also in precise alignment with the default starting position. Now imagine lifting the 210/180 ring and rotating it one tooth counter clockwise (CCW). There will be a tooth in the 210 side of the ring at the default starting position, but the 180 inside of the 210/180 ring won't quite align anymore. It is 0.286 degrees clockwise from the default starting position. If you repeat these steps 7 times you will be back at a position where there is an alignment point in line with the default starting position. You can use each of these intermediate positions to make a design with a gear that is at a reproducible and different starting point. This means that there are 1260 starting points for a design when using the 210/180 hoop like this. Visualizing the steps from one alignment point to the next. Starting at teal. Then next step takes you to red, where you can see the difference between the 210 (no boarder) and the 180 (black boarder) lines that show the beginning of the offset of the two sets of gears. Progressing through Yellow, Blue, Purple, Green, Black, and finally Teal. Each colour step show a widening gap between the 210 and 180 alignment until the 180 black line aligns with the 210 teal line. If you use 7 of the adjacent steps, which is the same space as making one design and counting one tooth over and repeating it, you can fit all these lines into it. At this density there is no white gap between the lines even at their maximum separation. If you use every second step, effectively 3 lines per tooth, then you get this. Still very dense but showing faint whisps of white between the lines. I made a magnet with an arrow on it to help me keep track of where the current position on the 210 ring was. In this photo set I use every second step to make the design. Design 1 (black), no offset. Hoop is at the alignment point and the default start position. Design 2 (red), the hoop has been stepped 2 steps CCW. The lines on the hoop help me keep track of which 180 tooth corresponds to which 210 tooth. The 60 gear is put on the tooth that lines up with the default start position (marked by the magnet with the arrow). Design 3 (green), the hoop has stepped another 2 steps CCW. The 60 gear is still positioned to align with the default start position, but is now shifted most of a gear tooth clockwise (CW) Design 4 (black), the arrow magnet has been moved CW 1 step and the hoop has reset the alignment point back to starting and is aligned with the arrow magnet. Different hoops have different ratios. By combining (with tape) the 210/180 and the 180/140 I made a 210/140 where every 3 teeth on the 210 are 2 teeth on the 140. This means that it can only make one extra step between teeth. In the pictures above the black lines are a regular design repeated 5 times each with one step of the 60 CW. The red lines are two repetitions of the design halfway between the black ones. Effectively at 1.5, and 2.5 teeth CW.
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The Ultra-Table has been updated!
It had a math error that made its results mostly incorrect! This has been fixed as of November 20th, 2024. Get the updated Ultra-Table at the same link as before. And save a copy to your google drive or locally to use it. Announcemetns and other news:1) New Gear Sets:
2) Wild Gears Ultra Table 3) Whole Shebang Price Change 4) Holiday Shipping Timelines Multi-Dense Non-Circular gear set The Multi-Dense Non-Circular gear set is the first gear set to explore high density pen holes, akin to the double dense gears for circular gears. These higher density pen holes are arranged in two ways: 1) vertically, like a standard double dense gear, and 2) laterally, as if to fit more columns of pen holes in the fan. Non-circular gears have pen holes arranged in a fan, not just a column. This means that the whole fan must be shifted vertically or laterally so a whole gear must be dedicated to just one pen hole size and type of high density pen hole. When the fans are labelled with letters 'A, B, C, D' then they are the more standard form of high density where A 1->B 1->C 1->D 1 then leads to A 2, just like in a double dense circular gear. When the fans are labelled with numerals 'I, II, III,' then the multi-dense fans are being translated laterally. For example in a fan the columns might be every 3 gear teeth. But now there are 3 fans (I, II, III) where fan II is offset by 1 gear tooth to the right, and fan III is offset 2 gear teeth to the right. This means that between the fans there is effectively a column of pen holes at every gear tooth. These high density gears make absolutely stunning designs.   Oblong Hoops gear setThe Oblong Hoops gear set is designed to be used in conjunction with the Hoops gear set. This gear set is a collection of oblongs, each of which pairs with one of the hoops from the Hoops gear set. The oblongs can be used as a simple ring, rolling gears around the inside and making designs that way. They can also be used in conjunction with a hoop that fits snugly between the parallel lines of gear teeth. That hoop can be repositioned between each iteration of a design making for a setup that has precise repositioning rotationally and laterally. This is a style of composition that was first made possible with the Nested Oblong gear set. It is technically more versatile and challenging and can make stunning, complex, compelling art. The gear set is cut from one 40 cm x 40 cm piece of acrylic and is divided into two 40 cm x 20 cm pieces, each of which contains a set of nested oblongs. Each oblong is marked with the tooth count, prime factors, counting tick marks, center line marker, and a number on the left side of the oblong that denotes what hoop matches it.  Extra Long Oblong Hoops gear setThe Extra Long Oblong Hoops gear set is very similar to the Oblong Hoops gear set and is designed to be used in conjunction with the Hoops gear set. This gear set is a collection of extra long oblongs, each of which pairs with one of the hoops from the Hoops gear set. The extra long oblongs can be used as a simple ring, rolling gears around the inside and making designs that way. They can also be used in conjunction with a hoop that fits snugly between the parallel lines of gear teeth. That hoop can be repositioned between each iteration of a design making for a setup that has precise repositioning rotationally and laterally. This is a style of composition that was first made possible with the Nested Oblong gear set. It is technically more versatile and challenging and can make stunning, complex, compelling art. The gear set is cut from one 60 cm x 40 cm piece of acrylic and is divided into two 60 cm x 20 cm pieces, each of which contains a set of extra long nested oblongs. Each oblong is marked with the tooth count, prime factors, counting tick marks, center line marker, and a number on the left side of the oblong that denotes what hoop matches it.  Oblong Enormous Hoops gear setThe Oblong Enormous Hoops gear set is conceptually similar to the Oblong Hoops gear set and is designed to be used in conjunction with the Enormous Hoops gear set. This gear set is a collection of oblongs, each of which pairs with one of the hoops from the Enormous Hoops gear set. The gear set is cut from one 60 cm x 40 cm piece of acrylic and contains a set of nested oblongs. Each oblong is marked with the tooth count, prime factors, counting tick marks, center line marker, and a number on the left side of the oblong that denotes what hoop matches it. The gear set includes 2 nested gets of hoops (128/84/56, and 125/100/75/50). Both sets are included because gear-in-gear designs with lots of shared prime factors are a popular design style to use inside an oblong setup. In the 126 set each inner ring is 2/3 the size of the previous ring. In the 125 set each ring decreases by 25. In both cases they have lots of shared prime factors.  Buy it here. Mammoth 2: modular compatible gear setThe Mammoth 2 Gear Set is made of 1/4 hoops that are modular and sized to work with all the modular gear set components. This gear set measures 80 cm x 80 cm (31.5 inches) and comes in four quadrants that snap snugly together. With this gear set you can make staggeringly large art. But even more than that you can combine these 1/4 circle arcs with other modular pars and shapes.  Travel gear set The Travel Gear set is a smaller gear set; 5.3 inches, 13.3 cm, a side. It is a collection of gears from the Compact gear set and the Full Page gear set. It is designed to give a taste of what Wild Gears can do in a small package. It doesn't have engraved counting marks or any doughnuts, but does manage to fit 9 gears and hoop into this diminutive gear set. Comes with a small cardstock slip cover to help keep everything together when not being used. A note on limited quantity gear setsThe Extra Long Oblong Hoops gear set and the Enormous Hoops gear sets are both made with sheets of acrylic which are 60 cm x 40 cm which is larger than the sheets that are used to make all the other gear sets. I only have about 30 sheets of it in stock currently, and restock acrylic very infrequently so when they're all gone it'll be a while before there can be more. If you are interested in these gear sets, get them while you can. Wild Gears Ultra TableFor years I've been asked for more tables about combining gear sets and there are so many combinations that I haven't been able to make them all. But now you can have any combinations of gear sets you want and have a petal table for those gears. Using google sheets I made a fancy spreadsheet where you can select which gear sets you want a table for and it will automatically recalculate and display the combined table. To get access to this cool new tool follow these instructions: 1) Open this link, it will take you to the Wild Gears Ultra-Table 2) If you are not signed into your google account, sign in now. The button is at the top right of the page. If you do not have or want a google account you can download an excel file copy from the Wild Gears downloads page. 3) Select the file menu, and from that choose "Make a copy" (see picture)  4) A window will appear: Rename your file as desired and press the 'Make a copy button' (see picture)  Congratulation! You now have your very own copy of the Wild Gears Ultra-Table Note: If new gear sets are added in the future, you will need to make a new copy of the Ultra-Table" Whole Shebang Price ChangeThe Whole Shebang listing, a collection of all Wild Gears gear sets has been updated to include the newly announced gear sets. It has, for a long time, been offered at a 40% discount off the individual price of the collected gear sets. That will change in just over 1 week from posting. On Tuesday November 12 the discount on the Whole Shebang will change to be a 30% discount. So if you've been on the fence about getting it, there are just a few days to do so before the price goes up. Other gear sets prices will stay unchanged. Holiday Shipping TimelinesWith the busy shipping season fast approaching it is important to get your orders in early. I recommend placing any orders that need to arrive by Christmas by the end of November. International delivery times, USA, Europe, and elsewhere, get less certain as the shipping rush happens. The frequency of packages delayed when clearing customs and crossing borders goes way up in late November and December. Delays are often a week or less but longer, 3 week delays, are more common this time of year. The sooner you get your order placed the more likely it is to be delivered quickly and not bogged down.
December 20th is the last day of the year that I will be shipping gear sets. Shipping orders will resume in early 2025. Also, there is a potential shipping disruptions with Canada Post as the union contract is being re-negotiated and that process has reached the point where strike action could be taken. If there are any critical developments I will provide updates. By comparing different sized pen holes you can find ones where the overlap. Using these will make parallel lines. To compare the pen holes start with the larges one and position it somewhere specific on the ring. Hold it still and draw a circle in the pen hole. Now move the gear aligning smaller pen holes with the same position. Look for pen holes that are fully inside the ring that you drew. If you are using 3 or more sizes of pen holes you can draw circles for each size to better see all the stages and how they fit. The Hoops gear set is an excellent companion gear set for either the Compact gear set, or the Full Page gear set. It gives a large selection of different sized hoops to make new designs with. In addition to acting as rings to roll gears inside of (or outside of) the hoops can also be part of multi gear systems to interesting results. What is the Hoops gear set: |
AuthorAaron Bleackley, designer of Wild Gears Archives
January 2025
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