On Promised Spreadsheets, Gear Set Details, and Triangle Layout
The excel document that I created to calculate the number of petals for any gear-ring combination is available here:
(please let me know if this link doesn't work properly)
The document has 5 tabs. One each for the Compact, Full Page, and Mammoth Gear sets as well as a calculator tab where you can enter any two numbers and it will return the number of petals that the gear-ring combination would make, and finally a comprehensive colour coded table for all numbers 1-360 which is more than a little overkill.
If you don't have excel the document should open in Numbers, Open Office (free), NeoOffice (free), or likely several other fine programs I am unaware of.
Gear Set Details
There are two things I think I should mention about the gear sets:
1) The gear sets will arrive with a sticky paper backing holding all the cut pieces in place. The easiest way to remove this backing is to place the whole sheet on a table (or other flat surface) so that no part of it is sticking off the edge and the sticky paper backing that is to be removed is face up. Begin peeling one corner of the backing off and work your way evenly across the entire sheet.
The only difficulty is that the smaller cut gears tend to try and go with the sticky backing. To prevent this peel the backing away from the acrylic sheet at a sharp angle and keep an even (downward) pressure (with your other hand) on the gears as they begin to be exposed. This will stop them from levering out of the sheet. The main reason to prevent them from lifting with the sticky paper is that if they slowly lever up rather than lift strait up out of the cut the gear teeth could be damaged. I haven't had this happen yet so I don't know how hard it is to break gear teeth, if anyone does have gear teeth break I'd like to hear about it.
2) Some of the holes cut in the gears have holes cut in them. Keep these pieces ('doughnut' pieces). Any circular piece with a hole cut in it can be used to make parallel designs. Any circular pieces that don't have holes cut in them are not particularly useful and can be kept or discarded at your discretion.
To make a parallel design start by making any design you wish while using any gear hole that has doughnut pieces that will fit into it. Once the design is done carefully place a doughnut piece in the hole that was just used to make the design and then, placing your pen into the hole in the doughnut piece, repeat the same design. It is important to keep the gear and the ring in the same position between the two iterations of the design otherwise the designs will be slightly offset.
As I've been adding holes to gears for the strange shapes gear set I realized that I should explain a little about why the holes in triangular gears are in such strange configurations. The following comments apply to all non-circular gears I've been making but I'll be confining the specifics of this discussion to triangular gears.
Triangular gears are made of arc segments from two different sized gears with the larger gear providing the sides of the triangle and the smaller gear providing the corners of the triangle.
Image #1 (above) will be our guide to the anatomy of the triangular gear. The numbers separated by a slash (36/18) tell you the circumference of the gears used to make the sides (36) and corners (18) of the triangle. These numbers are important because if you try and use it as a gear inside another ring the ring needs to be bigger than the side number (36) or it won't roll properly. Similarly, if you want to use the triangle as the ring the gear must be smaller than the corner number (18) otherwise it won't be able to roll properly. The other number (27) is the tooth count of the gear. This is useful to know if you want to predict how many petals the design will have.
In the next image I've added some red numbers and outlines so that I can more easily refer to several different aspects of the design.
Section #1: This area is centered around the center of one of the sides of the triangle. The left most column of holes is the same as you'd find is a size 36 gear. The difference in this case is that the triangular gear has a fan of the holes, usually distributed every two gear teeth over the width of one side of the gear. On a circular gear making a fan of holes doesn't give you more design possibilities because the gear is rotationaly symmetric whereas a triangular gear has fewer axis of symmetry so each hole in the fan of holes in section #1 will produce a different design. To be very through the fan should radiate symmetrically from the center row. That takes a lot of space and the same effect can be achieved by flipping the gear over when you need holes on the other side of the fan. This allows for the inclusion of other, different holes in the gear too, which I think is a good trade off.
Section #2: Very similar to Section #1 except that it is centered around the corner of the triangle and as such has a much smaller space to fill.
Section #3 & #4: Play the same roles as section #1 and #2 except for the fact that they use much larger holes. This allows for the use of doughnut pieces and the creation of parallel designs. As the triangular gears get bigger and there is more room fans of the large holes are generated too.
In many cases these fans of holes overlap and conflict. I've had to prioritize which is more important and my priories have been as follows: small holes above big holes, then sides above corners. Sides and corners (of the same size hole) rarely conflict. I made these choices because the sides are easier to use and proved a wider range of designs than the corners (due to the larger area). Similarly using smaller holes allows for a whole fan where only one larger hole might fit. Given the very limited space I think that this has been the best prioritization of its use as it maximized diversity, and ease of use.
The design of the second iteration of the strange shapes gear set is almost complete. It has taken much more time than I expected it would but I am glad it has as I have made something I am very happy with. One of the last bunch of gears I added to it recently was a set of three nested septagonal (seven sided) gears/rings.
I'll send more news when I have it. If there is anything still puzzling about the gears, their use, or their design, I'd love to hear your questions.