Overview
Gearboxes are used in a number of the more advanced buildings, normally to add a unique cost for each construction. Each gearbox takes an input shaft rotating and converts it via a gear train into up to 3 outputs. The process of designing a gearbox is to figure out which ratios are needed and to implement those ratios in the form of positioning various sizes of connected gears on a
gearbox assembly table.
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Gearbox design
Gears
There are 5 gear sizes available, measured by their number of teeth (or relative number of teeth):
| Gear Size | inventory item | cost in metal | optimization cost |
| 3 | small gear | 2 brass | 0 |
| 4 | small gear | 2 brass | 0 |
| 5 | medium gear | 20 iron | 1 |
| 6 | medium gear | 20 iron | 1 |
| 7 | large gear | 120 iron | 5 |
The total optimization cost provides a basis for comparing two different gearbox designs. Spacers and small gears are constrained primarily by the shaft and gear limits, rather than by material costs.
Constraints
Up to 15 shafts may be placed in the 8x8 grid on the gearbox assembly table. Each shaft may contain up to 3 gears, and a gearbox may have no more than 30 gears in total (including spacers). There must be at least one gear on the input shaft at 1A, and a connected set of gears leading to between 1 and 3 shafts on the output row (8A-8H, at the top). The output row 8 may contain a maximum of three occupied cells, presumably to be used as outputs - no extra transfer gear locations.
Meshing
If two shafts are near each other, a gear on one shaft may mesh with a gear on the nearby shaft. This depends upon the sizes of the gears involved, and how far apart the shafts are.
- Adjacent: gear sizes must sum to 6 (the only possible combination is 3 meshing with 3)
- Diagonal: gear sizes must sum to 8 (4 meshes with 4, or 5 with 3)
- 2 steps apart: gear sizes must sum to 11 (6 meshes with 5, or 7 with 4)
- "Knight's move", 2 steps away then 1 sideways: sizes must sum to 12 (6 with 6, or 7 with 5)
To mesh, gears must also be on the same layer, i.e. both being the first gears on their respective shafts, both second, or both third. If the sum of sizes of gears between a pair of shafts is greater than needed to mesh, they are too close and you must remove one. This includes spacers, which count as greater than 1 (but less than 2) for meshing purposes. For example you can not put a spacer adjacent to a 5 or 6 gear, and you can not put a spacer either adjacent or diagonal to a 7 gear.
To minimize conflicts with adjacent shafts, generally put your small gears on the bottom layer with your medium and large gears on the second or third layer.
Standard Gearbox Notation
example: 5/3 or (5/3) or 53 - a size 5 gear that meshes with a size 3 gear.
example: (5/3) * (7/4) - a size 5 gear meshing with a size 3 gear. On the same shaft as the size 3 gear is a size 7 gear, which meshes with a size 4 gear.
example: (7/4) * (5/3) - the 7 still meshes with the 4, and the 5 with the three, but this time, the 4 and the 5 share a shaft. Note that this results in the same output as the previous example - as long as all the same gears mesh, you can move it around in the chain without affecting the output speed.
The standard notation is concerned with Shaft Rotation Rates, not directly with the sizes of the gears. This can be a bit confusing as the drive gears are at the bottom of the gearbox assembly table, sort of upside down. The mathematics works like conventional algegraic notation. When designing a gearbox it's often useful to use factored notation, (6/5 * 5/3) * 5/3 = 655/533 (the multiplication is implied) rather than 333%, as it's much easier to visualize the common elements when using the factored notation.
Rotation Rate in Gear Trains
Each shaft has a rotation rate, based on the 1A input shaft being 100%. In a properly designed gearbox, you can trace any output back to the input via a single chain of meshed gears between shafts. The rotation of the output is driven by the rotation of the second-last shaft, and so on back to 1A.
If the meshed gears between a pair of shafts are the same size, then both shafts rotate at the same rate. If they are not the same size, the shaft with the larger gear rotates slower. For example, suppose shaft 1A has a 3-gear (with 3 teeth), meshing with a 5-gear on shaft 2B. Every 5 rotations of shaft 1A will pass 15 teeth through where the gears mesh. Those 15 teeth are only 3 rotations of a 5-gear, so shaft 2B will rotate 3 times for every 5 rotations of 1A. That is, a rotation rate of (3/5) or 60%.
The same principle can be used many times in a row by using the 3 different layers available. A 3-gear on 1A can mesh with a 5-gear on 2B on the bottom layer, meaning that 2B rotates at 60%. Then we can put a 3-gear on the second layer of 2B, meshing with a 5-gear on the second layer of 3C (with a 1-spacer on the bottom layer). So 3C rotates at (3/5) of 2B, which is in turn (3/5) of shaft 1A. The final rotation rate of 3C is thus (3/5)*(3/5) = 36%.
Putting it Together
The need for gears to mesh, together with how they determine rotation, means that any output can be expressed as a product of a limited set of fractions. The earlier example is (3/5)*(3/5), expressing that going from 1A to 2B we mesh a 3-gear with a 5-gear (in that order), and the same from 2B to 3C. To build a gearbox with outputs in a desired range, you just need to find a sequence of fractions that multiply to give the right numbers. Much of the work has been done already, with an online tool to help e.g.
silver's gearbox page. Ingenia also compiled a list of common
gearbox ratios that may be useful.
3/3 and 4/4 just carry a given rotation rate from shaft to shaft, and are comparatively cheap since gears of size 3 and 4 are small gears. Many designed gearboxes contain chains of gears -3-3-3 or -4-4-4 carrying a given ratio to the required output shaft.
3/5 and 5/3 are the next cheapest, since size 5 is a medium gear.
5/6 and 6/5 come next in cost order, with both 5 and 6 being medium gears.
3/6 and 6/3 are shorthand, with an implicit 5-gear in the middle since 3-gears and 6-gears cannot mesh directly. Hence this ratio costs 2 mediums and a small.
4/7 and 7/4 are much more expensive: a 7-gear is a Large gear costing 120 iron and requiring the master casting box.
More expensive still are the shorthand ratios of 3/7, 7/3, 6/7 and 7/6, all of which have an implicit 5-gear in the middle to allow the others to mesh. Finally there is 6/4 which has an implicit 5 and 7 in the middle. Fortunately these ratios are almost never needed.
The relative cost of the various gear ratios ignores the small gears and assumes that a large gear costs 5 times as much as a medium gear. A combination like (3/5*5/6) that has a shared gear will be a bit cheaper. Note that every change in speed requires a medium or large gear.
- Cost of 1 - 3/5 and 5/3
- Cost of 2 - 5/6 and 6/5
- Cost of 6 - 4/7 and 7/4 (or 5/7 and 7/5)
For those with Unix machines or possibly cygwin on Windows, you can use Kem's gearbox table simulator for offline design. It's actually
easier to see the gearbox design on this than on the in-game gearbox table. (If you have patches for the gearbox simulator, please feel free to contact Kem or Mjr.)
Tips for Multi-output Monstrosities
With advanced marble mechanics and Empty Hand Towers, you often need a single gearbox having multiple outputs. In theory, you can design these the same way as single-output gearboxes: work out the chain of fractions you need, and turn them into chains of shafts. In practice, there are both extra hurdles and significant savings to be found.
- You can re-order the chain of fractions freely. This helps when laying out which chains should go to which outputs.
- You can often choose chains that share a lot of fractions. Sometimes two or more outputs can even share the whole chain. You can re-order all the shared ratios to the start, and only branch off when the ratios differ. There are usually many possible chains for each output range in these gearboxes, and a good choice can save many medium gears.
- You must fit within the 15-shaft and 30-gear limit. This is not difficult for the 1-output boxes, but can be difficult on some 2-output boxes and may regularly drive you insane with 3 outputs. Sharing ratios is essential to the success of many designs since it saves both gears and shafts.
- Sometimes it is possible to save a few gears (mainly spacers) by changing which layers you use for which gears. In particular, if you have a line of 3-3-3 or 4-4-4 gears, it is usually best to try to put them on the lowest layer, without spacers. This can help with the 30-gear limit.
- If you have a three-output gearbox, you can share fractions on the first and third output with a crossover. A crossover uses two 7-4 or 6-5 interconnects on different layers--one vertical pair as part of the gear chain leading to the center ouput, and a horizontal pair crossing over the center chain and connecting the chains for the left and right output. This technique can be essential to some three-output designs.
- If you have two outputs which are one apart (e.g., 8B and 8D), you may be able to drive one from the other, if they are close enough in speed to be covered by a 5-6 or 4-7 pairing.
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