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Gearboxes

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).

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. 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.

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. Osmirik's Gearbox Finder and the TMEG Gearbox Tool

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 is the shorthands 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.

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.

Designs


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Last edited March 26, 2004 8:39 am by Teao (diff)
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