Gear Finder
The gear finder (for a given ratio) uses a dynamically created lookup table to dramatically speed things up. I tried a brute force method first and after 12 or so hours I stopped it. While a brute force method will find the results the time taken makes it un usable. For a quadruple reduction (8 gears) there are about 360,040,606,269,696 permutations with a choice of 66 gears from 12 to 100 teeth that I can make with my dividing head.
It is imperative that you first select the your dividing head/rotary table and any custom hole plates you may have. Building the data base will take 5 to 10 minutes and will happen automatically when you make your first calculation.
Specifying the ratio say 1.25 - 1, that means 1.25 turns on the input gear to get 1 turn on the output gear (just to avoid any confusion) and give a speed reduction. While 0.8 - 1 means 0.8 turns on the input gear gives 1 turn of the output gear, a speed increase. (0.8 - 1 is the inverse of 1.25 - 1)
Select the smallest and largest gears, 20 and 50 work well and will find most ratios.
Results is the most you want to be presented to you, 10 to 15 is lots
The error percent that is acceptable (to a minimum of 0.001 percent). Then select + - error or + error or - error.
Press the "Calculate" button and get your solutions.
A word about accuracy. Computers do not handle decimal numbers at all computers use fractional numbers and then display as a decimal number. There are very few decimal numbers that work out correctly as fractional numbers, computers just get as close as they can, All the calculations rounded to 6 decimal digits accuracy. For practical purposes this lots of accuracy.
The displayed results are in the form of fractions with the drivers on the top and the driven gears on the bottom.
There will be times when the ratio of a result will be exact but there will be a very small error percent. This is because the error is much to small to display in the ratio but is big enough as a percentage to show an error. There is nothing that can be done about this other than show you a number in scientific notation. The bottom line is that when the error is that small it is a difference that makes no difference in practical usage.
If you have forgotten your fractions there is just one thing you need to remember. The driver gears can be swapped around as can the driven gears, the order makes no difference to the gear ratio. Swapping the gears around can be useful for mechanically making things fit. Just do not swap driver gears with driven gears.
The results. This calculator will show you solutions using the least amount of gears. The calculator will try up to an 8 gear gear train before giving up. Giving up is unlikely.