Work is still keeping me busy (for about the next 2 weeks) then things should get much better. In the meantime, as a mental exercise, I decide to come up with the basic math for gear rations and size.
In the past when working on the wooden versions of the clock, I did some basic math to make sure the gears would work. However, the wood was much easier to correct if there was an issue. It was really easy for me to redo a gear if I needed it. With the metal gears, an awful lot of work goes into one of those gears. I can't afford to fake it anymore.
The problem is that given a particular distance between two arbors (axles) and what ratio of movement was needed (for every turn of one gear, the other should turn six times), I came up with a fairly simple formula.
d = distance between arbors
r1 = radius of smaller gear
r2 = radius of larger gear
t = ratio between gears
This is what I came up with.
r1 = distance / (t + 1)
r2 = distance - r1
Anyone care to check me on this? :) My address is medievalsmith@gmail.com if you don't have a Xanga account.
I hope to get back to the forge soon. When I do, I need to start being precise on my measurements, I am going to try to be very careful with this. However, I also want to try and be precise using what they may have done in the middle ages.
I will use a divider to do the formula above. For example, assuming a 6 inch distance and a need for ratio of 10 to 1, I will take the divider and attempt to divide the distance 11 times (remember the formula up above, ratio plus 1...). The measurement of one division would be equal to the distance on the divider. That will also be the radius of my smaller gear. The other radius would be 10 of those divider distances. It may sound complicated but it really is not that bad. I wanted to come up with a simple technique that would not require the use of a ruler marked to very fine degrees.
Another nice thing about doing it this way is that what few examples I have seen of medieval clockmakers, they always have dividers but I've never seen one depicted with a ruler.
NOTE: When I refer to a radius up above, it is the distance if the gears were simple wheels with their outer edge touching. For actually gear teeth I will have to add a bit to the size listed above to allow tooth contact. In most cases that will a little under 1/4" added to both gears.
Another thing is that up until now when I have been working on the clock I have often been experimenting. This means that I often rushed parts especially if I was doing it during a public demo. From here on out, I am going to try and adopt the attitude of making the final part. I don't want to have to redo many more parts...
