​

I have little experience with Ottoman empire firearms of this date. The Istanbul Military Museum has quite a number of early pieces in it, and it would be useful if one of the curators stopped by here- because it's very unlikely we'll otherwise decisively settle this. But we can narrow the possibilities a little.

The rack-and-pinon would have to be part of the gunlock. Now, 1621 is when the first true flintlock guns were being made in France by Bourgeoys, so in Europe there were wheel locks, matchlocks, snaphances, and flintlocks. Because a rack-and-pinon is a way to rotate something through a wide arc, it's very likely your source was referring to a wheel lock: the hammers , or cocks, of matchlocks, snaphances and flintlocks had to only pivot about 90 degrees or less, and they had a fairly heavy leaf spring that pushed down on a short lever ( the tumbler) to do that. Only the wheel lock needed more: in that, the cock held a piece of iron pyrite against a turning serrated wheel, which sent sparks into the pan. That wheel needed more than 90 degrees rotation, and so there was what looks like a short bicycle chain that went partially around the tumbler to turn the wheel. Notably, that flexible connection is also present in the very first drawing we have of a wheel lock: Leonardo da Vinci's fire starter.

Again, it would be enormously fun to fly to Istanbul, get permission to go into the collection and look at some locks. Often museums have damaged pieces or parts in the back rooms that give you a better look at the inside of things. But given the very common European design with a short chain, I would first do a check on the translation of the Wu Pei Chih , see if at some point there has simply been a translator shrugging his or her shoulders and filling in the blank for a technical term without being too sure of what it represents. In the King James translation of the Book of Samuel there's a mention of a file being used to sharpen something. That has often been cited as the first mention of a file: but really what happened was the translators had a word that only occurred once, that clearly meant something that sharpened. Lacking any other context or etymological roots, they just shrugged and wrote "file". The same thing could have happened here.