New Appreciation for Bachot
I recently learned that Tony Grafton at Princeton has a functioning book wheel. It was designed by Dante Gnudi for a 1992 exhibition curated by Grafton. This functioning machine provides the opportunity to address the question of how much knowledge was actually possessed by engineers like Ramelli and how much they depended on the tacit knowledge of artisans. I talked to the staff at NYPL--the original exhibition sponsors--to get additional information about the project. Unfortunately, their records probably offer little insight on the question.
Without third party information, I need to take a different approach. Brushing off my engineering degree, I decided to do the actual detailed design of a book wheel replica. It's a surprisingly difficult task. I pulled out my set squares and compasses and engaged in some "haephastaneutics", discovering meaning through the construction of artefacts (a more appropriate name for the approach is probably "experimental archaeology").
I've learned many things in the design process, not the least of which is just how complicated spur gear mechanisms can be. The geometries of Ramelli's gear arrangement just don't allow for a great deal of leeway. I think that a far better approach is to either reduce the number of shelves from eight to seven or six (see the book wheel at Wolfenbuttel), or to reduce the number of pinions from eight to four, each driving two gears off the hub-gear. Other details will have to wait for another day...
The other thing I learned is just how compass-friendly Ramelli's design is. In creating a detailed design I was almost mesmerized by the process of creating concentric circles with a compass. The layout, the spacing, basically everything can be laid out with a compass. There are, of course, also some compass challenges. Ramelli's pinions, for example, have six teeth. To draw a pinion with six teeth requires the designer to lay out 60-degree angles on a circle. I had to fall back on some of the engineering training--specifically the properties of the 1, 2, root-3 triangle--to create the required shapes. But some of the early engineering books contained a variety of compass hacks, notably Bachot's treatises and the work of Lorini. The Rosenwald Sketchbook also contains some interesting compass tricks.