Building the World's First Computer: Babbage's Analytical Engine

 It turns out that there is another gear loop in the Plan 27 design that needs to carefully designed to mesh correctly. The long pinion is connected to the anticipating carriage (which does addition and subtraction) by an intermediate transfer pinion. But sometimes during complex operations like division, an additional reversing gear needs to be inserted into the chain. Babbage does that by vertical motion of the transfer and reversing pinions, with the reversing pinion being double height. Here are the two configurations: non-reversing reversing Although clearly all three gears are never meshed as shown  in the plan view, the teeth need to be aligned in order for the vertical movements to happen without tooth conflicts.  There are far fewer degrees of freedom for axis positions here than for the 5-gear mesh described in the earlier posting. Given the constraints on locations of the gears to avoid interference, the first attempt failed to produce any solutions.  But ...

The gear loop mesh analysis program is now expanded to work on all three Mill groups in the Plan 27 layout: Babbage drawing A/093 from July 28, 1841 Each group contains a figure wheel stack (A), fixed and movable long pinions to effect shifts (L and S, respectively), and the necessary connecting pinions (G, J, C, and J). There are two anticipating carriages (F), which mesh to the fixed long pinions of the middle and right groups. The moveable long pinions are meshed with additional pinions (O) meshed to the rack that connects to the Store. You can see quite a few other wheel stacks in the drawing, which are there to implement multi-precision arithmetic and many other complex features. My simplified version omits them, and includes only the 22 stacks described above. Still, precisely positioning all the axle centers so that the various loops of gears mesh correctly is a challenge. Babbage's drawings and notes are not clear on whether he had gotten to do that yet. Each group has a le...