In this post, Tim Robinson explains the framework of the Analytical Engine. This work is part of ongoing research to demonstrate that Babbage's Analytical Engine was a practical design and to help in its construction.
By Tim Robinson
Here we share some thoughts on the issue of framework for the Analytical Engine. While Babbage provided exquisitely detailed drawings for most of the principal mechanisms, and showed exactly how they need to be situated relative to one another to form the complete data-path of the Engine, there are two major areas where he did not provide equivalent detailed designs, relying instead just on representative examples and demonstrations in principle that solutions are possible. The two major unspecified areas are first, the overall framework to adequately support the mechanisms, and second the massive amount of control linkages, which in turn will present major challenges to provide the necessary local support.
As a pedagogical tool to help explain the principles of the control mechanisms, Babbage produced the drawing BAB/A/094.1 This drawing is in a class of its own, as it clearly does not accurately represent the details of any particular mechanism, nor how they might be situated in the Engine as a whole, yet it does convey many of the principles of the control and driving. When looking at this drawing, notice how all the elements simply float in space with no means of support. Providing that support is the function of framework, nowhere specified. Given that this drawing represents just a minuscule fraction of the overall mechanisms, we see at once the great extent and complexity of the framework that will be necessary.
Perhaps we should begin by defining just what we mean by framework, outside of the context of any particular mechanism. Up to and including Plan 27, Babbage used the term Framework to refer to structural elements which are fixed in space and time, to provide support for the moving mechanisms. Later, in Plan 28, he extended this to include “moveable framework,” which supports a subset of the mechanism while itself being able to move relative to other elements of the mechanism, but that is not a significant concern here. The only moveable framework in Plan 27 is to provide isolation between the S Stepping pinions, as they must be raised and lowered, which we will cover later.
The data-path of the Engine is divided into what Babbage called Cages. A Cage represents the space in which the components of one digit's worth of the mechanism can fit. In Plan 27 there are 30 Cages for most of the mechanism. A special 31st Cage handles the sign in the Store and various special mechanisms in the Mill. This is the same general organization and terminology Babbage had been using since the original Difference Engine No. 1.
In most of the drawings, the Cages are delineated by horizontal plates one-half-inch thick. Now it is possible this representation is mostly for drafting purposes, because while they show up in the elevation views they are often not represented at all in the plan views, and there are a number of inconsistencies in the way they are drawn. In a Sketchbook entry from July 1837, where Babbage appears to be making notes to himself, he writes: ‘Explain that the framing plates shown in the drawings are fixed to a frame which is not shown.’2 Much of this implied framework was never elaborated at all, so we have some major gaps to fill. If we were to interpret many of the drawings literally, then we would conclude that there is a stack of 32 solid plates spaced every 2⅞ inches throughout the Mill. Since the data-path of the Mill has a footprint of some 3 by 5 feet, this would make most of the mechanism totally inaccessible, and nigh impossible to assemble or maintain. The Store would be less problematic because it is much narrower, being just columns of axes either side of the connecting racks. The sole Plan 27 drawing related to the Store is BAB/A/094, which only hints at the required framework. However, drawing BAB/A/121 from Plan 28 provides useful detail which can be adapted for use in Plan 27.
Below the data-paths of both the Mill and the Store is where the control and driving mechanisms reside. Here there is little or no regularity in the vast number of connecting levers and other mechanisms, and Babbage left us few clues as to his intentions regarding framework in these areas. It will not be possible to consider the necessary framework for this part of the Engine in detail, until the full extent of that mechanism has been worked out and its operation verified in simulation. We will not consider it further at this time.
Plan 27 was the first major Plan for which Babbage systematically lettered the drawings to identify individual Pieces and Working Points. As such, he was still developing the Notation he was using for this purpose, and he did not follow the rules he would later set down in 1851; nor was he entirely consistent.3 One significant detail though, was that a dot placed above a letter at this time generally indicates an object which is fixed; this would be an upper case letter for a Piece, such as a dead centre, and a lower case letter for an individual Working Point. In many of the mechanisms, this provides an important clue as to what is fixed and what is part of the moving mechanism.
One important principle, which Babbage fairly strictly enforced, was to provide isolation between Pieces which move relative to each other, so that there can be no inadvertent motion induced by friction in one Piece when an adjacent one moves. Consider for example a column of Figure Wheels with an axis through their centres. The axis needs to be able to rise and fall, and to rotate relative to the wheels. The wheels should not move, unless an arm attached to the axis explicitly contacts, and drives a particular wheel. To ensure there is no possible interference, the wheels are each supported vertically by fixed framing, separating them from the adjacent wheels, and further they turn on fixed sleeves, through which the axis passes, thus also isolating them from the axis. This is a very conservative approach, because in addition, Babbage had the extensive system of Locks, intended, among other purposes, to prevent accidental derangement when wheels are not intended to be moved.
An example can be seen in Figure 1, a detail extracted from drawing BAB/A/086. This shows, in elevation, two Figure Wheels, the axis with Giving Off arms, and a representation (in red) of the supporting framework. Note the intermediate framing piece labelled ṙ, separating the two wheels, and the sleeves, marked ė, formed as part of the framing plates, separating the wheels from the axis.
Forming the sleeves in this way, directly as part of major framing plates, would be somewhat impractical, and assuming the subtractive manufacturing which Babbage would necessarily have had to use, extremely wasteful of material. In several drawings we see a more practical solution. Figure 2 is a detail from the Anticipating Carriage in drawing BAB/A/092, where the isolating sleeve, again labelled ė, is clearly drawn as a separate Part, presumably press fitted into a recess in the framing plate. Babbage may have intended screws to attach the sleeve, but if so, they are not represented in the drawing. This drawing also shows that the framing plates require an elaborate set of cut-outs and reliefs to accommodate the motion of the various parts of the mechanism.
There is an apparent error in the lettering of drawing BAB/A/086 because the two Figure Wheels between the framing plates are lettered as if belonging to two different digit positions (3A.. and 2A.). This would put the two wheels of one Cage on either side of a framing plate, when generally the drawings show all the mechanism of a single Cage between a pair of plates. Errors in the lettering are not uncommon. This drawing also shows, in elevation, a proposed arrangement of major and minor framing plates (Figure 3). Here Babbage is suggesting more extensive framing plates only every four Cages, with minor plates to provide the isolation located between them by spacers. It is curious that Babbage put them every four Cages here; for an Engine with 30 main Cages, a spacing of five or six would make more sense. Conceivably, it is just an abbreviated representation of an arrangement in which the full plates are only located at the top and bottom. However, there are many minor axes which would require intermediate support to prevent deflection under load, making this unlikely. Babbage had originally thought about an arrangement such as this in connection with Plan 25, where he suggested intermediate support every fifth or sixth Cage.4 Indeed, it was the difficulties of making framework for that Plan which led him to first think about a rack based system of interconnection, which he of course then adopted for the Small Engine.5
Drawing BAB/A/092 hints at a similar arrangement, but there, shown in plan view only.
A major consideration in designing the framework for Plan 27 is just how the Engine will be assembled, and subsequently maintained. From the discussion so far, we envisage that the machine will have a substantial “exo-skeleton,” probably of cast iron, to which will be attached, at various levels, the numerous major and minor framing plates required to provide adequate support to the mechanism. One might think that the logical approach would be to construct and align the complete rigid framework first, and only then install into it the myriad of moving parts and mechanisms. However, this is unlikely to be a practical possibility. The data-path stands a little over seven feet in height above the control section, and contains a large number of vertical axes, each of which carries dozens of parts, such as arms and wheels. It is not practical to have such long axes supported only at the top and bottom of the data-path because rigidity will be essential for correct operation, and significant lateral forces will be present as motion is transmitted in parallel over all the wheels on the axis. Intermediate supports are essential. Yet, if the framework is fully assembled up front with all the necessary intermediate framing plates, then the only way to assemble these axes would be to somehow drop them in from the top, passing them down through all the tightly fitting parts which they must support between the various framing plates. This is not viable. What is more, the design of the minor framing plates, with the sleeves to support and isolate Figure Wheels, means that the wheels can only be fitted together with the plates as they are being assembled. There is no space to insert them after the fact. Another approach is needed.
We have practical experience from the construction of the Difference Engine No. 2, and the long term operation and maintenance of one of these machines at the Computer History Museum, in Mountain View, California. Although this machine is vastly simpler than Plan 27 of the Analytical Engine, it shares a number of significant features. For Difference Engine No. 2, Babbage did a complete detailed design of the supporting framework. It consists of a rigid cast iron outer framework to which horizontal framing plates are attached, very similar to what we propose here. However, there is a crucial difference, in that the data-path is compact enough that the main axes require support only in three places, namely at the top and bottom of the data-path, and at the bottom of the control section. Thus, there are no framing plates distributed within the data-path itself, as will be the case in Plan 27. In the case of the Difference Engine, the horizontal framing plates are divided into sections each corresponding to just one of the difference column groups. The machine was assembled from the bottom up, adding parts to the axes one by one, and when a group of axes was completed, the top framing plate was added. This allowed for incremental testing of each section of the machine as it was completed. It also facilitates ongoing maintenance when necessary, because it is possible to dismantle just a single section, first by removing all the parts above the top plate, removing that plate, then dismantling a single column, part by part, down to the part to be replaced.6
We can divide the axes of Plan 27 into two main classes. The first class consists of axes that carry a single set of pinions, or a set of arms of some form which are not interspersed with Figure Wheels. For these, there is no issue of isolation of the parts, and the axis needs simple lateral support at just the major framing plate locations. The other class are axes such as the main Figure Wheel axes where parts around the axis do require isolation. For these, we need the system of intermediate plates at every Cage (as shown in the drawing BAB/A/086 discussed above). The minor framing plates and the wheels will need to be assembled together, along with any other parts, such as arms on the axis, step by step as the Cages are built up layer by layer.
There is one special case, and that is the S stepping pinion axes. Here there is a need for vertical motion of the pinions, but there is no room for fixed framing plates, so Babbage used a system of small isolating plates which are secured to auxiliary axes which provide both the vertical motion and intermediate lateral support. Drawing BAB/A/099 provides the details. This should present no particular difficulty.
Plan 27 uses a single system of racks which connect both the Store and the Mill. Depending on the number of Store Variables implemented, and the choice of peripheral equipment, the racks will be roughly 12 to 15 feet in length. Babbage arranged to support them on rollers to reduce friction. The most detailed drawing is BAB/A/121, and while this is specific to the later Plan 28 it can easily be adapted to the dimensions required for Plan 27. In the Store the racks are centrally located with Variable columns both to the front and the rear, but in the Mill most of the mechanism is on the front side of the racks, with only the Table axes (which are almost identical to Store axes) to the rear. This central positioning necessarily means that the major framing plates will need to be divided, front and rear, with the framework which supports the racks also providing the support for the inner ends of these plates. If they were not divided, then it would be impossible to lift one out without dismantling the entire rack structure. Since the racks themselves should be removable from the end of the machine, it seems very unlikely it would ever be necessary to dismantle this inner framework structure for maintenance purposes. So, this structure, together with the exo-skeleton, should provide the initial rigid support we need to build up and test the rest of the data-paths of both the Mill and the Store incrementally, just as was done with the Difference Engine No. 2.
In designing the framework for Plan 27, it is vital to give detailed consideration to the division of the framing plates. Let us consider a maintenance operation, similar to that described above for the Difference Engine No. 2. Once again, after removing all parts above a top framing plate, that plate can be lifted off. But now, assuming we need to reach below the next of the several framing plates in the stack, then it will be necessary to remove all the parts from not just one axis, but from all the axes which pass through these particular plates, because only then will it be possible to remove the next lower plate. Careful choice of the divisions between plates will minimize the extent of this dis-assembly, and ensure that unrelated mechanisms need not be disturbed in the process. However, it will necessarily be a much more complex process than for the Difference Engine No. 2, since it is not practical to isolate individual axes. We should also note, parenthetically, that in order to be able to lift out lower framing plates, careful thought will have to be given to how they are attached to the exo-skeleton. The method used in Difference Engine No. 2 would not permit this.
Babbage often considered the effects of wear on the reliable long-term operation of the engine. For example, writing at the time of Plan 27 he said:
After the Engine has been used for some years the pinions on the axes most used should be removed to those axes where they will be less employed
After a further time the work of the highest cage should be placed in the lowest & so on all the cages being inverted
This will equalise the wear of the Engine7
He was clearly expecting major dis-assembly and re-assembly of the Engine to be necessary over its lifetime. We have been warned, so we should be prepared, by making this as easy as possible, while remaining faithful to his intent.
Images
Notes
- This drawing can be found on the London Science Museum website at the following url: https://collection.sciencemuseumgroup.org.uk/documents/aa110000233 ↩
- BAB/S/1/03.214, emphasis original. ↩
- Charles Babbage. Laws of Mechanical Notation (For Consideration). private, July 1851. ↩
- BAB/S/1/03b.045. ↩
- BAB/S/1/13.165. ↩
- Doron D. Swade. Difference Engine No. 2, Technical Description. Tech. rep. London: Science Museum, Mar. 2020. URL: https://www.sciencemuseum.org.uk/sites/default/files/2023-09/DE2_Technical_Description.pdf; Doron D. Swade. Difference Engine No. 2, User Manual. Tech. rep. London: Science Museum, Mar. 2020. URL: https://www.sciencemuseum.org.uk/sites/default/files/2023-08/User_Manual_PDF_Vsn_1.1_Final_SEC1.pdf. ↩
- BAB/S/1/03b.045. ↩
