the quest to avoid framing plates

In most of Babbage's designs, he calls for horizontal framing plates to separate each digit position in the stacks of digit wheels and pinions. Here's an example drawing from Plan 27. In this design each digit position is composed of a "cage" with digits from two interleaved numbers on the same stack.

There are two primary motivations for the framing plates: 

1. To provide a bearing surface for the wheels and pinions of a shaft so they don't bear on the ones below them.
2. to constrain, using close holes through the plates, the lateral motion of the shafts, to the extent that they might have a tendency to bend or were not manufactured sufficiently straight. After all, for designs with 30 digits the shafts might be 9 or 10 feet long.

But there are some significant drawbacks:

1. The massive weight of all those thick iron plates.
2. Obscuring the view of the mechanisms during operation.
3. Making detection and repair of problems difficult because parts can't easily be accessed.

So I have been on a quest, which may prove to be quixotic, to explore whether the framing plates can be eliminated. I'm hoping that (1) sleeves concentric to the shafts can provide stable bearing surfaces, and (2)  that the minimal lateral forces (as opposed to the larger rotational forces) will not deflect 1/2" (or larger if necessary) modern straight steel shafts. For 25 digits with our proposed 2.3" separation, the shafts should be just over 5 feet long.

There are three use cases of increasing complexity.

1. free-rotating pinions that need only be raised and lowered for meshing
2. Mill digit wheels for which only the internal fingers need to be independently lifted and rotated
3. Store digit wheels for which the wheels must be lifted and the fingers independently rotated. (See my previous blog entry for why they are different.)

free-rotating pinions

The idea here is to create "platforms" fixed to the shaft between which the pinions are constrained, by having teflon washers separated by fixed sleeves concentric to the shaft.  

The yellow sleeves are oil-embedded (Oilite®) sleeve bearings at the positions of the pinions.

This is trivial to assemble sequentially, which doesn't come as easily for the last use case.

To mesh with other gears, the entire shaft with the fixed sleeves and the pinions is simply moved vertically. This works well.

Mill digit wheels

Here we can similarly create fixed platforms for the digit wheels using concentric outer sleeves that are at fixed vertical positions. But the innermost shaft must be able to rotate the fingers affixed to it, and the fingers need to move vertically to sometimes be at the level of the giving-off nibs in the wheels. So the digit wheel separation sleeves must allow clearance for the finger hubs to move inside them, and they must have slots for the fingers to poke through to reach to the circumference of the wheel, where the nibs are. 

Here is what a digit wheel separation sleeve to accomplish this looks like. The total height of the sleeve is the cage separation distance of 2.3", and they butt up against each other. The combined height of the two digit wheels just fits between the inside surfaces of the flanges.

Here's what it looks like with only one digit wheel of the pair installed, so you can see what's inside. 

There are thus three concentric shells: the shaft keyed to the fingers, the finger separation sleeves, and the slotted digit wheel separation sleeves.

I originally used the 3D-printed plastic spacer shown, but having two plastic concentric parts required a big gap between the surfaces because the parts were excessively out of round. So I switched to making them out of aluminum.  

I now believe that the problem was actually caused by the ancient ten-year-old Lulzbot Taz 6 printer. I just got the latest H2D printer from BambuLab, which is absolutely amazing. I anticipate that it will substantially improve the accuracy of all the printed parts, which will be great relief.

Store digit wheels

Here the challenge is to simultaneously provide for vertical motion of the digit wheels and rotational motion of the fingers attached to the shaft.

If the shaft is to rotate, then the spacers that provide the "platforms" for the digit wheels cannot be fixed to it. That's fine; the spacers can be fixed to whatever lifter moves them relative to the whole machine frame. But then all the spacers have to be connected to each other so that the vertical motion is propagated to them all. They can't be permanently connected, because then the wheels and fingers can't be installed. How can that be done while allowing incremental assembly?

The trick is to use spacers that can be individually installed, but are then can be locked to each other  as the stack is assembled. 

The tabs at the bottom of each spacer fit into "twist lock" slots at the top of the next spacer down. But before that is done, the top wheel, the finger spacer, the finger, and the bottom wheel are installed. 

This works well. The bigger difficulty was actually at the bottom of the stack: providing for rotation of the inner shaft for moving the fingers, and fixing their vertical position relative to the frame, and at the same time allowing vertical movement of the twist-locked column of spacers that serve as the platforms for the digit wheels. 

The proposed solution uses a large diameter "vertical pusher" as the bottom twist-locked component, which accommodates a collar that locks the finger spacers to a fixed vertical position on the shaft. The large gear that rotates the shaft has slots to allow the pusher to penetrate through it while moving independently up and down to move the digit wheels. 

The video below shows three repetitions of reading ("giving off") a digit from the top wheel, reading a digit from the bottom wheel, and then returning to the home position where both digit wheels are locked. The rack was removed for this test.

There is actually a subtle motion happening on the leadscrew during giving-off that is too fast to see in the video unless it is played in slow motion. Here's why it is necessary: A digit wheel lift occurs when the leadscrew is rotated relative to the stationary shaft. But when the shaft (with the attached fingers) is rotated for giving off, the leadscrew is fixed, and so a small wheel lift also happens then! To avoid any lift, whenever the shaft is rotated, the leadscrew is rotated the exact same amount so there is no relative motion.

In the process of implementing that, I discovered another more general subtlety. For my microprocessor-controlled prototype, the stepper motors are driven with four "microsteps" per 1.8° winding step, which means 800 microsteps per revolution. Up until now I had been rounding to the integral number of microsteps required for a movement and ignoring the remainder. But that can lead to an accumulating error in the position. It now instead remembers the remainder as an exact integer fraction (no floating point!), and eventually incorporates it when it builds to a full microstep. There should be no cumulative position error, only a current error which corresponds to less than a single microstep.

The bottom line: so far I haven't found a fatal flaw in my elimination of the heavy horizontal framing plates. If it turns out that there is too much flex in longer vertical shafts that accommodate many digits, then one or two supplemental plates can be added at regular intervals. But at least there won't be one between every set of digits.