gear design success

Finally, I have a scheme for the gear design that seems to work. To cut right to the chase, here is a video showing a 4-digit number being flawlessly copied back and forth ten times between the two numbers on a digit stack, through both fixed and movable pinions  The "unit of time" is 0.157 seconds/digit, which is the speed Babbage proposed for Plans 16 through 28. The movable pinion also allows for shifting: multiplication or division by 10. 

the mini-tester for digit wheels and long pinions

How did I get here?

At the time of my July 11th posting about gears, I was still plagued with excessive backlash, among other problems. Tim Robinson came over for the day, and we brainstormed ideas.

We decided that the change to two teeth per digit had been a bad idea, and that we should go back to one. That simplifies the design because the gear teeth can again be used for locking, rather than having a separate locking wheel. But, critically, we would stay with two cycles of 0-9, which means that the teeth have diametral pitch of 6 and are huge. That comports better with the precision of 3D printing, and gives plenty of opportunity for the locks to correct misalignment.

new round-tipped lock

Speaking of locks: Tim has always said the Babbage insisted on having a lock after every three gear meshes. I thought it excessive, and was not doing that. The basic sequence -- digit wheel to small pinion to fixed long pinion to movable long pinion to small pinion to digit wheel -- is a series of six gears and five meshes, with locks only at the ends. I finally saw the light, and added a lock to the fixed long pinon in the middle of the train.  It helps! 

fixed long pinion locks

This is yet another example where Babbage was right all along. In fact, he thought locks so important that, according to Tim, "in a typical design, over 30% of the complexity in the control mechanism is devoted to the operation of the Locks".

I'm currently applying all three locks simultaneously. Tim says Babbage proposed applying the locks consecutively from source to destination, two per cycle. That would allow more misalignment to be corrected. I can certainly implement that in this prototype because it's just "a simple matter of programming", but it will be daunting to later implement that mechanically.

Another problem with the naïve change to DP 6 was that the large gears on the long pinions were so big that they interfered with the axles of the adjacent small pinions and with the inner gears when the movable pinon was in the shift position. But Tim observed that the long pinion large gears don't need to have the same number of teeth, since they mesh only with each other. So I doubled the number of teeth, and the geometry now works fine. (I did have to slightly reduce the "addendum" of the gear design, which controls the height of the tooth.)

movable long pinion

Another contribution to the success was a general improvement in the precision of the assembly. I had been pushing -- and finding -- the limits of "sloppy construction". The problem was mostly not in the 3D printed parts, but in the other stuff: shaft positions, spacer sizes, free play, etc. 

In order to be able to make more precise parts, particularly small section of aluminum tubes, I finally broke down and bought a small lathe on Craigslist

to which I added a digital readout. I can now reliably cut tube spacers to 10 or even 5 thousandths of an inch. That won't sound impressive to a real machinist, but it's definitely a step up.

Now I can go back to the anticipating carriage mechanism, and see if the lessons learned from achieving reliable digit transfers can be used to make a version of that work too. 

Rebuilding the larger prototype may precipitate getting yet another new tool: a larger digital router, so I can make my own framing plates. Then I can experiment with different designs -- and fix mistakes -- without having to plead for time in other shops. 

Thoreau said "beware all enterprises that require new clothes", but he said nothing about new tools.