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the freedom stw10 is an impressive mechanical calculator from the 50s and i sometimes get requests to take some footage of it but when i take it out after six months of not using it there is invariably something wrong with it usually not a big deal now that it has been fully repaired just a lazy lever here and there but it's never the same one and i always end up learning something new about this amazing machine this time though while i was running tests i discovered something i never knew was not working and that i had never fixed before [Music] in this case my problem was scary propagation it stopped after 12 digits here you can see the repaired machine being cranked by hand and the carry propagates in a ripple then stops it does this correctly now after 14 digits but why not the whole 20 digits it will take a little bit of a deep dive into the mechanics of the beast to find out oh this is very satisfying the first thing to notice is that there is a different number of digits in the different sections of the machine so 20 digits in the accumulator 11 on the counter 10 columns of digits in the main keyboard the multiplier over here has 10 digits and this is something quite usual that you see also in computers multiplication and registers usually are twice as large as the main bit width the multiplication of two 32-bit numbers will give you a 64-bit result here the freedom can multiply two 10-digit inputs and therefore needs a 20-digit result accumulator and then you see how that's going actually the calculating portion is only this wide 10 and it just steps through it so it only rotates here but something that i have not recognized is that since the calculation section is only year wide how does it do to carry through the whole thing and now how does it reach the end and the answer is that in some situations it does not let me show you so in this example that i'm just going to add one each time and i'm going to put everything at nine so 99999 so these are 10 units that are right over the mechanism so you expect that if i add 9 to this 1 2 3 4 5 6 7 8 9 10 to this 10 units it would add one to the next and it did so this number got it scary so okay that's all fine and dandy see how far it goes see if it does it okay still doing it 11 12 13 so 13 digits still does it 14 digits still works and see if it carries to the 15th digit and you can see it did not it's all zero so it's it stops propagating at 14 and when it does that it warns you about it you heard it dink and there's a test to make sure that the carry works properly which simply consists of making sure the bell rings in all overflow conditions but mine never rank so i soon figured out that the carry stopped at the 12th digit there's something very special that happened at the junction between 12 and 13. but you'll see that they went to quite an effort to get it up to 14. [Music] these are the little gears that turn the engage over here and deter the number so if you want to add four you just know get this one to turn four times and the way this is done in most machines i see i can focus manually on it it just has a set of gears with some partial teeth in it there you go the one with a lot of these there was a little few this in the middle there is a little gear that engages where is that one right here and so when it's at position nine it will face a gear that turns uh that has 90s 80s 70s 60s five now it uses the bottom gear four three two one and zero so let's put it at nine for example let's give it a 12 and you should see the top gear engage and turn nine times and then see this one will turn and it has turned exactly 90s so the partial teeth gear is the basic trick for counting and adding but you need one more trick obviously to make a real adder and the second one is to do carry and the way the carry is done is an interaction between the carriage and this little fellow here if you look at the carriage and you look underneath it has this little guys over here and these are the carry levers and every time it goes to nine let me see if i can catch it ah there you go so each time you go from nine to zero it blips the carry lever that carry lever engages into this little thing of the next digit so this digit carry lever engages into here and we'll engage this one and that will be the carry i'll set them all i set all the carries so they're all advanced by one let's do it again that's really neat so once again this one is in the cycle weight reset i cannot push it and same over here so let's try it again carrier apple and you might wonder oh how come you can calculate with a machine that doesn't propagate the carry all the way and it turns out in normal usage it doesn't matter very much because let's try to multiply a big ten digit number by another ten digit number and the first thing is going to do is going to clear everything so it's going to be all kind of zeros up in the register over here and then it progressively gets to it as long as there's an overlap with the 14 digit is going to no progressively get to it the carry only goes this way and it gets to it eventually same goes for division if i do a division and it's going to subtract from here and i'm going progressively to have zero so it really doesn't matter zeroing it out and no by the time the carries out of reach it's zero anyhow so it doesn't matter at all so the only time where it actually matters is if you have a very large number in the accumulator already and let's do one two three four five and so let's imagine i'm i'm bill gates and i'm counting my trillions of dollars and i'm adding one cent i'll put it back over here okay so we can see them all and now i'm going to add one and that didn't work right it didn't go to the number 15 so that's the only situation where it's a it's a problem and you could tell that it's an afterthought even to get it to uh 14 digits because the original machine uh has only up to 12. here's the freedom h8 the ancestor of our stw by many decades manually operated and if you look in the mechanism you can tell it's the same but it has only 12 rollers equipped for carry so clearly the 13th and 14th carry digits are an afterthought and you can easily tell that the 13th and 14th digit scary rollers are of a completely different design they are what they call the spring carry and these are the ones that were not working at all in my system so i could only carry up to the 12th digit phew sorry for the long-winded explanation i found about my problem in a roundabout way while doing a belt test the bell is supposed to warn you at the end of the carry chain to alert you that you had an overflow at the 14th digit and that your calculation is likely invalid pretty important bell it is but i was never hearing the bell at all and that's just not working and the reason turned out okay let's crank it there we go that it doesn't reset properly here and there is a little bar that moves let's do it again and it doesn't go far enough it never catches it should go further and i can't do it there you go and engage that thing and it never does uh and this is actuated by a cam which is also completely buried at the back of the machine let's see if i can show it and the cam well it's going to be totally impossible here you go here's the mechanism so here's the cam here is the roller that goes on it and it will move that little ratchet back and i have to bend the cam which will be an interesting thing so that never worked on my machine uh and i never knew so it's only when i did the the manufacturing test that i found out it took me a long time to even find the damn roller it's completely buried in the middle of the machine this bad boy out here grinding on this one right there and then there is an arm to the right of it that you have to bend somehow i remove the motor and it's not that hard actually just slides out and the way it's coupled is there is this paper disc there's another one on the other side and there's this that goes between this and the clutch and there's a similar part that mounts on the other side so that's pretty good and i found a spring i definitely found a missing spring that's in the division mechanism somewhere between this and that okay so the the roller itself is super hard to reach and the best way i found is to use some pliers in here and try to get to it unfortunately the division parts are in the middle i cannot get a good grab of it i was to the point where i could latch one of the two okay the left one is latching and drags the right one but not enough i did fight with the rollers and the levers forever and even removed locking claws trying to bend the second lever but i could never get the second lever to lock the roller and the cam had too much wear and i could not compensate for it by bending only it's almost enough but not quite enough this one catches this one is a little bit of encouragement so i'll just file it okay desperate moment after a full day of trying here comes the dremel almost almost almost [Music] there we go all right phew finally after a long day of work it's time to put the motor and the carriage back in for a test there you go yep well no i got one two three four five six seven eight nine ten eleven twelve thirteen i i did get everything i didn't get the 14. let me get the last one shoot dang there is progress we have one more carry on digit 13 but no cigar digit 14 still has no carry and i can clearly see that once uh spring transfer is working and the other is not they both reset correctly now i'll put them like this reset and if i set this one manually you know watch this shaft is going to move to it just moves one notch this way reset watch it again move it as it should but this one does not so i have to do both of them at the same time for it to work so this one will interlock the other one if i do this it did release the lever but that did not turn the wheel well i don't understand why that doesn't happen resets correctly and lashes correctly does not turn the wheel i i remove the uh the the catch bars here and i can activate it by hand you can hear this little ratchet and here it's not ratcheting it's buried down there okay so there's a part that's stuck there's a ratchet that's stuck on that one but how to get to it that's the problem i got it so there is a ratchet it's tiny it's black on black but i found a way to activate it more by feel than by seeing it and i use my ny oil and the deny all trick works if you can put it at the right place and if you can activate the thing if you can't activate it back and forth it won't do anything so but i found a way to pick it back and forth and it freed up after maybe 50 movements the first ones were very very tight i have to force it okay so i remounted my little claws here and didn't lose any of the springs in the machine and now you can see if i set the two transfers then the two two caps work as intended yeah it works my bell works again because only sensitive on the last digit that's over the last transfer so now that i am in the home position if i do minus one thing i have and those are my spring transfers 13 and 14 so they all work alright we're all set we can hear our warning bell but i definitely learned a thing or two and i hope you did too so now it thinks correctly but interestingly multiplication with large numbers work but if you want to do an addition it only works up to 14 more digits than the current position of the carriage wouldn't you know it