[MOC] (V3) Mechanical Calculator "Technivac III"

[2GodBDGlory]

So, after posting my tongue-in-cheek "Electrical Calculator," I'm back with my third version of an actual mechanical calculator, the affectionately named Technivac III. This one is a development of the ideas I've started in my last two calculators, combing the differential-adder mechanism of my original calculator with the extra digits (four total) and carry mechanism of V2. Overall, I'm still not happy with it, because a late addition I hadn't anticipated needing ended up bringing the levels of backlash past the acceptable level, but it is my best one yet, and I do have a completely different idea for V4, should I ever decide to build it (namely, measuring numbers with linear motion rather than rotary motion.) Anyways, I'll try to explain this thing, but it's very complicated, so I may not succeed. I've also got a video at the bottom, so that's an option too.

 

To try to keep my description in order, I'll propose an outline here:

I. Theory

     A. Power Supply

     B. Gearboxes

     C. Spirals/Buttons

     D. Adders

     E. Locks

     F. Carry Mechanism

     G. Dials

     H. Reset

II. Results

So, (gulp) let's start:

I. Theory

     A. Power Supplies

The first thing in the mechanism is the power supplies, which provide the power to rotate everything down the line. This calculator differed from my previous ones in being primarily crank-driven, which helped because the user could be intelligent about how much torque was needed at different times. There was also a PF L-motor running the setup through two clutch gears, but it didn't seem possible to tune it to slip the clutches when the buttons were pushed but still have enough torque to work the carry mechanism, so I generally just left it disconnected and ignored it. The motor was reversible, as was the crank.

     B. Gearboxes

There were two main gearboxes before the spirals. The first of these was a simple distribution gearbox operated by the Num 1/Num 2 lever, allowing the user to switch between powering the upper and lower sets of spirals, which resulted in either the first or second number being inputted.

Spoiler

The second gearbox only applied to the second number, and was a simple forward/reverse gearbox allowing one to choose between inputting a positive and negative number. I didn't need one of these on the first number, because the calculator doesn't work with negative numbers, so there is no need to input a negative as the first number. It was operated by moving the red axle up and down. Because when the spirals were reversed, the prongs sticking out from the shaft would be pressing against the opposite side of the axle pushed down by the number buttons, they were offset by a fair bit, so to ensure that the correct numbers were still inputted when subtracting, I added a lever that allowed me to change the labels of the numbers when subtracting. Essentially, I had to reverse the order, and offset it by two.

Spoiler

(It was rather buried and hard to see)

     C. Spirals/Buttons

The basic working principle of this calculator, as in my previous ones, is the "spiral," or axle with protrusions as close to every 10 degrees as I could get. I ran out of the old toothed connectors with this calculator, since eight spirals were needed (Two per digit, since I needed one for both the first and second numbers.), so I have a few 3D-printed stand-ins, which are only "cheating" in that they allowed me to save money, since they have no functional advantage here (they may be stronger, but that wasn't important.) The buttons worked similarly to before, with axles coming down from each button to block the spiral at a specific degree, but I also had them connected to long vertical axles, which pushed rocker arms, which pushed up more axles in the opposite direction, to block the lower spiral from the bottom. Again, as in the past, it is set up so that pressing any button will press down a linkage that engages a driving ring on the spirals corresponding to that digit.

Spoiler

     D. Adders

The adders here are easier to understand (I think) than those in V2, and allow for the reversing to happen before the spirals, cutting backlash, but also introduce some backlash of their own. They are a simple differential mechanism, using the 24/16t differentials to add up the outputs from the top and bottom spirals for each digit. Drive was transferred to them in most cases by a pair of 24T gears on each side of the diff (the units place used a 16:8:16 gearing in order to reduce the direction, because it didn't have secondary reversing in the carry mechanism), and the differential's 24T side then drove a 12T gear, which doubled the speed to correspond for the halving of speed caused by driving one of a differential's traditional outputs.

Spoiler

     E. Locks

The adding mechanism was nice and simple, but after building it, I realized that when one spiral drove an input, it might drive the dial as it should, but it could easily just send the power out through the other input, backdriving the other spiral. To prevent this from happening, I had to add a selectable lock to lock the unused input. This was done by sliding bevel gears (20Ts for the units place, 12Ts for the rest) which were attached slidably but not rotatably (real words, and awesome ones) by having their drive axle slide through the side axle hole on gear lever parts. These gears would mesh with gears on the input shafts one at a time, locking them up. They were controlled by a lever marked Num 1 and Num 2, which was actually mechanically connected to the lever for the Num 1/Num 2 gearbox, so you could get away by just pushing this lever, though it was best to push both. This lever moved a bunch of linkages to allow for the sliding of these axles.

Spoiler

 

     F. Carry Mechanism

I thought the carry mechanism would be a fairly simple stepper mechanism using 10T splat gears, so that's what I built. Like a fool, I had started filming before testing the carrying (I'm kind of paranoid about testing, to my own loss), discovered that it took far too much effort, thought about solutions, and realized another problem (namely, that when carrying, it would backdrive the spiral for the next number, which would cause a button press in that digit to add an incorrect amount, essentially negating the carry.) I then had a fun little evening of thinking and came up with a solution that worked in theory. I then built it, and fell in love with its relative elegance--it was really one of the most thrilling "Eureka!" moments of my Technic career. This solution was to retain the basic 10T stepper, but to use the splat gears as a basis for a custom differential, and to set up the gears so that instead of moving a full tooth (1/10 rev), it would only rotate a half tooth (1/20 rev) when triggered. This wasn't repeatable, but it didn't have to be, since this calculator only does one operation before resetting it. The reason I had to halve the rotation is because of the doubling of speed of the output when driving the carrier while holding one output, as was happening here. The output then drove the lever for the stepper for the next digit. Additionally, the differentials were locked in place by two different methods. There was one spring-loaded beam on the bottoms that pressed a flick-missile bar between the teeth, locking it. When the lever that engaged it neared the point where it actually stepped a tooth, the round end of a gear selector part bumped the lock out of its locked position, allowing it to rotate 1/20th of a rotation, at which point the upper spring-loaded beam moved down, locking the gear again with two offset connectors. The whole locking mechanism didn't work as well in theory as I'd hoped, but I thought it was clever nonetheless. Anyways, the reason that this worked while my simple solution didn't is that the output dial could move independently of its spiral when being carried, because of the differential. This part's late addition did add a lot of backlash within the spider gears, as well as wiggling of the carrier. 

Spoiler

Stepper lever and differential. Note gear selector part.

Lower lock

Carry in operation and upper lock.

     G. Dials

The dials were just basic dials based on tires. There's not much to say about them, except that the direction was reversed with each place.

Spoiler

     H. Reset

In order to reset the calculator, each spiral had to be engaged by selecting the correct gearbox settings and engaging its driving ring by either pushing some button that didn't interfere or just pushing the linkage manually. The crank was then rotated backwards until its spiral hit its stop. This was all pretty simple, but the stops themselves are a bit more complex. The ones for the first number weren't too complex, with a 3L half-beam rotating until it hits a T-beam. This T-beam has a slight bit of movement allowed to it, resulting in the stop being engaged when the 3L half-beam is vertical no matter which direction it comes from. The top had a similar working principle, except that the 3L half-beam equivalent (connector, 2L axle, and half-bush) had to be able to rotate backwards past center when subtracting, which was not possible with a "dumb" stop like on the bottom. As it turns out, in order for the stop to work, the T-beam has to be right next to something (1L beam on the first number), so on the top I set up a fancy linkage connected to a lever that moved one of the pinhole/axle connectors one stud, allowing the stop to be disengaged under operation, or for it to be engaged while reversing. It was spring-loaded to unlock by default, but I had an extra little control that let me lock it in the engaged position as well. It was a weird mechanism, but it worked!

Spoiler

Bottom lock

Top lock disengaged

Top lock engaged

Engaged

Disengaged

II. Results

In the end, like I said, accuracy was poor, with there generally being a +/-1 inaccuracy per digit, which is enough to render this calculator useless (if it weren't already! ). Also, I am doubtful that more than one carry at the same time would have worked. Otherwise I think everything worked, such as adding and subtracting, carrying a single digit, inputting the numbers, and resetting it. I'm not too disappointed with this result, since it's extremely complicated, though it isn't the end of my calculator mission as I'd hoped... Oh well, V4 will probably also be fun to build!

More pictures here: https://bricksafe.com/pages/2GodBDGlory/technivac-iii

Edited April 5, 2022 by 2GodBDGlory

[Jurss]

Good, now just make that app ;)

[glowytheglowbug]

thats so cool! danm i wish i had that many parts and the time aaand good at math

[Davidz90]

Very impressive build, even if not working perfectly yet. Gear backlash is a huge issue I'm also struggling with when doing calculations in my clocks (like moon phase etc.), controlling it in a build this big is a really hard problem. 

I'll need more than one view to fully understand all of this mechanism, but it seems like a bit of an overkill for addition/subtraction? I do not mean to criticize, it is certainly an unique and impressive way of doing this. 

[2GodBDGlory]

16 hours ago, Jurss said:

Good, now just make that app ;)

Thanks! You're referring to my post from a few days ago? I did actually program that calculator shown in the video there, but the idea was for it to just be funny that I did such a useless thing without the appeal of it's being mechanical.

 

15 hours ago, glowytheglowbug said:

thats so cool! danm i wish i had that many parts and the time aaand good at math

Thank you! It did take a lot of parts, but surprisingly little math. The tricky part was just in covering simple math operations into workable mechanims.

 

1 hour ago, Davidz90 said:

Very impressive build, even if not working perfectly yet. Gear backlash is a huge issue I'm also struggling with when doing calculations in my clocks (like moon phase etc.), controlling it in a build this big is a really hard problem. 

I'll need more than one view to fully understand all of this mechanism, but it seems like a bit of an overkill for addition/subtraction? I do not mean to criticize, it is certainly an unique and impressive way of doing this. 

Yeah, the backlash was disappointing. The nice thing here was that any backlash before the spirals didn't affect accuracy, but even with that it ended up being too much. Yeah, this is totally overkill for the basic math it can go, but I at least haven't been able to think of any way to simplify the design, though as I mentioned I've got vague ideas for one using linear motion instead, which could change a lot, and get rid of a lot of backlash. I've even got hopes that the working principle will allow me to add multiplication and division for the first time, but that'd be pretty hard.

[technicfanatic]

This is fabulous. Well done. Hope you will end up putting it on Rebrickable. 

[2GodBDGlory]

1 hour ago, technicfanatic said:

This is fabulous. Well done. Hope you will end up putting it on Rebrickable. 

Thanks! It's not really suitable for Rebrickable, though, because not only would the complexity deter all but a few people, but the unreliability and need for constant troubleshooting by someone with a deep understanding of the machine would make it extremely frustrating for the few who might build it. Perhaps one day I'll come up with something practical enough for that, though!

[glowytheglowbug]

On 4/6/2022 at 9:47 AM, 2GodBDGlory said:

Thanks! It's not really suitable for Rebrickable, though, because not only would the complexity deter all but a few people, but the unreliability and need for constant troubleshooting by someone with a deep understanding of the machine would make it extremely frustrating for the few who might build it. Perhaps one day I'll come up with something practical enough for that, though!

tbh anything works for rebrickable even a simple studio model, its pretty useful for finding ideas etc

[2GodBDGlory]

1 hour ago, glowytheglowbug said:

tbh anything works for rebrickable even a simple studio model, its pretty useful for finding ideas etc

I suppose that's true, but I've never really gotten good at Stud.io, so none of my models have any files for them.

[glowytheglowbug]

53 minutes ago, 2GodBDGlory said:

I suppose that's true, but I've never really gotten good at Stud.io, so none of my models have any files for them.

ah gotcha yep doing things like this in studio is a nightmare rotating parts, gears, collisions etc

[aeh5040]

Amazing work - thanks for sharing! Sufficient precision and torque are of course the eternal headaches with things like this. I hope you are not discouraged by the difficulties, and continue to work on this awesome project.

For a slightly different direction, have you considered trying a binary (rather than decimal) system? Obviously it would not be so convenient as a calculator, but it might help overcoming some of the challenges.

Edited February 6 by aeh5040

[2GodBDGlory]

4 hours ago, aeh5040 said:

Amazing work - thanks for sharing! Sufficient precision and torque are of course the eternal headaches with things like this. I hope you are not discouraged by the difficulties, and continue to work on this awesome project.

For a slightly different direction, have you considered trying a binary (rather than decimal) system? Obviously it would not be so convenient as a calculator, but it might help overcoming some of the challenges.

Thanks!
I haven't thought too much about doing a binary system, though I do imagine it would be a lot easier. I guess I just made it an arbitrary goal to make it work in base-10!

I was trying a new line of attack, in which numbers would be stored via linear motion rather than rotary motion, and made a fairly successful calculator that could add two single-digit numbers, but I guess I never got around to posting it anywhere. The linear concept has the advantages of minimal backlash and a greater possibility of incorporating multiplication and division, but it'll take more development to reach this level of functionality.

Maybe I'll try to get that calculator up soon, but I'll have to see when/if I get enough time to give this new concept more of a try!

[Davidz90]

2 hours ago, 2GodBDGlory said:

haven't thought too much about doing a binary system, though I do imagine it would be a lot easier. I guess I just made it an arbitrary goal to make it work in base-10

If I can add my 2 cents, base-10 approach might actually be easier with Lego. Binary mechanical calculators are a rarity, and compared to base 10 ones there is usually much more parts. Binary numbers are simply bigger (more digits), so there are more carries etc. Less precision is needed in the sense that all is cool as long as 0's are not mistaken as 1's and vice versa, but in electrical system it means that the signal in the circuit is amplified to proper level every few logic gates.

How about simply gearing things up so we have a rotary dial with 10 numbers, but inside the calculator 1=1 rotation?   That could be easily processed in a differential for addition/subtraction. It is hard to get a backlash so bad that output is full rotation behind input.

[2GodBDGlory]

2 hours ago, Davidz90 said:

If I can add my 2 cents, base-10 approach might actually be easier with Lego. Binary mechanical calculators are a rarity, and compared to base 10 ones there is usually much more parts. Binary numbers are simply bigger (more digits), so there are more carries etc. Less precision is needed in the sense that all is cool as long as 0's are not mistaken as 1's and vice versa, but in electrical system it means that the signal in the circuit is amplified to proper level every few logic gates.

That makes a lot of sense, good point!

2 hours ago, Davidz90 said:

How about simply gearing things up so we have a rotary dial with 10 numbers, but inside the calculator 1=1 rotation?   That could be easily processed in a differential for addition/subtraction. It is hard to get a backlash so bad that output is full rotation behind input.

Interesting thought; I'm having a hard time knowing what my thoughts on that would be, simply because I tend to work myself into a "calculator-design-brain-mode" when I build calculators, and then kind of let that all go in off times. My thought, though, is that it would be challenging to limit the shafts inside the calculator to amounts of rotation above one full turn, but it could be an interesting avenue to explore.

 

EDIT: After consideration, limiting it that way actually looks really easy and helpful, and I'm working in a prototype now!

Edited February 6 by 2GodBDGlory

[Davidz90]

2 hours ago, 2GodBDGlory said:

After consideration, limiting it that way actually looks really easy and helpful, and I'm working in a prototype now!

Great to hear! Good luck!

[Davidz90]

I'm not sure how relevant that is, but recently I found this mechanical calculator:

and it seems very doable in Lego form. It even uses 40 tooth gears!

[2GodBDGlory]

4 hours ago, Davidz90 said:

I'm not sure how relevant that is, but recently I found this mechanical calculator:

and it seems very doable in Lego form. It even uses 40 tooth gears!

Hmm, that's a cool machine!

You're right, I imagine that could be done with Lego pretty simply!

I think my personal goal is still to build an accurate, reliable, button-operated one, rather than something like that stylus mechanism, but it could be interesting for someone to try sometime!

[KirTech LAB]

This is an incredible piece of engineering, it will take a lot of time to understand how it works, awesome model!

Can you recommend good source of information, how to calculate differential transmissions with adders and subtractors?

[2GodBDGlory]

6 hours ago, KirTech LAB said:

This is an incredible piece of engineering, it will take a lot of time to understand how it works, awesome model!

Can you recommend good source of information, how to calculate differential transmissions with adders and subtractors?

Thanks! Sorry, I'm not familiar with a resource like that.

[Davidz90]

6 hours ago, KirTech LAB said:

Can you recommend good source of information, how to calculate differential transmissions with adders and subtractors?

Here's a helpful video that explains addition/subtraction with differential and how it can be used to get prime number gear ratios (like 1:17) that are impossible otherwise:

 

[KirTech LAB]

10 minutes ago, Davidz90 said:

Here's a helpful video that explains addition/subtraction with differential and how it can be used to get prime number gear ratios (like 1:17) that are impossible otherwise:

Thank you.