# Working 3 digit mechanical computer built from LEGO Technic...

I just wanted to de-lurk to mention that I've completed construction of a working LEGO Difference Engine. (i.e. a Babbage Engine)
It has over 200 gears, 20 shock absorbers, and is about 18 inches tall by 25 inches wide. It is purely mechanical in nature, requiring over 100 turns of the crank for each answer.
http://acarol.woz.org
The web page has several detailed pictures, theory of operation, and a mechanical description.
It can evaluate any polynomial of the form ax^2 + bx + c, up to three digits.
Enjoy!
----- Andy
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A truly stunning achievement! Charles & Ada would be proud of you. Not wishing to get you to start rebuilding or anything but what does it do if b^2 <4ac?
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It doesn't solve for roots, it evaluates for x = 1, 2, 3, etc. It would be used to build a table of results for a polynomial.
The most common one I run for testing is x^2. It outputs: 1, 4, 9, 16, 25, 36, 49, 64, etc.
I am considering expanding it to 4 digits and adding another set of adders so it can evaluate cubic polynomials.
---- Andy
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f(x) x 2*x^2 + 3*x + 5 First Difference Second Difference 1 10 9 4 2 19 13 4 3 32 17 4 4 49 21 5 70
Why don't you look @ it this way:
f(x) = a*x^2 + b*x + c
First Differance: a*(2x-1) + b Second Differance: a*2
Always...
:) Wouter
<Andy Carol> wrote in message said:

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You are correct that would be more general. I did it with actual numbers simply for the ease of conveying the basic principle to people who want an overview of how the machine works.
--- Andy
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Some of us over in LUGNET noticed it as well - *very* nice, and a lot of us are very curious about the details. It needs about a 100 turns?!? Use an RCX as a dumb battery box to motorize it ;-). Someone on LUGNET also recently posted a working knitting machine. Now we need the machine inbetween (Jaquard [sp?] loom).
--
Brian Davis

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I'm guessing that's becuase lego gears are small and weak. A big gear for a big crank would probably help a lot.

The one I've seen:
http://homepage.mac.com/aklego/PhotoAlbum22.html
Does spool knitting, which is trivial compared to a regular knitting machine -- even one without a ribber. Mind you, I'm impressed, but it is a baby step towards knitting. All you get is a lucet cord.
Elijah ------ can see a Jacquard loom being much more difficult
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There is a LOT of friction in moving 200 gears, along with the mechanisms they drag along. There is also a detent which causes each digit to "click" into place.
The original Babbage design was 1:1. The version of his machine made by the London Museum was 1:4. Mine is about 1:105
On the other hand, the movement is very smooth and light. Part of the issue is that I only have a specific set of gear sizes available. I would have been happy to have 1:80, but I had a choice between too low or too high and too high simply won't work, so I'm stuck with too low.
--- Andy
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Andy Carol writes:

It's very impressive. I sent the link to our High Performance Computing group, so they can see how to make real calculators. :-)

I didn't quite understand how it works. I suppose it takes a bit of experimenting to figure it out. Please let us know, if you expand the explanation.
Play well,
Jacob
--
City X'ers mail van (building instructions):
http://lego.jacob-sparre.dk/CityXers/Postbil /
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Andy:
What a fascinating thing this is. I gave a quick study of the device and am amazed what can be built with Lego. Being a student of mathematics myself, this is really quite exciting!
Great Work!
Best Regards,
Mark
<Andy Carol> wrote in message