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

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Subject Author Date
Working 3 digit mechanical computer built from LEGO Technic... Andy Carol 01-27-2006
Posted by on January 27, 2006, 12:03 am
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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



Posted by John Mycroft on January 27, 2006, 7:47 am
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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?



Posted by on January 28, 2006, 12:49 pm
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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?

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



Posted by Wouter on February 2, 2006, 4:20 pm
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Your table:

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
>
>> 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?
>
> 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
>
>



Posted by Andy on February 5, 2006, 1:34 am
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> Your table:
>
> 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

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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