Subject:
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Re: Surely we cannot be outdone?
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Newsgroups:
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lugnet.robotics
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Date:
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Sun, 30 May 2004 12:02:31 GMT
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Viewed:
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970 times
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In lugnet.robotics, Øyvind Steinnes wrote:
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“Steve Baker” lego-robotics@crynwr.com wrote in message
news:40B93E57.5030709@airmail.net...
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Babbages’ Difference Engine in Meccano:
http://www.meccano.us/differenceengines/rde1/index.html
Now *surely* someone here can do better with Lego?
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And if that someone can get it powered by a pnaumatic engine we got a
airpowered calculating machine :)
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I doubt that would be possible, certainly very difficult as it works with
decimal digits. Maybe possible to build a binary difference engine with
pneumatics.
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Is there any place where the principles of Babbage’s Difference Engine is
explained??
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It is really quite uncomplicated, google “babbage difference engine” returns
some good pages eg: http://ed-thelen.org/bab/bab-intro.html
It basically works by having as many difference columns as the degree of
polynomial you want to evaluate. At each step, the value in each column is added
to the one beside it, the farthest column returns the result. It’s a bit like a
fibonacci series where the next number is the sum of the last 2, except in this
case for each step, each column is the sum of itself (at the last step) and the
next lower one.
To use the x^3 example, suppose the wheels were initialised thus (Read each
column downwards to see the value of the column):
R D1 D2 D3
0 0
0 0 0
0 0 0 0
0 1 6 6
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One operation (4 turns of the crank in the meccano model) adds D1 to R, D2 to
D1, and D3 to D2, resulting in:
R D1 D2 D3
0 0
0 0 0
0 0 1 0
1 7 2 6
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Notice that the value in the R(esult) column is now 1, or 1 cubed.
A second operation results in:
R D1 D2 D3
0 0
0 0 0
0 1 1 0
8 9 8 6
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Resulting in 8, or 2 cubed. You can see that the next operation will result in
8+19, or 27, which is 3 cubed, and so on. The important thing is that each
column is calculated using addition only - the difference engine is just a big
block of multiple adding machines.
But quite a deal of force is needed to operate all those mechanisms, the meccano
one does each step in 4 sub-steps, to simplify it a bit. Even a 3rd degree
engine like that meccano one would be difficult with LEGO, because of the number
of mechanisms involved. But not impossible, maybe?
ROSCO
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Message has 1 Reply:
 | | Re: Surely we cannot be outdone?
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| In lugnet.robotics, Ross Crawford wrote: (snip) Thanks for the explanation of DE principles, Ross. I spent some time looking at that site. I would have to say that DE is a Meccano "tour de force" Lego is not quite as good at complex geared (...) (20 years ago, 30-May-04, to lugnet.robotics, FTX)
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Message is in Reply To:
| | Re: Surely we cannot be outdone?
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| "Steve Baker" <lego-robotics@crynwr.com> wrote in message news:40B93E57.503070...ail.net... (...) And if that someone can get it powered by a pnaumatic engine we got a airpowered calculating machine :) Is there any place where the principles of (...) (20 years ago, 30-May-04, to lugnet.robotics)
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