Author Topic: Home Brew Analog Computer System  (Read 110155 times)

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Offline GK

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Re: Home Brew Analog Computer System
« Reply #100 on: June 14, 2013, 01:04:00 am »
It would be really difficult to estimate the total time spent; Hundreds of hours. Note that those integrator boards pictured constitute probably ~5% of the total circuitry. I reasoned that the cost in monetary terms is justified alone by the educational benefit conferred by having a full blown differential analyser on which to apply problems in physical systems modelling and differential calculus.
If you can pardon my immodesty, I think this is going to be quite an impressive (two relay-rack) machine when finished. An eventual hyperlink to a full expository technical write up on my web domain probably won’t hurt my resume either.
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Offline GK

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Re: Home Brew Analog Computer System
« Reply #101 on: June 20, 2013, 01:31:57 am »
I used to have a box of mechanical sine/cosine resolvers and hundreds of other styles of synchros and resolvers, they were parts of anb autopilot. We were cannibalising them for spares to fix moving map displays and other synchro indicators


Hey, you wouldn't happen to have by chance a few sine-cosine potentiometers laying around, would you?

I've got a prototype matrix computational circuit on the go which transforms the Cartesian coordinates (X,Y,Z) of 3-dimensional objects and graphs into 2-dimensional polar coordinates (X,Y) for isometric projection on a 2-dimensional display.

However at the moment the angles of rotation of the isometric projection around the x and y axis' are fixed and in order to make them independently and continuously variable I require a pair of sine-cosine law potentiometers.

Such things still appear to be available new: http://www.precisionsales.com/potentiometers/singleturn/sinecosine.htm
.........however I'm afraid to even bother asking what they cost.

One possible alternative is to fake the dual sine-cosine law with digital pots driven by a rotary encoder via a uC programmed with appropriate look up tables (or just solving each increment) but even with lots of "linear" bits to work with the steps still get quite chunky at the extremes where the rate of change is high and many "counts" are skipped. A pair of "old school" pots are still the preferred option.

These kind of pots were used extensively back in the day for radar displays (2-D projection of 3-D) and early medical imaging equipment. 

 
« Last Edit: June 20, 2013, 01:39:32 am by GK »
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Offline SeanB

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Re: Home Brew Analog Computer System
« Reply #102 on: June 20, 2013, 04:18:22 pm »
Sorry, they stayed when I left.
 

Offline GK

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Re: Home Brew Analog Computer System
« Reply #103 on: June 21, 2013, 02:07:06 am »
Poo.

It looks like I'm stuck with digital pots and a uC. Looking at the datasheets a little closer those sine-cosine pots from Precision Sales aren't the right type anyhow. I reguire a pair of the quad wiper radar display types which operated over 90 degrees of shaft rotation.

A pair of A5204's and a PIC16F874 with sin/cos look-up tables it is for now.
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Offline chickenHeadKnob

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Re: Home Brew Analog Computer System
« Reply #104 on: June 21, 2013, 03:26:02 am »

I can't tell what kind of latency you need from your synthetic pots, but you might find the classic CORDIC algorithm a useful speed/accuracy/table size trade-off. CORDIC by its very nature simultaneously computes SIN and COS for a given theta and requires a much smaller table once the number of bits of resolution desired goes up.
 

Offline GK

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Re: Home Brew Analog Computer System
« Reply #105 on: June 21, 2013, 06:50:06 am »
Hmmm......... looks interesting. However if I am restricted to the 8-bits of a typical digital pot there really isn't any point in attempting to rotate my isometric projection in steps of finer resolution than 1 degree. The full sine/cosine lookup table (0-90 degrees) is therefore only 182 bytes and for simplicity can hardly be beat.

An 8-bit approximation (rounding down to the nearest integer) doesn't seem to be quite that bad or excessively chunky for the most part after all:


 
« Last Edit: June 21, 2013, 06:54:18 am by GK »
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Offline chickenHeadKnob

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Re: Home Brew Analog Computer System
« Reply #106 on: June 21, 2013, 08:53:30 am »

Ya, for 8 bits out there is no sense going beyond straight lookup. Due to symmetry in the trigonometric functions you can further compress the domain to 0 - 45 but beyond that it  isn't worth the effort.
 

Offline GK

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Re: Home Brew Analog Computer System
« Reply #107 on: June 29, 2013, 02:14:00 am »
BTW, here is the Lorenz Attractor in isometric projection. The angles of rotation on both the X and the Y axis are still fixed at 45 degrees (by a fixed resistor sin/cos matrix) as I haven't ordered my digital pots yet. Some boof heads require Matlab to produce a display like this  ::) I do it with op-amps and a Tek545 ;D

I'll make a video of the display when I get my sin/cos synthesized digital pots wired into the transformation circuit. It will look pretty cool when I can twiddle a pair of pots to fully manually rotate the projection on both axes.

« Last Edit: June 29, 2013, 02:16:18 am by GK »
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Offline baljemmett

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Re: Home Brew Analog Computer System
« Reply #108 on: June 29, 2013, 02:54:40 pm »
Some boof heads require Matlab to produce a display like this  ::) I do it with op-amps and a Tek545 ;D

Oh, very nice work, sir!  A thumbs up is definitely in order ;)
 

Offline megajocke

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Re: Home Brew Analog Computer System
« Reply #109 on: June 30, 2013, 04:53:08 am »
Cool! Nice progress   O0
 

Offline Rerouter

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Re: Home Brew Analog Computer System
« Reply #110 on: June 30, 2013, 05:31:08 am »
what is the cause of the blip on the 3rd gratical to the right and 1 down? appears there is a similar blip on the same position on the other side of the oscillation,
 

Offline GK

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Re: Home Brew Analog Computer System
« Reply #111 on: June 30, 2013, 10:51:59 am »
That I believe is due to a transfer non linearity in my dodgy and barely adequate multiplier stage temporarily knocked up on breadboard.   
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Offline robrenz

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Re: Home Brew Analog Computer System
« Reply #112 on: June 30, 2013, 02:39:46 pm »
A fine example of analog Beauty in both computation and display :-+

Offline jahonen

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Re: Home Brew Analog Computer System
« Reply #113 on: June 30, 2013, 04:15:17 pm »
Apparently fairly simple circuit is enough to produce the Lorenz attractor, as shown here by Paul Horowitz himself:



Regards,
Janne
 

Offline GK

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Re: Home Brew Analog Computer System
« Reply #114 on: June 30, 2013, 11:46:01 pm »
Yes, the circuit I used is quite similar. However it requires a few more o-amps to make a 3-dimensional projection unit.

If you compare Pauls 2D display of the LA to mine, you can easilly make out the 45 degrees of rotation on both the X and Y axes:

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Offline GK

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Re: Home Brew Analog Computer System
« Reply #115 on: July 01, 2013, 09:53:23 am »
Some more experimentation with the isometric projection unit. Once again the angle of rotation / perspective on both axes is fixed at 45 degrees as I haven't prototyped the synthesized sin/cos pots yet to make them (angles of rotation) fully variable. My two AD5204 quad digital pots are supposed to arrive tomorrow. I'll post up full circuit details of the 3-D projection unit once I have verified the design and finished building it.

It is the operation of the projection unit that I was trying to show off in the Lorenz Attractor example, as at the time I just happened to have had a bread-boarded generator circuit for this 3-dimensional object on the bench to act as the signal source. This evening I knocked up some generator circuitry for some much simpler 3-dimensional objects (a straight spring and a conical one). With these simpler objects the nature of the 3-D projection is much more obvious.

   


« Last Edit: July 01, 2013, 12:02:46 pm by GK »
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Offline GK

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Re: Home Brew Analog Computer System
« Reply #116 on: July 01, 2013, 01:05:20 pm »
I made a boobie!   :o

However I still need to implement a multiplexer to get a pair on the screen rather than just one. No time to do that now as it's 10:30pm and time for bed  :'(  Oh man this analog computer project is going to be so awesome! When I have the multiplexer implemented along with the synthesized sine/cosine "pots" in the projection matrix/transformation circuits I'd be able to project a full boobie pair in any 3-dimensional, fully rotatable viewing angle!

Woo hooo!  ;D


« Last Edit: July 01, 2013, 01:07:57 pm by GK »
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Offline GK

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Re: Home Brew Analog Computer System
« Reply #117 on: July 02, 2013, 07:53:51 am »
Done!

Now that I've had my CRT boobie fix I promise to keep the thread a little more mature from now on.  ;D

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Offline SeanB

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Re: Home Brew Analog Computer System
« Reply #118 on: July 02, 2013, 07:16:23 pm »
C cup, as they are 3 divisions each........... ;)
 

Offline GK

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Re: Home Brew Analog Computer System
« Reply #119 on: July 04, 2013, 12:58:31 pm »
Interesting conversion factor. Which manual did you get that from?  ;D

I've now written the uC code for the synthesised sine/cosine pots. The 3-D projection unit requires 8 pots in total; 4 with a sine law and 4 with a cosine law. They are arranged into two quad gangs; each quad gang comprised of two sine law pots and two cosine law pots.
One quad gang controls the angle of rotation of the 3-D projection around the Y axis and the other quad gang controls the angle of rotation around the X-axis.

Instead of using a pair of rotary encoders for the manual adjustment of the Y & X angles of rotation I ended up using a pair of single gang potentiometers across a voltage reference; their position read by the internal ADC of the PIC uC.

All I have to do now is wire in the two AD5204 quad digital pots and then I'll have full manual control over the "perspective" of the 3-D projection, rather than the currenly fixed 45/45 degree one. The first thing I'll video is the Lorenz Attractor being manually rotated on its axes.

Time for bed again, right now though.

 

 
« Last Edit: July 04, 2013, 01:01:04 pm by GK »
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Offline GK

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Re: Home Brew Analog Computer System
« Reply #120 on: July 05, 2013, 08:34:51 am »

 Due to symmetry in the trigonometric functions you can further compress the domain to


Yes, of course. You just read the table in the opposite direction for cos instead of sin or sin instead of cos:


« Last Edit: July 05, 2013, 08:37:19 am by GK »
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Offline woodchips

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Re: Home Brew Analog Computer System
« Reply #121 on: July 05, 2013, 10:11:31 am »
Wow, found this post and delayed going to bed by a couple of hours!

Some comments, my interests are in mechanical analogue computers so similar. Have you seen the differential analysers by Vannevar Bush etc in the 1930s? Also an earlier one, 1890s, for calculating tides but I can't at the moment track this down as to the why or how.

What is the current book collection? A list of author, title and brief comments would be useful. Another interest of mine is wind turbines so I have some books on waveforms as regarding electromagnetism, again, similar but not identical.

Hewlett Packard and Tektronix made large screen monitors, occasionally available. I have a HP 143S which works to 15MHz in X and Y. There is also the Kikusui 5121A but that is electromagnetic deflection so 1kHz X and 10kHz Y.

I have some sine cosine pots, somewhere. They were rescued from some 1950s aircraft navigation equipment, mechanical analogue computers.

In post 44 a comment was made about circular slide rules. Find a 1 arc second theodolite for the glass discs and reading method. Another wonderful piece of technology that electronics has consigned to the scrap heap.

Bob

 

Offline GK

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Re: Home Brew Analog Computer System
« Reply #122 on: July 06, 2013, 01:40:00 am »
Hi Bob,

I'll keep an eye out for those X-Y monitors you mention, thanks! I'm not particularly familair with any of the old mechanical analog computers. My book collection is almost exclusively concerned with electronic analog computers. Not sure if it is still of interest, but on the bookshelf I currently have:

1)
Analog and Hybrid Computing
Hyndman, D. E.
2)
Fundamentals of Analog Computers
Weyrick, Robert C.
3)
Analog computer programming
Michael G. Rekoff
4)
Introduction to analog computation
Ashley, J. Robert
5)
Analog Computation and Simulation: Laboratory Approach
Jenness, Roger R.
6)
Introduction to Electronic Analogue Computers
C. A. A. Wass
7)
Analogue Computing at Ultra-High Speed
Donald Mackay
8 )
Computation by Electronic Analogue Computers
Borsky, V. and Matyas, J.,
9)
Electronic Analog Computer Primer
Stice, James E. & Bernet Swanson
10)
Analogue Computers
I. I. ETERMAN
11)
Introduction To Electronic Analog Computers
Warfield, John. N.
12)
Analog/logic computer programming and simulation
Fred J Ricci
13)
Computer Handbook
Huskey, Harry D.
14)
Principles of Analog Computation
Smith, George W. and Roger C. Wood
15)
Basic Analog Computation
Gerald R. Peterson
16)
Analog computation in Engineering Design
Rogers and Connolly
17)
Analog methods
Karplus and Soroka
18)
Analog simulation
Karplus
19)
Hybrid computation
Bekley and Karplus
20)
High Speed analog computers
Tomovic and Karplus
21)
Design fundamentals of analog computer components
R. M. Howe
22)
Analog computation
Albers S. jackson
23)
Electronic analog computers
Korn and Korn
24)
Electronic analog and hybrid computers (DC analog computers)
Korn and Korn
25)
Methods of solving engineering problems using analog computers
Leon Levine
26)
Analog computer techniques
C. L. Johnson

« Last Edit: July 06, 2013, 01:44:15 am by GK »
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Offline SeanB

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Re: Home Brew Analog Computer System
« Reply #123 on: July 06, 2013, 05:07:05 am »
Those vector analysers that were on here a few months ago would have made nice XY monitors, they have equal bandwidth in both channels, and the signal amps inside have sine and cosine generators.
 

Offline woodchips

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Re: Home Brew Analog Computer System
« Reply #124 on: July 06, 2013, 04:59:06 pm »
GK, thanks for the book list, only have a couple of them. They are full of calculus and similar and my maths simply isn't up to that.

Had a scrummage in the library and the following might be of interest. Again, more towards mechanical analogue computers or electromagnetism but if you see them for a £ (or local currency of course) or two then worth buying, I reckon anyway.

1)
Electronic Digital Integrating Computers, Digital Differential Analysers - Mayorov
2)
Electronic Computers, Principal & Application - Ivall (trivial level)
3)
Graphical & Mechanical Computation - Lipka
4)
The MIT Radiation Laboratory Series, 28 volumes but in particular
     Theory of Servomechanisims - James
     Computing Mechanism & Linkages - Svoboda
     Components Handbook - Blackburn
     Waveforms - Chance
5)
The Journal of the Franklin Institute, articles about the Bush differential analyser

These are electromagnetism books, but might have some ideas for programs to run
6)
Elementary Treatise on Curve Tracing - Frost
7)
Practical Curve Tracing - Duncan
8)
Alternating Current Waveforms - Kemp
9)
Waveform Analysis - Manley
10)
Practical Geometry & Engineering Graphics - Abbott
11)
No particular book but equalisation of telegraph lines, under the ocean etc, not trivial!

Otherwise, I have found one of the sine/cosine pots. It is 14.4k and in a servo size 15 case. Came from a co-ordinate converter used in the navigation system (Green Satin) used in 1950s bomber aircraft, no tolerance specs but must be pretty good. The tide predictor was designed by Thompson, Lord Kelvin, in the 1890s but still can track down the article. Some in the Britannica to give a flavour.

Hope this is of some interest.




 


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