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Low frequency oscillators, an electrical harmonograph

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Nik

Mon Jun 06 2016, 02:44AM

Registered Member #53 Joined: Thu Feb 09 2006, 04:31AM
Location: Ontario, Canada
Posts: 638

A normal harmonograph machine uses a number of pendulums to guide a pen across a sheet of paper to produce interesting pictures:

I just picked up an XY chart recorder and I would like to make an electrical equivalent of the harmonograph by generating a couple decaying sin waves into the chart recorder. I could do this with software and feed the output from the audio card into the recorder but that's cheating (if I wanted to print a picture I have a perfectly good printer already), what I would like to do is make a pair of oscillators that have a little bit of adjustment (like less than 5%) and run at around 1hz (the chart recorder can only move the pen so fast).

My first intuition was to use a simple LC circuit, it would naturally decay, takes a minimum number of parts, can be tuned easily and is easy to explain to others. However this would require coils and capacitors in the henries and farads range of values and there would be some serious energy involved. I'm ok with that (it would actually be really cool) but big high current coils and caps are expensive and well, big. I've looked at phase-shift oscillators and Wein Bridges but using op-amps takes away some of the intuitive "oh now I get it" that I hope to convey with this project. (Kinetic energy could be compared to the magnetic field in the coil and gravitational potential could be compared to the energy stored in the capacitor.) I also thought of using a small DC motor with a fly wheel to "act" like a big coil, spinning up and then partially recharging the capacitor from the energy stored in the fly wheel but I suspect that the losses would be too high for this to go for more than 1 or 2 cycles.

So before I go out and build a (really bad) quarter crusher just to make a pretty picture, is there simple way to generate a dampened 1hz sin that I have missed in my Googling?

Thanks,

-Nik

ps: I've been playing around in software and have had some pretty interesting results regardless of whether I get this project off the ground:

Dr. Slack

Mon Jun 06 2016, 06:47AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

State variable filters. Use reasonably big non-polar Cs (low leakage), 10-100uF range is easily possible, and big Rs, and low bias current opamps. With an SVF you can control the centre frequncy and Q independently, so make a high Q filter and kick it with an impulse, adjust the Q carefully and you might get minutes of decaying oscillation. The better the bias current / C ratio, the longer you will be able to get stably.

Nik

Mon Jun 06 2016, 01:24PM

Registered Member #53 Joined: Thu Feb 09 2006, 04:31AM
Location: Ontario, Canada
Posts: 638

Awesome, I'll hit the circuit simulator again on night shift and see if I can make something that will do the job. Thanks!

Dr. Slack

Tue Jun 07 2016, 07:58AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

In theory, any filter with a high enough Q will do, kick it and watch it ring. In practice, it's getting stable high Q that is the issue.

For instance, with an equi-component Sallen Key, the filter response can be adjusted using the opamp gain, which goes through infinite Q as the gain goes through 3. But to adjust it to 2.9999 or whatever is quite twitchy.

OTOH a SVF is built round two integrators, fed back with a 180 phase shift. Those alone make a resonator. The better quality the components, so low loss caps, very high gain op-amps (and at 1Hz almost any op-amp will have a huge gain), the more accurate will be the resonator. As integrators automatically have 90 degrees phase shift, the circuit will settle down to resonate where the loop gain is 1. Controlling the gain therefore controls the frequency at which the gain is 1. Imperfections will result in a small amount of loss or growth of amplitude each cycle, and Sod's Law says it will be loss. Now into this stable oscillator can be injected a tiny bit more loss (or growth, if you want to control it to make a stable level controlled oscillator).

A large fixed resistor shunting one of the caps is a convenient place to introduce loss and degrade the Q, which is pretty much equivalent to what the official designs show, which is bringing resistors into the virtual ground of the inverter. Use the other phase for growth.

Bored Chemist

Tue Jun 07 2016, 08:44PM

Registered Member #193 Joined: Fri Feb 17 2006, 07:04AM
Location: sheffield
Posts: 1022

You could fix a weighted pendulum to the shaft of a potentiometer...

2Spoons

Wed Jun 08 2016, 01:14AM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615

And when you get bored with decaying sine waves you might like to look at chaotic oscillators.

radiotech

Wed Jun 08 2016, 09:20PM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
Location:
Posts: 1546

Helmholtz, and his crowd, used a 'phonautograph'. Doing what you are engaged in.Their papers were made by
a smoking kerosene flame.

136 years later, the tuned port speaker cabinet is still used.

1465420826 2463 FT176940 On The Sensation Of Tone Helmholtz 1885

Nik

Thu Jun 09 2016, 04:06AM

Registered Member #53 Joined: Thu Feb 09 2006, 04:31AM
Location: Ontario, Canada
Posts: 638

Bored Chemist wrote ...

You could fix a weighted pendulum to the shaft of a potentiometer...

Har har (I'll probably end up trying this at some point).

Radiotech, interesting you mention that, I did a video not long ago talking about beat frequencies where I produced an image similar to that one in software.

Dr. Slack, haven't had time to do any work yet (damn actual job getting in the way) but that sounds very much like what I am aiming for.

2Spoons, like the Lorenz attractor? I have seen it run very quickly on a scope but I will need to limit it to the drawing speed of my XY recorder. I have a feeling that XXL component values might be involved.

klugesmith

Sat Jun 11 2016, 11:36PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

>> You could fix a weighted pendulum to the shaft of a potentiometer...
> Har har (I'll probably end up trying this at some point).

+1 on using gravity pendulums, if your rules of engagement permit. Eccentrically weighted bicycle wheels can give you periods of many seconds with reasonably high Q, and look good in a showcase.

To avoid the friction of a potentiometer bearing, the pendulum could move some kind of vane through the gap of an opto-interrupter sensor. To match an angular range of many degrees to an optical stroke less than 1 mm, you could use an eccentrically mounted round disk.

No need for external supply of electric power. The pendulum can move a magnet near a coil, or vice-versa. A typical hard-disk-drive head positioner include efficient magnet & coil assembly with a ball bearing pivot! Could also look good.

Passive LC resonators must indeed be sort of big to get low frequencies. For inductors wound with ordinary copper, the characteristic time constant L/R inevitably goes down with decreasing size and weight. It might be enlightening to chart L/R versus mass, for off the shelf inductors and "reactors". Superconducting magnets have L/R time constants off the top of the chart, but come with a lot of baggage.

Nik

Mon Jun 13 2016, 04:22AM

Registered Member #53 Joined: Thu Feb 09 2006, 04:31AM
Location: Ontario, Canada
Posts: 638

Heh, if I have to start sourcing liquid nitrogen in order to make an analog "wobbly-bike-wheel" I may just go with the wheel.

Unfortunately work has been nuts lately but I did manage to coax my PC into spitting out some sub-hz which gave ok results. There is some backlash in the mechanism but with larger strokes and slower pen movements I still think this could work out.

1465791723 53 FT176940 Img 20160609 063351

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