Saw the damnest thing today

If you know the date and time, and your location, it ought to be pretty simple to put a servo drive on it to keep it focused too.

I have a bunch of students dealing with the same thing. Once you figure out you need to toss the X-Y-Z mount and set up an equatorial mount, things go a LOT easier. The equitorial mount sets up a plane that mimics the path of the sun for any given day, you just need to rotate the collector on that plane to keep it in focus.
Stuart Wheat>> A parabolic reflector mirror, made of the stuff that is inside those

This one swung horizontally, and there was an adjustment knob for the height of the hot spot on the pot.
Steve

I would think the easiest thing to do would be to use optical pickups to activate servo motors. Seems pretty simple to me. Put optical relays at the bottom of tubes mounted just off parallel to the axis of the parabola. Set it on a 365 day timer that rough positions the dish at sunset for each day of the year, and then shuts down the controller tubes until sunrise time. From one day to the next the track of the sun isn't going to be much different than the day before, so you could just swing it back to rest at sunset on one axis and let your alignment relays do the fine adjust when the sun comes up the next day. Maybe add some kind of light level meter to deal with cloudy days if this is intended to be a totally unattended installation.

Unless I misunderstand, this will only work if the reflector rotates around the focus (which is likely impractical). Otherwise, you have to find a way to split the angle between the sun and the pot, not keep the reflector pointed at the sun...

If the reflector assembly rotates around its center of gravity it should point half way between the sun and the pot roast, which isn't a point target and doesn't require precise focus.
I think I would passively drive the reflector with a surplus gearmotor or a cheap small motor with string pot feedback for time-of-day position and fine tune it by balancing the radiation intensity between sensors on either side of the target, facing the reflector. The sensors might be copper tubing heat pipes with a diode bridge clamped on, a significant temperature difference would unbalance the bridge, giving a magnitude and direction output.
jsw

Do a search on some of the solar energy groups, forums they have several system designed to do this. Mike

Use an equatorial mount like many telescopes do to automate the tracking.
That would make a great hot-water heater for camping or temporary home use, too.
Aim your sunbeam at a cobbled together tank-radiator showerhead/sink....

I have used the simple bag Solar Showers, and come back to camp after a day out, and had to add cool water because the water was just too hot to shower in. A poor boy system like you suggest would be a good camping thing, and easy to do. I had considered it in my camping days, then got into motorhoming and forgot all about it. ;-)
Steve

Nope. Just like an old style satellite dish swings to point along the line of geo syncs along the equator it would swing so that the axis of symetry is always pointed at the sun. You just suspend your pot roast in front of the dish from struts at the focal point. Or your kettle of liquid salts as the case may be.