Thanks go, again, to reader Richard who suggested another approach using fewer parts for the drive mechanism:
This is a view from either the top or from the side, depending on how you want to run the drive bar. The circle is a roller or a bearing which reduces friction. Bearings were not unknown in the 19th century: John Harrison, of Longitude Prize fame, used roller bearings for his clocks in the mid-18th century. Also see the awesome film about the Prize, Longitude (2000). However, given their expense even today (the cheapest retail I could find was $1.50 for 1/8" I.D. 3/8" O.D. ball bearings, and $0.69 for approximately the same size on eBay), I wouldn't use bearings. I'll stick to simple rollers.
In the zero state, the rod spring is compressed, and the rod is prevented from moving by the drive bar. When the drive bar is pulled, the spring expands, and the rod will either move if not inhibited, or remain where it is if inhibited. The force required to pull the drive bar depends on the force of the spring and the friction between the roller and drive bar (and the drive bar and its race).
To reset, simply push the drive bar back, which pushes all the rods back to the zero state. The force required to push the drive bar depends on friction, plus 2x the spring's force, because of the 45-degree angle on the drive bar, and the fact that the force is redirected through 90 degrees.
If a rod needs to follow another rod, the same mechanism without the drive bar or roller is used, which supports modularity:
The drive bars could be moved by levers, and there could be different drive bars for rods on the same plane that need to be activated at different times.
(Update 2010 Feb 28: I just realized that if a rod is followed by another rod, then that rod doesn't need a spring. The spring on the follower rod provides the tension for both rods, but may need to be slightly stronger to overcome the additional friction.)
Being that there is now only a single spring, it should be very easy to find springs of the right diameter and spring constant. The rods are 1/4" x 1/8", so the inner diameter of the spring should be above 0.28" (being the diagonal of the rod). The spring needs to exert some force, say 0.25 lb, when compressed one unit, which we decided was 5/16". This gives a rate, k, of 4/5 = 0.8 lb/in.
McMaster-Carr sells continuous lengths of compression springs, in 11", 12", 20", and 36" lengths. Each of their springs is assigned a "spring constant", which is not the same as the physical spring constant k, which they call the spring rate. Let's call their spring constant C. They say that to determine the length of the spring to cut off the continuous length, take C, divide by the spring's number of coils per inch (n), and divide again by desired k. Thus, the units for C are coil-pounds/in. For 3/8" outer diameter springs, I get completely ridiculous lengths for even the weakest spring. That spring has C = 32.3, n = 7.7, and so C/(nk) = length = 5.2 inches!
Clearly the continuous-length springs aren't going to work. For non-continuous length springs, the weakest spring has a k = 1.02 lb/in, and a length of 1.5". Sadly, these are highly expensive springs: $1.57 each. That, too, is ridiculous.
However, the next spring up, k = 1.09 lb/in, also with length 1.5" is $0.57 each.
Alternatively, I could make my own springs with a spring-making machine. And here is everything you want to know about making springs for yourself. After seeing the list of equipment needed, I don't think making springs myself is for me.
Finally, the above site lists a bazillion manufacturers of springs. I suspect that most deal with industrial customers. Ideally I would like to get down to about $0.10 per spring. There is absolutely no way a spring shop would custom make these things without an order of thousands of pieces, and there's absolutely no way I could use thousands of springs. I would like a long continuous length that I can cut down to the appropriate size. It's just that McMaster-Carr doesn't sell any of the right type.
With that conclusion, I Googled for "continuous length compression springs" and found Associated Spring Raymond. They have many springs, with all sorts of parameters. I looked at one with a spring rate (this time defined as C/n) of 0.61 lb, "hole size" (whatever that means, I'm assuming inner diameter) of 3/8", in 10" lengths for $3.02 each. I would cut this into 3/4" springs. That gives me 13 springs per length, or $0.23 per spring.
That's not so bad, and gives pretty much exactly what I need.