This uses universal joints to transform tbe circular motion of the drive wheels into up/down and back/forth of the legs - it's rather bulky, but is probably the best that can be done with standard Lego bits. The diagram below is an attempt to show how the legs work. (Click on it for a bigger picture.)

Here's a modification with smaller leg joints, using a few non-Lego parts (heresy!) - instead of the universal joints and 2-stud axles, I've used a 1/2" bit of thin plastic rod, saving about 2-3 studs worth of space on each leg. The other changes are to make the beastie more robust - there is tighter reinforcement top to bottom, to stop it shaking apart; and the RCX has been mounted crosswise.
I still haven't done anything about ensuring synchronisation of the two sides: must get round to getting (or making) some angle sensors sometime...
There are a few other web sites with more interesting spiders than mine: however, I've found that both that I had linked from here have vanished/moved. I've taken the lazy option now, and suggest that you look at Lego MindStorms Internals site which references virtually every MindStorms related site in the world!
The other thing I'm tryng to do is bung a bit of intelligence in the RCX - for this, I'm starting with very simple mechanics, just a light sensor and a pair of independently driven wheels, as shown below, and using native code (under legOS) to make it do something interesting. More later, when I have time to actually do something!
The one below has a lower gearing, and is a bit easier to control.
Last modified on 3rd June 1999