There were some examples stated in the topic I posted earlier. Maybe the most common/useful one is making a pre-stressed part, or a tension spring (I don't know if there's an official term for this, but those are two terms I've heard).
Let me explain. Make three masses, mass a, b, and c, and connect a to b, and b to c, using zero length springs. Then connect a to c using a longer length.The result is a tense spring that has mass b in the middle. These are used in many models; look in the zoo and I think you'll see. Also, using this same method, you can make tense springs that have as many masses on them as you want. Furthermore, you can mix different lengths in with the zero-lengths to make the "middle masses" settle in different places.
You can also use it to make polygons. Make a ring of masses connected by zero-length springs, and then connect every other mass on the ring using the same length. The result will be a polygon. Doing this with 8 masses is how Kevino made his 8 point motor that we just recently saw. You can also use the measured length as diagonals, instead of connecting every other mass.
And then of course there is the strange square that this topic is all about. The four sides of the square are zero-length.
Hope this helps.
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