This article summarizes the presently available general theory of rigidity of 3-dimensional structures. We explain how a structure, for instance a bar and joint structure, can fail to be rigid for two quite different types of reasons. First, it may not have enough bars connecting certain sets of nodes. That is, it may faij for topologlcrl reasons. Secondly, although it may “count” correctly, it may still fail to be rigid if it is set up with some special relative positions of its nodes and bars; This second type of failure is a question not of topology but of projectbe geometry.
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