A recently established criterion
for stresses on any bar and joint framework with a complete bipartite graph is
converted into explicit criteria for infinitesimal motions of the framework. These
criteria, based on quadric surfaces through the joints, include and complete those
developed in recent years in the study of geodesy with range satellite networks. The
infinitesimal motions are displayed in a simple geometric form, appropriate to any
dimension. This geometric description is used to establish necessary and sufficient
conditions, based on ruled quadric surfaces, for which bars may be added
to a bipartite framework without removing a prior infinitesimal motion.
These criteria are applied to the behaviour of structural engineering space
frames.
