On spatial networks of overconstrained linkages

Abstract Some preliminary guidelines have already been put forward for the synthesizing of mobile spatial networks, but they are restricted, in the main, to topological considerations. We draw from this prior work here to show in detail the analytical niceties involved in attempting such a task. Our first example is a spatial ensemble of Bennett linkages inspired by a planar Kempe network. The second, more ambitious, incorporates Bennett and Bricard loops. In analysing the latter network, we are led to discuss some novel geometrical relationships concerning the hyperboloid of revolution of one sheet.