Graphs of groups were introduced by Bass and Serre in the 1970's, inspired by Ihara's proof of that every torsion-free discrete subgroup of SL_2(Q_p) is a free group. In this talk I will describe how to use graphs of groups to model motions of articulated structures in a variety of spaces. Our approach is axiomatic, and allows to study a great variety of rigidity problems by varying the groups on the vertices and edges of the graph of groups.

(This is joint work with Joannes Vermant)