Bond theory for pentapods and hexapods

This paper deals with the old and classical problem of determining necessary conditions for the overconstrained mobility of some mechanical device. Methods from algebraic geometry have already been used to investigate these mobility conditions, and we propose some tools specifically developed for the so–called n–pods. In particular, we focus on the conditions which are imposed on an n–pod by the existence of points of particular kind, which lie on the boundary of the set of self–motions of the n–pod when we consider a specific compactification of the group of direct isometries of R. Furthermore we set up a photogrammetry–like technique which allows to establish necessary conditions for movability of 5–pods.