Infinitesimal flexibility of higher order for a planar parallel manipulator (Q2717156)

A framework \(F\) consisting of a vertex set \(V\) and an edge set \(E\) is called infinitesimally flexible of order \(n\) iff (1) for all vertices out of \(V\) there exist polynomial vector functions in \(t\) of degree \(n\) such that the rod lengths for all rods in \(E\) remain constant up to the \(n\)th derivative with respect to \(t\) and (2) these vector functions do not belong to a motion of the whole framework \(F\).NEWLINENEWLINENEWLINEThis definition is set up in order to discuss higher order infinitesimal flexibility in the \(n\)-dimensional Euclidean space. For some particular planar frameworks flexibility analysis is shown in detail: If the framework contains a four-bar linkage, the higher order infinitesimal flexibility is firmly connected with the discussion of point paths whith higher order osculating circles.NEWLINENEWLINEFor the entire collection see [Zbl 0944.00034].