Generic properties in Euclidean kinematics (Q1117719)

The motion of n-dimensional rigid bodies is investigated as a path in the configuration space i.e. Euclidean isometry group E(n). A stratification of the jet bundles \(J^ k(R,E(n))\), \(k=1,2\), is obtained which gives generic properties of rigid body motions via the transversality theorem. The analytic definitions of centrodes and axodes are given. It is shown that if n is even, centrodes may be constructed except at isolated instants and they are nonsingular curves, if n is odd axodes may be constructed at each instant and they are noncylindrical ruled surfaces. Examples from the theory of mechanisms and classical mechanics are considered.