Generic properties in Euclidean kinematics

Abstract

The motion of a rigid body in a Euclidean space E n is represented by a path in the Euclidean isometry group E(n). A normal form for elements of the Lie algebra of this group leads to a stratification of the algebra which is shown to be Whitney regular. Translating this along invariant vector fields give rise to a stratification of the jet bundles J k (R, E(n)) for k=1, 2 and, hence, via the transversality theorem, to generic properties of rigid body motions. The relation of these to the classical centrodes and axodes of motions is described, together with applications to planar 4-bar mechanisms and the dynamics of a rigid body.