Simple singularities of space curves

Abstract

The genesis of this paper lies in theoretical questions in kinematics where a central role is played by naturally occurring families of rigid motions of 3-space. The resulting trajectories are parametrized families of space curves, and it is important to understand the generic singularities they can exhibit. For practical purposes one seeks to classify germs of space curves of fairly small A e -codimension. It is however little harder to list the A-simple germs, which includes all germs of A e -codimension ≤11: that then is the principal objective of this paper.