Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Simple singularities of space curves

C. G. Gibsona1 and C. A. Hobbsa1

a1 Department of Pure Mathematics, University of Liverpool, P0 Box 147, Liverpool L69 3BX

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 Ae-codimension. It is however little harder to list the A-simple germs, which includes all germs of Ae-codimension ≤11: that then is the principal objective of this paper.

(Received March 04 1992)

(Revised May 05 1992)