On kinematic singularities of low dimension.
This thesis is an investigation into the types of singularities that can appear
on trajectories of rigid motions, kinematic singularities, motivated by problems
in mechanical engineering of designing mechanisms. Here we consider rigid motions
of the plane and space with one and two degrees of freedom.
In order to study these singularities weprove a multi-germ transversality result
and also a result about the restrictions on the codimension of the singularity
given by the number of degrees of freedom of the motion. Some of the classifications
of the singularities we are interested in have already been completed
but all the simple singularities of space curves and also most of the multi-germs,
both of the plane and of space, are classified here. We also study the unfoldings
and bifurcation sets of all the kinematic singularities on our lists.