  An elementary proof is given to show that a parametrised algebraic curve in
the plane may be traced out, in the sense of A. B. Kempe, by a finite pinned
linkage. Additionally it is shown that any parametrised continuous curve
\gamma: [0,1] to R^2 may be traced out by an infinite linkage where the
valencies of the joints is uniformly bounded. We also discuss related Kempe
universality theorems and give a novel correction of Kempe's original argument.
