In
Representation of links by braids, a new algorithm (Math. Helvetici 65 (1990), 104-113),
Vogel describes an algorithm to manipulate a link diagram in such a way that an equivalent
braid word may be read from it
(
Paper via SpringerLink).
Andrew Bartholomew describes the algorithm in
great detail in
one
of his papers as well.
We have implemented the algorithm in
GAP,
and it can be tested from this very website. In case of problems, please contact
Dan Roozemond. One word of warning:
For the moment, the algorithm only works for knots, i.e. links with only one component.