We present an evolution-based method for optimal mechanism
synthesis. It is based on the embedding of the Euclidean motion group
in the space of affine displacements upon which an object-oriented
Euclidean metric is imposed. This Euclidean structure allows the use
of curve and surface evolution techniques from computer aided design
and image processing. We demonstrate the algorithm by synthesizing
planar four-bar mechanisms and we show how to adapt it so that the
resulting four-bar is free of circuit defects.