  The induced metrics of Dupin cyclidic systems, that is, orthogonal coordinate
systems with Dupin cyclides and spheres as coordinate surfaces, were provided
by Darboux. Here we take a more geometric point of view and discuss how Dupin
cyclides and Lam\'e families of Dupin cyclidic systems can be obtained by
suitably evolving an initial circle or a Dupin cyclide, respectively. This
approach reveals that those Lam\'e families are given by parallel surfaces in
various space forms.
