  We analyse weak and strong controllability notions for the locomotion of the
3-link Purcell's swimmer, the simplest possible swimmer at low Reynolds number
from a geometric framework. After revisiting a purely kinematic form of the
equations, we apply an extension of Chow's theorem to analyze controllability
in the strong and weak sense. Further, the connection form for the symmetric
version of the Purcell's swimmer is derived, based on which, the
controllability analysis utilizing the Abelian nature of the structure group is
presented. The novelty in our approach is the usage of geometry and the
principal fiber bundle structure of the configuration manifold of the system to
arrive at strong and weak controllability notions.
