  Swimming micro-organisms such as flagellated bacteria and sperm cells have
fascinating locomotion capabilities. Inspired by their natural motion, there is
an ongoing effort to develop artificial robotic nano-swimmers for potential
in-body biomedical applications. A leading method for actuation of
nano-swimmers is by applying a time-varying external magnetic field. Such
systems have rich and nonlinear dynamics that calls for simple fundamental
models. A previous work studied forward motion of a simple two-link model with
passive elastic joint, assuming small-amplitude planar oscillations of the
magnetic field about a constant direction. In this work, we found that there
exists a faster, backward motion of the swimmer with very rich dynamics. By
relaxing the small-amplitude assumption, we analyze the multiplicity of
periodic solutions, as well as their bifurcations, symmetry breaking, and
stability transitions. We have also found that the net displacement and/or mean
swimming speed are maximized for optimal choices of various parameters.
Asymptotic calculations are performed for the bifurcation condition and the
swimmer's mean speed. The results may enable significantly improving the design
aspects of magnetically-actuated robotic microswimmer.
