  In this paper we study the self-propulsion of a dumbbell micro-robot
submerged in a viscous fluid. The micro-robot consists of two rigid spherical
beads connected by a rod or a spring; the rod's/spring's length is changing
periodically. The constant density of each sphere differs from the density of a
fluid, while the whole micro-robot has neutral buoyancy. An effective
oscillating gravity field is created via rigid-body oscillations of the fluid.
Our calculations show that the micro-robot undertakes both translational and
rotational motion. Using an asymptotic procedure containing a two-timing method
and a distinguished limit, we obtain analytic expressions for the averaged
self-propulsion velocity and averaged angular velocity. The important special
case of zero angular velocity represents rectilinear self-propulsion with
constant velocity.
