Notes on geometry of locomotion of 3-dimensional version of the Purcell's swimmer

We analyse the geometry of locomotion of 3-link mechanism inspired from the Purcell’s swimmer at low Reynolds number, the simplest possible swimmer conceptualized in [1]. The literature has extensively analyzed the problem of plananr locomotion of the Purcell’s swimmer [2], [3], [4], [5]. [6] analyzes its locomotion problem in geometric framework, again for the planar case. The condition of being at low Reynold’s number and slenderness of the links in mechanism leads us to a purely kinematic form of equations. Literature does not indicate any conditions of low Reynold’s number theory for slender bodies which entail restriction to only planar locomotion. We extend the work to a more general, more challenging and more interesting generic 3 dimensional locomotion problem.