text: In his original paper, Purcell proposed a simple example of non-reciprocal body deformation, now commonly known as the Purcell swimmer. This simple swimmer possess two degrees of freedom for motion: a two-hinged body composed of three rigid links rotating out-of-phase with each other. However, any body with more than one degree of freedom of motion can achieve locomotion as well.
  In general, microscopic organisms like bacteria have evolved different mechanisms to perform non-reciprocal motion:
  *Use of a flagellum, which rotates, pushing the medium backwards — and the cell forwards — in much the same way that a ship's screw moves a ship. This is how some bacteria move; the flagellum is attached at one end to a complex rotating motor held rigidly in the bacterial cell surface.
  *Use of a flexible arm: this could be done in many different ways. For example, mammalian sperm have a flagellum which, whip-like, wriggles at the end of the cell, pushing the cell forward. Cilia are quite similar structures to mammalian flagella; they can advance a cell like paramecium by a complex motion not dissimilar to breast stroke.
  Geometrically, the rotating flagellum is a one-dimensional swimmer, and it works because its motion is going around a circle-shaped configuration space, and a circle is not a reciprocating motion. The flexible arm is a multi-dimensional swimmer, and it works because its motion is going around a circle in a square-shaped configuration space. Notice that the first kind of motion has nontrivial homotopy, but the second kind has trivial homotopy.