  This work studies the motion of Purcell's three-link microswimmer in viscous
flow, by using perturbation expansion of its dynamics under small-amplitude
strokes. Leading-order expressions and next-order correction terms for the
displacement of the swimmer are obtained for the cases of a square or circular
gait in the plane of joint angles. The correction terms demonstrate the
reversal in movement direction for large stroke amplitudes, which has
previously only been shown numerically. In addition, asymptotic expressions for
Lighthill's energetic efficiency are obtained for both gaits. These
approximations enable calculating optimal stroke amplitudes and swimmer's
geometry (i.e. ratio of links' lengths) for maximizing either the displacement
or Lighthill's efficiency.
