  A model of three-disk micromachine swimming in a quasi two-dimensional
supported membrane is proposed. We calculate the average swimming velocity as a
function of the disk size and the arm length. Due to the presence of the
hydrodynamic screening length in the quasi two-dimensional fluid, the geometric
factor appearing in the average velocity exhibits three different asymptotic
behaviors depending on the microswimmer size and the hydrodynamic screening
length. This is in sharp contrast with a microswimmer in a three-dimensional
bulk fluid that shows only a single scaling behavior. We also find that the
maximum velocity is obtained when the disks are equal-sized, whereas it is
minimized when the average arm lengths are identical. The intrinsic drag of the
disks on the substrate does not alter the scaling behaviors of the geometric
factor.
