DNA sequencing through a nanopore is a great challenge in the field of biotechnology. Recent experiments on voltage-driven DNA and RNA translocations through a nanopore indicate that the size and geometry of the pore are important factors in polymer dynamics. A molecular dynamic approach is presented here which explicitly takes into account the effects of the size of the nanopore. It is shown that the diameter of the pore is crucial for DNA translocation. Motivated by the experiment in which a DNA strand is threaded through a cyclodextrin ring by applying external force to differentiate the purine from pyrimidine, we studied the hydrodynamic properties of single-stranded DNA in free solution by molecular dynamics simulations and calculated the friction and diffusion coefficients of single stranded DNA threaded through a cyclodextrin ring. Three different pore sizes are used for DNA translocation to see the effects of the pore size and the geometry on friction and diffusion of the DNA molecule when it translates through a nanopore.