Due to the current focus on understanding conformation-dependent biochemical processes such as transcription and translation, we utilize polymer modeling techniques to study the conformational changes of nucleic acids. In order to model the dynamics occurring at the mesoscopic time scales in an efficient manner, we need to reduce the degrees of freedom. We do this through coarse graining and by constraining the polymer motions to a lattice. In this model, the nucleosides are the monomers and the phosphodiester bonds between the nucleosides are the links. In this manner, fundamental interactions such as stacking and hydrogen bond formation can still be incorporated. The second important physical aspect of our model is the lattice structure. Our lattice is a face-centered cubic lattice which provides a larger number of possible configurations for a polymer than a cubic lattice, making it more similar to the continuous real space. Now that the coarse-grained biopolymer is situated in a three-dimensional lattice, it must be able to move in a physically intuitive way to provide insight into biochemical processes and to fully traverse the conformational space. Many algorithms have been proposed to implement the motions of the polymer in the lattice, yet many of these still result in trapping. Here we systematically analyze the properties of these algorithms, such as ergodicity, and compare their performance to a recently proposed generalized algorithm for polymer dynamics in order to make improvements to the generalized case.