There is now a certain consensus that transcription factors (TFs) reach their target sites, where they regulate gene transcription, via a mechanism dubbed facilitated diffusion (FD). In FD, the TF cycles between events of 3D diffusion in solution (jumps), 1D diffusion along DNA (sliding), and small jumps (hopping), achieving association rates higher than for 3D diffusion alone. We investigate the FD phenomenology through molecular dynamics simulations in the framework of coarse-grained modeling. We show that, despite the crude approximations, the model generates, upon varying the equilibrium distance of the DNA-TF interaction, a phenomenology matching a number of experimental and numerical results obtained with more refined models. In particular, focusing on the kinematics of the process, we characterize the geometrical properties of TF trajectories during sliding. We find that sliding occurs via helical paths around the DNA helix, leading to a coupling of translation along the DNA axis with rotation around it. The 1D diffusion constant measured in simulations is found to be interwoven with the geometrical properties of sliding and we develop a simple argument that can be used to quantitatively reproduce the measured values.