Disconnection motion along (10
12) and (11
21) twins in Zr is investigated using atomic-scale simulation. In particular, the high mobility of glissile disconnections is studied in terms of the atomic shears and shuffles involved. Using a quasi-static simulation procedure, the displacements of individual atoms are followed as they transit from matrix sites, through interfacial sites, and hence to twin sites by repeated passages of disconnections along the interface. It is found that the overall displacements for the cases studied are those predicted by the Bilby and Crocker (1965) theory which invokes homogeneous shear deformation. However, the present work enables atomic tracks to be followed through the cores of moving disconnections. The combinations of shears and shuffles in the two twinning systems are found to be quite distinct. In addition to tracking their coordinates, the variation of hydrostatic pressure experienced by the atoms is also quantified.