Molecular machines play pivotal roles in all biological processes. Most structural methods, however, are unable to directly probe molecular motions. Here, we demonstrate that dedicated NMR experiments can provide quantitative insights into functionally important dynamic regions in very large asymmetric protein complexes. We establish this for the 410 kDa eukaryotic RNA exosome complex that contains ten distinct protein chains. Methyl-group and fluorine NMR experiments reveal site-specific interactions among subunits and with an RNA substrate. Furthermore, we extract quantitative insights into conformational changes within the complex in response to substrate and subunit binding for regions that are invisible in static cryo-EM and crystal structures. In particular, we identify a flexible plug region that can block an aberrant route for RNA towards the active site. Based on molecular dynamics simulations and NMR data, we provide a model that shows how the flexible plug is structured in the open and closed conformations. Our work thus demonstrates that a combination of state-of-the-art structural biology methods can provide quantitative insights into large molecular machines that go significantly beyond the well-resolved and static images of biomolecular complexes, thereby adding the time domain to structural biology.