The invention provides an expanding and collapsing apparatus and methods of use. The apparatus comprises a plurality of elements (52) assembled together to form a ring structure (54) around a longitudinal axis. The ring structure is operable to be moved between an expanded condition and a collapsed condition by movement of the plurality of elements. At least one set of structural elements (56) each having a first end and a second end are operable to move between the expanded condition and the collapsed condition by movement of the first end in an axial direction, and by movement of the second end in a radial dimension. At least one set of elements is operable to be moved by sliding with respect to one another in a direction tangential to a circle concentric with the ring structure. In another aspect, the plurality of elements (82) comprises at least one set of structural elements (86) extending longitudinally on the apparatus and operable to slide with respect to one another, wherein the sliding movement in a selected plane perpendicular to the longitudinal axis is tangential to a circle in the selected plane and concentric with the longitudinal axis. Applications of the invention include oilfield devices, including anti-extrusion rings, plugs, packers, locks, patching tools, connection systems, and variable diameter tools run in a wellbore.