A mounting apparatus for repeatable positioning of an item may include a first mount, a second mount, and a third mount. The first mount may be configured to receive a first member coupled to the item wherein the first mount may constrain the first member against movement along three mutually-orthogonal directions. The second mount may be configured to receive a second member coupled to the item and constrain the second member against movement along two of the directions. The third mount may be configured to receive a third member coupled to the item and constrain the third member against movement along one of the directions. The first, second, and third member may be at least partially-spherical and may be engaged to the respective first, second, and third mount.