According to a precision assembly technique, a first subassembly is precisely aligned relative to a plurality of alignment features in an alignment fixture and at least three non-coplanar flexures having complementary alignment features are located with respect to corresponding alignment features on the alignment fixture and mechanically attached to the first subassembly. The first subassembly with the attached flexure sheets is removed from the alignment fixture and located with respect to a second subassembly having a plurality of alignment features identical to the alignment features in the alignment fixture using the alignment features on the second subassembly and the complementary alignment features on the flexure sheets to precisely align the first subassembly with the complementary alignment features on the second subassembly. The flexure sheets are then mechanically attached to the second subassembly, whereby the first and second subassemblies are aligned and rigidly connected to one another.