The flexible coupling for driving a gyroscope is machined from a solid disc. Four holes of triangular cross-section with curved sides and rounded corners are cut through the disc. A curved slot (52) extending through an arc of 200 deg. is cut in each end surface. The slots are diametrically opposite and their depth is slightly greater than half the disc thickness. A circumferential slot in the plane of the disc is then cut which runs into the curved slot so that the disc is almost separated into two similar discs being connected only by the thin wall of metal (46) and the flexible strips (26, 28). A further machining operation reduces the width of the strips and separates them with a central slot in the plane of the disc.