An instrument wrist uses members having epicycloidal and hypocycloidal surfaces to bear loads and preserve a separation of reference points in the same manner as circles rolling on each other. The cycloidal surfaces can be uniform, stepped, or blended and can be arranged to ensure geared motion of members without addition of additional gearing structures. A hypocycloidal surface provides a concave contact that improves resistance to deformations under load. The wrist mechanism is tendon stayed, which keeps members in contact, and optionally gear structures can be integrated into the members to ensure geared motion and support roll toques.
