Enhanced mechanical designs are provided for weak-link rotary mechanisms for implementing angular rotations with a defined angular travel range and positioning resolution, for example, with ten-degree-level travel range and ten-nanoradian-level positioning resolution. A weak-link rotary structure has a predetermined pattern for implementing angular rotations with repeatable and reliable angular travel range and positioning resolution including a plurality of connecting links radially extending from a central portion with a predefined angular separation between the connecting links; each said connecting link having at least one pair of weak-link connections; alternate connecting links being coupled to a respective terminal, each said respective terminal being mounted to a connecting carriage; remaining other connecting links being coupled to a respective mounting portion of a mating part of the weak-link rotary structure.