In this paper, we propose a scheme for measuring the focal length of a collimating optical instrument. First, a mathematical model for measuring the focal length of a collimator with double gratings is derived based on the moiré fringe formula and the principles of geometric optics. Mathematical simulation shows that a slight difference in the focal length of two collimators has an important influence on the imaging law of moiré fringes. Our solution has a good resolution ability for focal length differences within 5‰, especially in the small angle range below 4°. Thus, the focal length of collimators can be measured by the amplification of the slight difference. Further, owing to the relative reference measurement, the measurement resolution at the symmetrical position of focal length is poor. Then, in the designed experiment, a corresponding moiré image at different angles is acquired using collimators with known focal length. The experimental results indicate that the root mean square error (RMSE) of the collimator corresponding to grating angles of 2°–4° is better than 4.7‰, indicating an ideal measurement accuracy of the proposed scheme. This work demonstrates that our proposed scheme can achieve an ideal accuracy in the measurement of a symmetrical optical path.

In this study, an optimization method for the motion trajectory of attitude actuators was investigated in order to improve assembly efficiency in the automatic docking process of large components. The self-developed dual-attitude adjustment mechanism (2-PPPR) is used as the research object, and the structure is symmetrical. Based on the modified Denavit–Hartenberg (MDH) parameter description method, a kinematic model of the attitude mechanism is established, and its end trajectory is parametrically expressed using a five-order B-spline curve. Based on the constraints of the dynamics and kinematics of the dual-posture mechanism, the total posturing time, the degree of urgency of each joint, and the degree of difficulty of the mechanism’s posturing are selected as the optimization objectives. The Lévy flight and Cauchy variation algorithms are introduced into the salp swarm algorithm (SSA) to solve the parameters of the multi-objective trajectory optimization model. By combining the evaluation method of the multi-objective average optimal solution, the optimal trajectory of the dual-tuning mechanism and the motion trajectory of each joint are obtained. The simulation and experiment results show that the trajectory planning method proposed in this paper is effective and feasible and can ensure that the large-part dual-posture mechanism can complete the automatic docking task smoothly and efficiently.