Two different analytical methods, the first-order paraxial approximation method and the nonparaxial ray tracing method, are applied to determine the steering mechanism of the Risley prism system, including the pointing prediction and the complete and exact inverse orientation solutions. The analytical results obtained with the two different methods are investigated in detail about the pointing prediction and the two groups of inverse orientation solutions, respectively. Risley prism equipment for wide angular range beam scanning is assembled and the experimental setup is built to test the steering mechanism of the Risley prism system. Experimental results validate the availability of the nonparaxial ray tracing method to discuss the beam steering mechanism for the Risley prism system.

Based on the vector form Snell’s law, ray tracing is performed to quantify the pointing errors of Risley-prism-based beam steering systems, induced by component errors, prism orientation errors, and assembly errors. Case examples are given to elucidate the pointing error distributions in the field of regard and evaluate the allowances of the error sources for a given pointing accuracy. It is found that the assembly errors of the second prism will result in more remarkable pointing errors in contrast with the first one. The pointing errors induced by prism tilt depend on the tilt direction. The allowances of bearing tilt and prism tilt are almost identical if the same pointing accuracy is planned. All conclusions can provide a theoretical foundation for practical works.

Micro-stepping motion of ultrasonic motors satisfies biomedical applications, such as cell operation and nuclear magnetic resonance, which require a precise compact-structure non-magnetization positioning device. When the pulse number is relatively small, the stopping characteristics have a non-negligible effect on the entire stepwise process. However, few studies have been conducted to show the rule of the open-loop stepwise motion, especially the shutdown stage. In this study, the modal differences of the shutdown stage are found connected with amplitude and velocity at the turn-off instant. Changes of the length in the contact area and driving zone as well as the input currents, vibration states, output torque, and axial pressure are derived by a simulation model to further explore the rules. The speed curves and vibration results in functions of different pulse numbers are compared, and the stepwise motion can be described by a two-stage two-order transfer function. A test workbench based on the Field Programmable Gate Array is built for acquiring the speed, currents, and feedback voltages of the startup-shutdown stage accurately with the help of its excellent synchronization performances. Therefore, stator vibration, rotor velocity, and terminal displacements under different pulse numbers can be compared. Moreover, the two-stage two-order model is identified on the stepwise speed curves, and the fitness over 85% between the simulation and test verifies the model availability. Finally, with the optimization of the pulse number, the motor achieves 3.3 µrad in clockwise and counterclockwise direction.

Precise cable drive has been developed as an alternative transmission element to gears, belts and pulleys, chains and sprockets in electro-optical tracking system. The analytical method is developed to predict the transmission backlash of precise cable drive to enable designers to better assess the precision performance in the design study phase. Slip angle of precise cable drive is studied, and the effect of the rotational velocity and inertia of cable on the force equilibrium of contact region is considered. The deformation of cable in slip region and free region is calculated respectively and theoretical formulation of transmission backlash for precise cable drive system is carried out. Parametric sensitivity is investigated to evaluate the relationship between the transmission backlash and precise cable drive parameters including preload tension, load tension, friction coefficient, center distance and output drum radius. Experimental setup is built and the transmission backlash is tested. Effect of preload tension on the transmission backlash is tested. Results show that the experimental value and the theoretical curve of the transmission backlash fit well, which validates the theoretical method developed in this article.

With the advantages of high resolution, structural simplicity, reliability, compact size, and high sensitivity, inductive sensors have been widely used in nanopositioning systems. However, the measuring range of traditional inductive sensors are usually limited to 0.2 mm. A novel analysis and design methodology of the miniaturized inductive sensor with large measuring range and nanoscale resolution is proposed. Firstly, an accurate leakage inductance model is established. Secondly, a design rule of armature size is proposed by considering the fringing effect. Then, the error terms introduced by the measurement circuit of differential inductive sensors are analyzed and the corresponding error suppression methods are illustrated. Moreover, A design rule of selecting the optimal excitation frequency is proposed to meet the requirements of high Q value and high bandwidth, and to minimize the impact of core loss resistance on the performance of the sensor. Validated by the experiments, the proposed analysis and design method can effectively guide the design of the miniaturized inductive sensor with nanoscale resolution in the measuring range of ±0.5 mm. The overall size of the fabricated sensor prototypes is less than 6 mm × 6 mm × 3 mm. Combined with large range, high resolution and ideal miniaturization, this inductive sensor can be well suitable for compact and large stroke nanopositioning systems.