Fine manipulation systems generating six-degree-of-freedom motion can increase efficiency of operations and execute complex tasks with dexterity. Such devices require precision six-degree-of-freedom sensor systems to measure and control the required motion with high accuracy. Six-degree-of-freedom sensor systems can also provide complete information in motion and vibration analyses. So, they are applicable in many fields: precision machine control, precision assembly, vibration analysis, and so on.
This thesis presents a new six-degree-of-freedom displacement measurement system utilizing typical features of a diffraction grating. It has a simple structure, which consists of one source and one reflective target, since it can use several diffracted rays generating from a diffraction grating target. Through semi-conductor fabrication or replication process, miniaturized grating targets can be manufactured easily, and applied to milli-structures.
It is composed of a laser source, a diffraction grating target, three convex lenses, and three two-dimensional detectors which sense the movement of three diffracted rays, +1, 0, -1 order diffracted rays. When a miniaturized diffraction grating, which acts as a small reflective target, moves inside an incident ray that has a larger diameter than this grating, this movement changes the generating position and propagating directions of diffracted rays. This results in the variation of detecting positions of diffracted rays and the information on six-degree-of-freedom displacement can be obtained from the coordinates of diffracted rays.
The six-degree-of-freedom displacement of an object is calculated kinematically from the coordinates of the diffracted rays on the detectors. The calculation process consists of two steps: a forward and an inverse problem solving step. In the forward step, the coordinates of the diffracted rays on the detectors are estimated. In the inverse step, an actual six-degree-of-freedom displacement is determined from the coordinates of the diffracted rays. The solutions of the forward problem, which are the coordinates on the detectors, are calculated with the grating equation and ray optics assumption. Since they are obtained as six nonlinear equations, the inverse problem is solved through a numerical iterative method, Newton’s method.
In this measurement system, a quadrant photodiode detects the two-dimensional movement of the diffracted ray. Two axial outputs of the quadrant photodiode are the difference signals calculated from the voltage outputs proportional to the intensity of an incident ray on each photodiode cell, and so affected by the intensity distribution and power of the incident ray. Therefore, to analyze the sensitivity of the six-degree-of-freedom measurement system, we need not only kinematic analysis that derives the relationship between the coordinates of the diffracted rays and input displacement, but also optical analysis that calculates the intensity distributions of the diffracted rays.
To analyze and design the measurement system, several design indices representing the performance of the measurement system were derived from the Jacobian matrix obtained through kinematic and optical analysis. To enhance the performance, we adopted additional optical elements and optimized the design indices. The improvement of performance was verified by evaluating resolution, accuracy and crosstalk of each design example. The optimized measurement system shows resolution of 0.1 mm for translation and 0.5 arcsec for rotation. As an application, we measured the six-degree-of-freedom motion of a bimorph-type piezoelectric actuator and obtained its frequency response function.
