A new measuring system is proposed that can measure the motions of arbitrary rigid bodies moving in 6-degrees-of-freedom. The measurement principle is based on the detection of laser beams reflected from a specially fabricated mirror that looks like a triangular pyramid having an equilateral cross-sectional shape. The mirror has three lateral reflective surfaces inclined 45° to its bottom surface. This mirror is referred to as 3-facet mirror. The 3-facet mirror is mounted on the object whose position and orientation are to be measured. It reflects a laser beam, generated from a source, in three different directions, depending on the motion of the object of interest. The reflected beam is then detected by three position-sensitive detectors (PSDs). From the signals of the PSDs, the 3-dimensional position and orientation of the mirror can be calculated, thus enabling us to determine the 3-D position and orientation of the object.
The measurement is operated by a laser-based optical system composed of a 3-facet mirror, a He-Ne laser source, three position-sensitive detectors (PSD). In the sensor system, three PSDs are located at three corner points of a triangular formation, which is an equilateral triangular formation lying parallel to the reference plane. The sensitive areas of three PSDs are oriented toward the center point of the triangular formation. The object whose 6-DOF motion is to be measured is situated at the center with the 3-facet mirror on its top surface. A laser beam is vertically incident on the top of the 3-facet mirror. The laser beam is reflected at the 3-facet mirror and splits into three sub-beams, each of which is reflected from the three facets and finally arrives at three PSDs, respectively. Since each PSD is a 2-dimensional sensor, the information on the 6-DOF motions of the 3-facet mirror can be obtained.
A mathematical model is constructed to relate the 3-D position and orientation of the object with the outputs of three PSDs. The model is based on geometric optics, in which a laser beam is regarded as a simple straight line or a set of straight lines, and diffraction effect is neglected. The model is proved to determine the unique 3-D position and orientation of the mirror from the PSD signals. And it can also estimate even the 2-dimensional position of the laser beam while it is not given. From this fact, the model provides a couple of different approaches depending on whether the position of the laser beam is fixed known or variable unknown. In this dissertation, both of the approaches are investigated.
The method that fixes the position of the laser beam can measure high-speed motions, but its measurement range is limited within the small area illuminated by the laser beam having fixed position. Thus, it is suitable to vibrational motions.
The method that regards the laser beam position as variable unknown can extend the measurement over the size of the laser beam, while the laser beam should track the 3-facet mirror. A tracking method, utilizing the light powers incident on the PSDs, that helps the laser beam keep track of the 3-facet mirror without additional sensors is proposed. Through this tracking method, the larger motions of 3-facet mirror can be obtained, but it might have some measurement speed limitation due to the tracking task.
An application study that measures the motions of a HDD slider flying on the magnetic disk has been performed. To measure the dynamic motions of the slider transferring between the data tracks the laser beam has been swung by an additional mechanism that is synchronized with the swing arm of the HDD.
A series of experiments have been performed to demonstrate the effectiveness and accuracy of the proposed method. The experimental results show that the proposed sensing system can be an effective means of obtaining 3-dimensional position and orientation of arbitrary objects. The resolution of the experimental system is found to be approximately two micrometers in translation and five micro-radians in rotation. By virtue of the easiness in application, the measurement principle can be applied to a wide range of applications such as 3-D motion of manipulators, machining tools, sliders flying on magnetic disks of HDDs, positioning stages, etc.
