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Research Express@NCKU - Articles DigestResearch Express@NCKU Volume 6 Issue 2 - October 17, 2008[ http://research.ncku.edu.tw/re/articles/e/20081017/2.html ]An optoelectronic measurement system formeasuring 6-DOF vibration motionCJ Chen (Chen, Chun-Jen) 1 ,PD Lin (Lin, Psang Dain) 1,* , WY Jywe(Jywe, Wen-Yuh) 21 Department of Mechanical Engineering, National Cheng Kung University2 Department of Automation Engineering, National Huwei University of Science and Technologypdlin@mail.ncku.edu.twOptics Express, Vol.15, no. 22, pp. 14601-14617, 2007.This paper has presented and verified a 6-DOF optoelectronicmotion measurement system [1] constructed from 3 laser-diode/PSDpairs and a pyramid-polygon-mirror. The skew-ray tracing was usedto model the system and determine the system equations forexpressing the 6-DOF motion. To improve computational speed forthis proof-of-concept paper, we employed a first-order Taylor seriesexpansion to obtain a linear form of the system equations. Theproposed system was validated using a laboratory-built prototype toperform calibration and stability experiments. Calculations showedposition and angular motion measurement ranges of ±3.5mm and±2.5, respectively. Stability testing for 5 minutes of continuous operation showed position and angularmeasurement variance in the range of ±1 μmand ±1.5 arc sec, respectively.Fig. 1: Schematic diagram of a 6-DOF motion measurement system with a 3-sided pyramid-polygonmirror.1 of 5
Research Express@NCKU - Articles DigestFig. 2: Photograph of lab-built 6-DOF motion measurement system.A rigid body in 3D space may have three angular motionsand three translationalmotions. To measure all of these six motions simultaneously and accurately is achallenging task. Presently available PSDs are planar devices which output 2 readings capable ofmeasuring at most 2 DOF. Consequently, some arrangement of multiple sensors, lasers and mirrors isrequired to detect 6-DOF motions. Literature is meager for literature related to 6-DOF rotary systemmeasurement but includes 5-DOF motion error measurement of translational parts [2], 4-DOF motionmeasurement of an indexing (rotary) table [3] and 6-DOF measurement of vibration [4].The optoelectronic hardware of the proposed system employs 3 laser diodes and 3 2-axis PSDs and apyramid-polygon-mirror of three sides (see Fig. 1). The 3 laser diodes and 3 2-axis PSDs (UDT SC-10D,active area 100mm 2 ) are arranged evenly around the circumference of the pyramid-polygon-mirrorwhich is mounted rigidly and centered axially on the vibrating object to be measured. The light rays fromthe laser diodes (λ=635nm, 5mW) are projected onto the respective mirrors, then reflected to anddetected by the respective PSDs. Each PSD outputs the position of the incident light beam on the surfaceof the PSD along the axis in question. These relations can be expressed by Snell’s Law such that the unitdirectional vectors of a reflected laser ray depends on the unit normal vector of the mirrors.Consequently, the 6-DOF motions, and , of a vibrating object can bemeasured by the following equations:Figure 2 shows the lab-built prototype system with d=70mm. The outer mirrored surfaces of acommercial corner cube are used as a pyramid-polygon-mirror. Because no system can be fabricatedwithout manufacturing errors, each of the lasers and PSDs and the holder of the pyramid-polygon-2 of 5
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