6 A Mathematical Model for Determining the Pose of a SLDV 65 Fig. 6.7 (a) Internal mirrors configuration of the Polytec PSV-500 system, and (b) the corresponding mathematical model of the structure, and one additional reference point is selected on each raised block. A frame can be formed by the six reference points (Fig. 6.8b). In order to evaluate the reliability of the proposed methodology, two different sets of reference points are selected to calculate rotation matrices at the three locations. The reference points on the main surface are the same in the two sets and different reference points on the raised blocks are selected (Fig. 6.8b). Rotation angles of two mirrors (obtained by the corresponding input voltages and sensitivity of the scanner) and initial distances corresponding to different reference points are listed in Table 6.1. With the procedure in Sect. 6.4, Rand t are obtained at the three locations, as listed in Tables 6.2 and 6.3, respectively. Table 6.2 shows that the rotation matrices calculated from two different sets of reference points are almost the same at the three locations, which indicates that the proposed methodology is reliable. Note that the SLDVs at location 2 and location 3 have large angles with the normal direction of the scanned structure, which indicates that the methodology can be used to calculate any orientation of a SLDV. Translation vectors calculated from Set 1 and Set 2 in Table 6.3 slightly differ since t is calculated from mean values of coordinates, as shown in Eq. (6.10). Different sets of reference points have different mean values, which causes slight differences of t. In order to evaluate the accuracy of the rotation matrices and translation vectors, twenty scan points with known coordinates in the SCS are selected and their corresponding input voltages are measured. One also can calculate the rotation angles by the following equations based on the mathematical model in Fig. 6.7b: p0 DRT .p t/ (6.27) ˛ D 1 2 tan 1 z0 x0 ; ˇ D 1 2 tan 1 y0 x0 cos.2˛/ d! ; r D x0 cos.2˛/cos.2ˇ/ (6.28)
RkJQdWJsaXNoZXIy MTMzNzEzMQ==