The mechanical assembly dimensional measurements with the ...

J. Rejc et al. / Expert Systems with Applications 38 (2011) 10665–10675 10669StartProtectorProtectorImageacquisition19B 14F42Imagesatisfactory?E110 D68117E352EA 13E3124EE5Fig. 7. Search areas and measured dimensions.6E A ¼ 1; x; x 2 ; ...; x n ; ð2ÞE7h i 1p ¼ A T A A T y; ð3Þ^y ¼ p 0 þ p 1 x þ p 2 x 2 þþp n x n :ð4Þ8101214EEEdimension AE9E11E13EThe same sequence is repeated in the case of the bimetal edge,marked with number 2. Searching procedure is in the extremeupper right area of the image in the rectangle whose position isalso predefined by the user. In this area another user predefinedrectangle is present and used for finding the upper edge of the limitelement, marked with the number 3. The next event mathematicallydescribes both, the edge of the bimetal and the upper edgeof the limit element (numbers 2 and 3). With this information adistance between these two lines is calculated, on the Fig. 7marked with a letter F and on the Fig. 6 with a step number 4.The calculation of the distance F is needed to recognize possibledeviations that suggest poorly configured protectors. In this caseno further analysis is required and the program terminates.All the required distances are calculated by defining the intersectionpoints between mathematically approximated lines andthen by Eq. (5) the distances between these points are calculated:EqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidðA; BÞ ¼ ðx 2 x 1 Þ 2 þ ðy 2 y 1 Þ 2 ; ð5ÞEndEFig. 6. Software flow diagram.checks if all left area in the square is black. If not, an error is returnedand the measurement procedure is stopped. Determinationof the left vertical edge proceeds by finding the edge on the binaryimage. Then the method of the least squares (Eqs. (2) and (3)) isused, through the stored coordinates of the edge points. The polynomialof 1st order that is equal to the linear line is approximatedthrough the binary edge points (Eq. (4)). This method is used for alledge approximations, both for linear and higher order polynomialapproximations. The procedure filters the edges, which is importantdue to small dust particles that can appear on edges. Whenusing mathematical equations also the distance calculations aremore accurate. In the case that error occurs during the mathematicaledge approximation, the program informs the user and procedureis terminated. On the diagram such an event is marked withthe letter E.In Fig. 6 number 5 shows a step in which the lower edge of thelimit element is found and mathematically approximated by thelinear line. This procedure is performed on the right side of the image,still within the specified rectangle. By setting this line, the limitelement thickness is calculated, marked with the letter E andnumber 7 in Fig. 7. The tests showed that measurements of dimensionE are not as accurate as we wanted, as a consequence of thelimit element material reflectivity. This reason can cause the thicknessof the limit element to be too small, up to 0.02 mm comparingto the manufactured dimension. The limit element material ismanufactured by the EN ISO 9445: 2006 (International StandardISO, 2006) standard, class P. This standard defines limit elementthickness of 0.200 ± 0.008 mm. Due to the standard’s very narrowtolerances, in the further calculations a value of 0.20 mm is used.In the next step, based on the defined edges, the left edge or ahook of the limit element is defined. In the utmost point of thehook the vertical line from step 1 is applied again. This line ismarked with the number 6. In the middle of these two parallellines, the perpendicular distance D is calculated, on Figs. 6 and 7marked with line number 10. In the design drawings for protector