��hmax= s/600.The crane rail is measured using a classical polar surveying method for detail points. Characteristic points are determined indirectly by measuring the position of the ��L�� platform. According to the selleck chem Dovitinib required precision and the principles of the method, the proposed approach may be used if two conditions are met:A total station providing adequate basic measurement precision of at least 1 mm must be used.A target point can be unambiguously signalized in a way that ensures sub millimeter accuracy of centering.The homogeneity of the measurement precision is maintained by measuring all points from a single instrument station. The instrument must be set in a stable position which enables the visibility of all desired detail points of the rail.2.1.
InstrumentAccording to the required measurement precision derived from standard [1] we define the requirements that the instrument should meet. Given the dimensions of the crane rail, the required accuracy of the point determination can be computed.Cartesian coordinates of a single detail point are calculated from the measured polar coordinates (s��horizontal direction, z��zenith angle. d��slope distance):[xyz]=[sins?sinz?dcoss?sinz?dcosz?d].(1)Using error propagation law, the precision of coordinate determination can be calculated according to the measurements precisions:��xyz=J?��szd?JT.(2)Matrix J represents Jacobian and contains derivatives of Equations (1) with respect to each measurement. If J is an invertible matrix, the procedure can be inverted.
Therefore, the required measurement precisions can be determined according to the desired coordinates precisions:��szd=J?1?��xyz?(JT)?1.(3)We are mainly interested in differences between coordinates. The rail span is the difference between the x coordinates and the elevation difference equals to the z coordinate differences (see Section 3.2) of two points, point 1 and point 2. Coordinate differences Brefeldin_A between two points of each profile can be written as:[��x��y��z]=[x2y2z2]?[x1y1z1]=[sins2?sinz2?d2?sins1?sinz1?d1coss2?sinz2?d2?coss1?sinz1?d1cosz2?d2?cosz1?d1].(4)When meantime we try to use the inversed error propagation law in Equations (4), we face a problem. The Jacobian is neither square nor an invertible matrix. System (4) is therefore expanded with three additional equations for the averages of all three coordinates. Equations complement the system in a way that all the equations are independent and J becomes invertible again.According to the desired coordinate difference precisions, we calculate the required precisions of measurements. They are represented in Table 1.Table 1.Calculation of the required measurement precisions for the cases of two profiles (in the beginning and at the end of rail).