Description
The purpose of the research was the development of a method and an apparatus for the measurement of straightness, that have the following advantages:
 the initial reference line is ideal, without discrepancy, and it is determined through calculus;
 no adjustments are needed in order to position the metering device on the slide;
 the straightline of the slide can be quickly and easily measured even if it has a horizontal, vertical or oblique position;
 increasing the measuring precision by removing the influences of the errors introduced by the depreciation of the sensors;
 increasing the measuring precision by removing the influences of the position errors of the device;
 it is permitted the increase of the mobility of the device and implicit to increase the measurement efficiency
SOLUTION
In order to apply this method one has to use three detecting elements assembled in the measure equipment with a distance d between each other. The support feelers P1 and P2 are assembled in the measure equipment as in figure 2.
The theoretical reference line is presented by the straightline that passes through the points A0 and B0 of the two detecting elements T1 and T2. When adjusting to zero, the detecting element T3 depends on this line. The points M0 and N0 of the support feelers are also on this line.
The measuring of the straightline is done by the movement of the measure equipment along the slide on distances d. At every positioning the measure equipment leans upon the surface that is to be measured in points Mi and Ni, that differ from the points Ai, Bi, Ci… in which the measurement is done, as in figure 3. The reference line has, in this case, a different position from the line that passes through the points Mi, Ni of the support feelers. The xi, yi, zi indications of the three detecting elements must be read. There values are used for determining through calculations the deviation from liner.
The next steps must be followed for each position i of the device:

 the distances xi, yi, zi, between the points A0, B0, C0 and the points Ai, Bi, Ci, are measured according to the indications given by the three measuring head (fig. 6); the points A0, B0, C0 are collinear and they determine the line m of initial adjustment of the measuring heads, rotated with an anglei in relation with the reference line formed by the extension of the segment AiBi, according to the position of the device; Ai, Bi, Ci represent the extremes of two consecutive segments, from those n equal segments in witch the length of the profile one has to measure has been divided and they are specific to one position i of the device;
 the angle i is determined (i has very small values, for which sin i= tg i=i):
 the distance zi* between the point Ci on the profile that one wants to measure and the line m* obtained by shifting the line d in the point Bi:
 the distance hi between the point Ci on the measured profile and the reference line formed by the extension of the segment AiBi,:
 it is calculated, for each positioning, the angle 1 formed by the straightline that passes through the points Ai, Bi and the straightline that passes through the points Bi, Ci (figure 7):
 it is calculated, for each positioning, the angle *1 between the straightline that passes through the points Bi, Ci and the initial reference line that passes through the first point Ai, Bi of the profile:
 it is calculated, for each positioning, the distance h*i between each measured point and the first initial reference line:
 it is calculated the distance between each measured point and the straightline that passes through the beginning and the ending points of the profile that is to be measured (fig. 8):
 where the value of the angle is determined by using the formula:
 the deviation from the liner is also calculated