Abbe principle is also called the wiring principle, the principle of series, is an important principle in length measurement. It's usually definited as :"If you want to make the correct measurement results for the measuring instrument, you must install the instrument gauge on the material's centerline of the extension cord.” Errors caused by violation of Abbe principle named Abbe error. Error caused when it's agree with Abbe principle named the secondary error. This error can be ignored when it occurred in the situation that the angle between gauge rod and the centerline of the measurement is very small. Error caused when it's disagree with Abbe principle named the first error. This error must be taken into account.
The most typical instruments which are according to the abbe principle are abbe length comparator, vertical optical gauge, length measuring instrument, etc.
Therefore, the influence of the tilt Angle that resulted from the not straight guide rail will create quadratic error. So the requirements of the guide rail straightness can reduce in the device, this also can help to reduce the instrument manufacturing cost. But the shortcoming is this kind of train arrangement will increase instruments’length and size, and temperature influence on deformation becomes bigger. Thus, in some situations, we have to violate the Abbe principle, and adopt the parallel arrangement. For example, during the vernier caliper measurement artifacts, the universal tool microscope longitudinal measurement ,ect, in order to reduce producing measurement error (first-order error), on the one hand, we need to improve the machining precision of the lead rail, on the other hand, should shorten the distance between gauge and materials to be measured.
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