The problem of determining displacements of objects is an important and current issue, in particular in terms of operational safety. This is a requirement that covers geodetic, periodic control measurements in order to determine horizontal and vertical displacements. The paper is focused on the analysis of vertical displacements. Geodetic measurements and their interpretation allow to reduce the risk of possible structural catastrophes. The major research topic of the majority of available papers is displacement determination of individual controlled points, in a situation where there are identified as fixed reference points. There are cases making identification of such points difficult or impossible to use in displacement analysis. This paper addresses a rare case of determining vertical displacements in unstable reference systems. Due to the fact that most of the existing and known literature methods do not always bring satisfactory results, the paper propose a new method of vertical displacement determination in the absence of reference points in the local coordinate system. Practical considerations on simulated data show that the presented method performs the task correctly.

The paper presents an off-line application that determines the maximum accuracy of the reference points for the given dynamics parameters of a CNC machine. These parameters are maximum speed, acceleration, and JERK. The JERK parameter determines the rate of change of acceleration. These parameters are defined for each working axis of the machine. The main achievement of the algorithm proposed in the article is the determination of the smallest error specified for each reference point resulting from the implemented G-code for the considered dynamic parameters of the CNC machine. The solutions to this problem in industry consider the improvement in the accuracy of hitting the reference points, but they do not provide information on whether the obtained solution is optimal for such parameters of the machine dynamics. The algorithm makes the accuracy dependent on the adopted dynamic parameters of the machine and the parameters of the PLC controller used in the CNC machine.