Calculation of the moving mechanism on a trajectory described by a planar differentiable curve is challenging. The difficulty arises in compliance with high-precision movement. The new method of calculation based on the intrinsic properties of the plane is proposed. The method is based on mathematical linguistics and relational algebra. First, these disciplines are applied to analyze the intrinsic properties of the Euclidean plane. Calculation of classic and new methods for moving point for the flat rod is shown for comparison. Analytical formulas for Jordan curves can be obtained in some cases. The experiments in the areas of geometric modeling and control of a robot are listed briefly. The analytic solution was obtained by nontraditional methods not only for centrally symmetric conic sections but also for Jordan curves.

This article is focused on the search for potential collision of a moving object (as a mobile robot is) with the environment. Application of the proposed and presented method requires existence of the three-dimensional model of the environmental space. In this case, the models are generated automatically with the help of mobile measurement platform developed by authors and are available to other applications. Models of moving objects are loaded by the proposed application from external files. The method is based on data fusion, using data from a laser scanner, global positioning system, and inertial navigation system; however, it can also be used for data obtained by other ways. Its correctness was experimentally proved by several experimental tests. Output is in the form of calculated coordinates of the point in which a moving object would potentially collide with the environment if no avoiding action is taken. Such an object may represent an oversized load transferred by a truck, train, ship, the transport means itself or even a person.

This paper evaluates the results of research aimed at changing the rolling speed and the effect of foreign particles in the steel strip, as well as the forces in the rolling process. It also compares the correlation of lab results, theoretical expectations and real-life observations. It supplements the already existing practices aimed at strip-break elimination that were developed and implemented worldwide. Records from a five-stand tandem mill were used for the data analysis. The historical databases developed based on incidents (strip breaks) since 2013 were used; the detailed position of each strip break was documented, along with defects found at the portions of steel strips that broke or the information that no defect was found. The paper contains an evaluation of metallographic analyses of the samples of the strip breaks.

This paper describes attributes of newly designed variant approach of computer support system of technological preparation of production. Knowledge system for automation of production of technological documentation was developed for technology of surface processing of metal. The paper describes the design of coding system for sorting mechanical parts into groups with similar mechanical parts, either by their shape, dimensions or used technology. Subsequently, it points out to attribute of the system – uploading and modification of sample technological documentation.

In addition to other things, a robot’s design also determines its singularity configurations and points in the workspace. In designing the robot’s working trajectory, one of the main issues of robot steering is avoiding singularities. The article proposes a different approach to calculating the inverse task, which lies in the random mapping of the robot mechanism’s workspace through searching for points closest in proximity to the trajectory in question. The new methodology of mapping and detecting the states of singularity in the workspace is actually based on Monte Carlo analysis, since we were also interested in the number of occurrences. In terms of mathematical analysis, this method is less demanding, because in searching for joint variables suitable for the given trajectory, it does not use inverse calculation. It is important that the method is chosen appropriately. The method is sufficiently illustrative in the form of a graph, making, e.g., programming optimization simpler. The ultimate effect is the reduced time needed for computing joint variables and the availability of an option to select a robot configuration suitable for carrying out the required work. The paper offers an example of an analysis concerning three different robots.