Currently, there is a need in the industry for design changes to existing installations, such as conveyor lines, various machine tools, 3D printers, and so on. Designing delta robots for 3D printers reveals the advantages of using delta robots as working parts of printers compared to traditional designs. In this article, the direct and inverse problems of the kinematics of the delta robot are solved in a geometric way. Also, dependencies for the search for angular velocities and accelerations of the input links were obtained, which allows in the future to design more accurate working bodies of 3D printers. The research was carried out through mathematical modeling.

One of the traditional problems in air-traffic management is optimal safe scheduling aircraft at a point of air-routes join. However, this problem implies another one, namely, the problem of guiding the aircraft to the prescribed point of its route at the necessary instant. The latter problem is studied much less attentively. Change of the arrival instant can be provided by alternating the aircraft motion trajectory on the basis of near-airport air-routes scheme or by alternating its velocity. Such a control can be worked out as automatically by the aircraft autopilot as manually by an air-traffic controller. But it can be difficult to an air-traffic controller to construct such a control especially during rush hours in loaded airports. In this paper, the authors suggest an optimizational formalization of the problem of automatic directions generation for such a guiding. The criterion to be minimized in this formalization is the number of controller-pilot interactions, because each such an interaction is a long, difficult process liable to linguistic, technical, psychological, and other errors. Since the criterion and other processes are of discrete kind, the formalization is done in the framework of mixed integer quadratic programming. The obtained problems are solved numerically by means of MIQP-solver provided by the Gurobi library. Each subproblem is solved quite fast within 0.1-0.5 seconds. So, solution of the entire problem (which includes enumeration of trajectories and choice of the optimal velocity regime for each of them) takes one-two seconds. Thus, the problem for the entire group of aircraft can be solved during a time acceptable for a real time application.