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The purpose of the study was to develop mathematical models and proposals for improving the technology and equipment for the supply of roll packaging materials. The analysis of features of systems for transportation of packing materials, dynamics of transient processes, research methods concerning movements of rolled materials, features of loadings in systems of cyclic action with springy elements are resulted in the article. It is shown that the modern theoretical basis of synthesis of technological machines on the basis of use of film rolled materials combines possibilities of the account of technological requirements, indicators of high productivity, neighborhood conditions, restriction of power parameters. Mathematical formalizations concerning the ratios of force factors in systems of transportation of loads of cyclic action at the levels of external force actions, generated friction forces, geometrical, kinematic and dynamic parameters were obtained. Mathematical models concerning runaway modes and estimation of stiffness of springy bonds, on the basis of film materials, methods of estimation of system parameters were offered. Synchronized combination of operations, the use of optimal laws of movement of working bodies, limitation of dynamic loads was carried to the positive directions of creating efficient technological machines and lines. It is proposed to determine the ratio of the run-out time of rolls of variable mass by the ratio of the squares of the initial and final radii. The solution of the problem of kinetic energy recovery in systems of periodic action is simultaneously connected with the restriction of the non-uniformity of the drive of machines.

The article is devoted to the analysis of the prospects of the complex use of the accumulated potential energy on the example of a mechanism for lifting, horizontal movement and loading of cargoes, for example, in transport container with limitation of dynamic loads. On the basis of the analysis of the peculiarities of the shock loads in two-mass systems, the possibility of using the rigidity of the springy pendant as a variable factor to achieve the given relations between static and dynamic loads during their course in the gravitational field was determined.

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