According to the proposed design scheme of the overhead crane, with the use of blocks package SimMechanics Second Generation of MATLAB, a conceptual block diagram of connections was developed, according to which the was created Simulink-model of the mechanical system of the bridge crane with PID regulator. Simulink-model allows us to study the operating modes of the overhead crane on the its design stage.

In this paper, we propose a method and a mathematical model for solving the problem of cargo transportation on a suspension rope by a bridge crane following a predetermined trajectory in the absence of uncontrollable pendulum sways. To this end, the principle of reduction of the secondorder linearized differential equation, which describes sways in the 'point of suspension-cargo' system, is applied. As a result, a first-order differential equation is derived, in which the control action consists in the required acceleration of the cargo. The proposed method allows a rapid synthesis of an optimal trajectory of the suspension point for ensuring the required cargo movement trajectory in the horizontal direction without either complex mathematical calculations of the optimal control theory or the laborious algorithms of multidimensional or iterative optimization. This method can be used in the systems providing the automated control of bridge cranes with the function of restricting uncontrolled cargo sways, as well as in those having a new prospective function of cargo transportation maintenance along a predetermined trajectory.

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Reducing the vibration effects on a human operator of a construction, road or handling machine is an urgent task, since the vibration loads produced by the internal combustion engine, vehicle engine interacting with the support surface microrelief, as well as the machine working attachment, adversely affect the machine operator and increase the machine parts and assemblies wear. The operator may develop occupational diseases caused by vibrations. In this regard, the research objective is to develop the mathematical apparatus simulating the dynamic processes of the passive vibration protection systems oscillations at the design stage. Therefore, the problem developing a mathematical model that makes it possible to study the oscillations of a single degree of freedom passive vibration protection systems with any given static characteristic, was solved. On the basis of the dynamic equations of a single translational degree of freedom vibration system describing the vibration protection suspended operator’s seat, the mathematical model solving the differential equation of the system oscillations taking into account the spring loaded mass displacements damping and three-segment static characteristics of the vibration isolation mechanism with limiters was simulated using the package Simulink of MATLAB system. An example of using the developed mathematical model for modelling vibrations of a spring-loaded mass under the sinusoidal external influences is given. The preset vertical displacements of the machine base, i.e. its base chassis act as the external influences. The examples of the obtained simulation results, namely the vertical displacements and accelerations of the spring-loaded mass are presented. The maximum accelerations of the spring-loaded mass were found out to significantly increase, when the machine base forced displacements amplitude exceeds by half of the horizontal section of the quasi-zero static characteristic of the vibration protection suspension.