## 3 Methodology of Numerical Tests of the Platform
### Functional Testing of the Platform Using the MBS Method  
Due to the design stage of numerical tests, it is necessary to represent the boundary and initial conditions and appropriate models of reduced loads corresponding to selected operational variants of the platform application. For this purpose, the analytical method and numerical 3D models of the basic platform composed of rigid bodies were used. The main components of the platform, their connections, maximum permissible loads with the cargo transported on the platform, as well as the boundary and initial conditions corresponding to lifting the platform with the permissible cargo load using the hook mechanism, which was considered dimensioning for this type of structure, were represented in them. Such models and the MBS methodology were used to determine the maximum external loads corresponding to the operating load variants. Three-dimensional models and the MBS methodology were used in dynamic simulations to determine the reduced loads acting on the end carriage hitch (Figure 6) during the simulation of hook lifting of a simplified rigid platform model with the representation of the state of constant equilibrium corresponding to a uniform movement with the end of the platform raised from the side of the hitch of the hook device and moving in conditions of contact with the ground of the other end of the platform under various extreme friction conditions with coefficients \(\rm{\mu_{min}=0.45}\) and \(\rm{\mu_{max}=0.6}\). The direct purpose of the MBS dynamic analysis is to determine the limit component forces (Figure 6) in the hook lifting of the platform-container module for rigid and rotating rollers for the minimum and maximum coefficient of friction. The analysis was performed using the professional MBS software [32; 33], to which the 3D geometric model of the platform module was imported. On its basis, in the multi-body software environment, a multibody model of the platform consisting of rigid bodies connected by appropriate external and internal nodes was compiled--movable connections between the individual components of the platform were represented. A model of a horizontally oriented, perfectly rigid ground was also built, on which the model of the platform was placed. Between the models of the platform and the ground, the contact phenomenon and various friction conditions were defined, which simulated the boundary effect of the ground resistance forces when simulating the shifting of the platform during its hook lifting. The model with the ground in the MSC Adams software is shown in Figure 6.  
Dynamic analyses were performed for two variants of cooperation between the platform model and the ground:  
* Variant I--Introduction of rotational nods relative to the longitudinal axis of the hook mechanism rollers--rollers rigidly dragged when moving the platform on the ground during representation of the hook lifting operation (Figure 4b);
* Variant II--Rollers with the possibility of rotation relative to the longitudinal axis of the hook mechanism rollers--the rollers rotate while rolling on the surface of the rigid ground (Figure 6) when moving the platform on the ground during representation of the hook lifting operation. Dynamic MBS simulations of the platform with its own load and the maximum load weight of P\({}_{\text{max}}\) = 100 kN in the conditions of motion initiation with representation of the initial phase of the platform motion during hook lifting were performed by defining different sets of component forces on the end carriage hitch (Figure 6), changing in individual cases of the analysis from the zero value to limit values, determined analytically (Section 4.3 of the paper), reduced by 50 N and increased by 50 N, respectively.