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Modelling and Simulation Research of the Gripper Manipulator

Uzny S., Sokół K.

Machine Dynamics Research

2015

Vol. 39, No. 2

5-14

In this paper the boundary problem of instability of single slender system with consideration of Timoshenko theory is presented. The investigated structure is loaded by Euler’s force (the most common type of loading); additionally the different boundary conditions are taken into account. Simulated type of external load is characterized by constant line of action regardless to deflection of the system. In order to achieve more general form of the investigated system the springs limiting the rotations and displacement of both ends are used. Boundary problem is formulated on the basis of the minimum total potential energy. The results of numerical simulations obtained with Timoshenko and Bernoulli-Euler theories are compared. The simulations are done at different magnitudes of slenderness factor as well as translational and rotational springs stiffness. On the basis of the obtained results the difference in critical forces calculated on the basis of both theories can be easily presented.

The Regions of Local and Global Instability of a Two-Member Slender System with Grack

Uzny S., Sokół K.

Machine Dynamics Research

2014

Vol. 38, No. 2

75-83

In this paper the instability phenomenon of a column composed of two elements with different bending and compression stiffness's is presented. In the one of elements the crack modeled by means of rotational spring with linear characteristic is present. The boundary problem of an instability has been formulated on the basis of the minimum total potential energy principle. In this study only the results corresponding to the magnitude of bifurcation loading of the two element system are presented (rectilinear form of static equilibrium). These results were compared to the critical loading magnitude calculated for single element system (a system without crack). Finally the comparison of the bifurcation loading of a two element system to the single element one under consideration of different magnitudes of bending rigidity factor allows one to present the regions of local and global instability of the considered complex system.