APPLICATION OF THE THEORY OF THE MULTICOMPONENT DRY FRICTION IN SOME OF CONTROL ROBOT SYSTEMS

Abstract

The implementations of the theory of multicomponent dry friction [1-19] for analyze the dynamics of some robotic systems, such as a butterfly robot [16-18, 20] or a humanoid robot is proposed. Since the main controlled element of these systems is a spherical, elastic composite shell, it is required to calculate the distribution of normal contact stresses inside the contact spot. The contact pressure distribution for such elements is constructed using the S. A. Ambartsumyan’s equation for a transversally isotropic spherical shell. This equation is modified by introducing the averaged contact pressure and normal displacements for the shell. The construction of the resolving integral equation for the contact pressure is based on the principle of superposition and the method of Green's functions. For this, the corresponding Green's function is constructed, which is the normal displacement of the shell as a solution to the problem of the effect of concentrated pressure. Green's function as well as the contact pressure, it is sought in the form of series expansions in Legendre polynomials, taking into account additional relations for the reduced contact pressure and normal displacements. Using the Green's function, an integral equation solving the problem is constructed. As a result, the problem is reduced to determining the expansion coefficients in a series of the reduced contact pressure. Restricting ourselves to a finite number of terms in the series of expansions, using the discretization of the contact area and the properties of Legendre polynomials, the problem is reduced to solving a system of algebraic equations for the expansion coefficients for the reduced pressure. After that, from the additional relation, the coefficients of the required expansion of the contact pressure in a series in Legendre polynomials are determined. To describe the conditions of shell contact with the surface, the theory of multicomponent anisotropic dry friction is used, taking into account the combined kinematics of shell motion (simultaneous sliding, rotation and rolling). The coefficients of the dry friction model can be calculated using simple explicit formulas [1-19] based on numerical experiments.