ИСТИНА

It is proposed applications of the theory of combined dry friction [1] in the problem of the ball rolling on boundaries of two identical frames. This model can be used in investigation of the dynamic of the a so-called “Butterfly” robot, consisting of two identical shaped plates rigidly placed parallel to each other on a small distance aimed at manipulating a ball that can freely roll on the plates’ boundaries as on rails [2]. The friction force and torque are computed by the integration over the contact area so that the exact dynamically coupled integral model accounting the relationship of all the components of friction is obtained. This exact model is replaced by approximated model [3] which is the ratio of the linear form to square root of the quadratic form that permits to escape using not smooth functions in the cases when velocities are changed their signs and completely satisfy to all analytical properties of integral model as function kinematics parameters without increasing the number of coefficients.