Modelling of the force state of contact of a solid Ball moving along two incline rails Available to Purchase

The further development of the investigation, beginning at the works [1-3] and the firstly presented in [4] is proposed in this work. Distinguish features of these investigations are using of the theory of multi-component dry friction [5-22] in the numerous engineering applications. Dry friction model of a solid ball rolling on boundaries of two identical frames constructed in works [1-3] is generalized for the case of the two incline 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 [17]. The difficult control systems considered in [23-24] are another engineering application of the combined dry theory. Following developed in previous investigation approach, 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 analytical model which is completely satisfy to all analytical properties of integral model as function kinematics parameters without increasing the number of coefficients.