The Second Approximation of the Averaging Method in the Dynamics of Controlled Motions of Vibration Systems with Dry Friction

The second approximation of the averaging method is constructed in the problem of motion along a horizontal rough plane of a vibration-driven mechanical system consisting of a carrying body (robot housing) in contact with the plane and two internal masses oscillating vertically and horizontally according to a harmonic law with the same frequency. In the absence of a phase shift in the first approximation, the directed motion of the system as a single whole (locomotion) cannot be detected. In the second approximation, an expression for the average velocity of motion is obtained. The values of velocity calculated using the obtained formula are in good agreement with the results of numerical calculations. The described technique for constructing the second approximation can be used to solve other problems with dry friction.