Dynamics of a Flat Rigid Body on a Horizontal Plane

Introduction. The study of the motion of a rigid body carrying moving masses greatly simplifies the design of capsule robots that can move inside aggressive environments and perform the required operations. The following cases have been studied quite well: movement during interaction of a solid body with a reference plane and in aggressive environments; vibratory displacement of bulk media and solids on a vibrating base; optimization of rigid body motion; variation of average speed and acceleration at different intervals of motion; dependence of average speed on task parameters; control of the motion speed of the internal mass for the fastest possible rotation of a rigid body. However, at present, insufficient attention has been paid in the literature to the problems of studying the motion of a heavy flat body along a horizontal plane under the action of a harmonic force directed at an angle to the horizon, specifically, in terms of taking into account all possible driving modes and their features. This does not allow determining the optimal parameters of the problem. Therefore, the objective of this research was to identify the features of all possible modes of motion of a heavy solid body along a horizontal plane under the action of a harmonic force directed at an angle to the horizon. Materials and Methods. The equations of motion of the mechanical system were used. Both analytical approaches and numerical methods were used to solve the steady-state equations of motion of the system. The dry friction model was adopted as a friction model, which made it possible to obtain accurate solutions for positive and negative values of the slip velocity up to constants. Values of these constants were determined from the docking conditions and the periodicity of the solution. Results . An analytical solution to the problem for periodic solutions was obtained. Three possible motion modes were identified. Using numerical analysis, the dependences of the average speed of a body motion over the period on the angle of inclination of the force to the horizon were constructed. The optimal direction of force was established. Discussion and Conclusion. The results of the conducted research allowed us to determine the optimal values of the problem parameters in order to reach the required value of the average velocity of a solid body. In particular, optimal values of the amplitude of the force and its direction can be found to reach the maximum value of the average velocity of motion of a solid.