The rectilinear motion on a horizontal rough plane of a vibration-driven system consisting of a carrying body, which interacts with the plane directly, and of internal masses that perform harmonic...

The paper deals with the dynamics of a mobile robot with four Mecanum wheels. For such a system the kinematical rolling conditions lead to non‐holonomic constraints. From the framework of non‐holonomic mechanics Chaplygin's equation is used to obtain the exact equation of motion for the robot. Solving the constraint equations for a part of generalized velocities by using a pseudoinverse matrix the mechanical system is transformed to another system that is not equivalent to the original system. Limiting the consideration to certain special types of motions, e.g., translational motion of the robot or its rotation relative to the center of mass, and impose appropriate constraints on the torques applied to the wheels, the solution obtained by means of the pseudoinverse matrix will coincide with the exact solution. In these cases, the constraints imposed on the system become holonomic constraints, which justifies using Lagrange's equations of the second kind. Holonomic character of the constraints is a sufficient condition for applicability of Lagrange's equations of the second kind but it is not a necessary condition. Using the methods of non‐holonomic mechanics a greather class of trajectories can be achieved.

The motion of a finite chain of identical bodies along a straight line in a resistive medium is studied. The major aim of this study is to investigate the fundamental properties of such systems, in particular, their ability to move from a state of rest and sustain the motion at constant average velocity in media with different resistance properties and the influence of the control strategy on the motion. The motion is excited and controlled by changing the distances between the bodies of the chain. For a given friction law, the necessary and sufficient conditions for the system to be able to move from rest are established.