The drum mower blade is freely rotatable around the fastening pin. During the operation of the mower, the centrifugal force and the resistance of the mowing material act on it. The presented article studies the effect of these forces on the behavior of the blade, in particular its oscillation around the steady state, depending on the properties of the cut material.
We start by formulating geometrically the Newton’s law for a classical free particle in terms of Riemannian geometry, as pattern for subsequent developments. For constrained systems we have intrinsic and extrinsic viewpoints, with respect to the environmental space. Multi–particle systems are modelled on -th products of the pattern model. We apply the above scheme to discrete rigid systems. We study the splitting of the tangent and cotangent environmental space into the three components of center...
The paper deals with asymptotic motions of 3-parametric robot manipulators with parallel rotational axes. To describe them we use the theory of Lie groups and Lie algebras. An example of such motions are motions with the zero Coriolis accelerations. We will show that there are asymptotic motions with nonzero Coriolis accelerations. We introduce the notions of the Klein subspace, the Coriolis subspace and show their relation to asymptotic motions of robot manipulators. The asymptotic motions are...
A trajectory tracking problem for the three-dimensional kinematic model of a unicycle-type mobile robot is considered. It is assumed that only two of the tracking error coordinates are measurable. By means of cascaded systems theory we develop observers for each of the error coordinates and show the K-exponential convergence of the tracking error in combined closed-loop observer-controller systems. The results are illustrated with computer simulations.