Improving Motion Stability of the Plane 3-RPR Parallel Manipulator at Singular Configuration

Kinematic parameters have significant influences on the motion stability of parallel manipulators at singular configureations. Taking the plane 3-RPR parallel manipulator as an example, the motion stability at different types of singular configurations corresponding to the angular speed and velocity of the movable platform are investigated. At first, the second order of uncoupled dynamics equation for the 3-RPR parallel manipulator is established with the aid of the second class Lagrange approach. According to the Lyapunov first approximate stability criterion, the approximate conditions for the 3-RPR parallel manipulator with a stabile motion at singular configurations are determined based on the Gerschgorin circle theorem. Next, the exact Hurwitz criterion is utilized to study the motion stability and the load capability of the manipulator corresponding to the angular speed and velocity of the movable platform, as well as the directions of the external forces at two kinds of singular configurations: with a gained rotation-type DOF, and with a gained translation-type DOF, respectively. The results show that increasing both the angular speed and the velocity of the mass center of the movable platform can efficiently improve the motion stability of the 3-RPR parallel manipulator at singular configurations.

On the Stability of an Intermediate Coupled Ocean-Atmosphere Model

The explicit finite difference scheme for solving an intermediate coupled ocean-atmosphere equations has been proposed and discussed. The discrete Fourier analysis within Gerschgorin circle theorem is applied to the stability analysis of this numerical model. The stability criterion that we obtained includes advection, rotation, dissipation, and friction terms, without any assumptions, which is also including the Courant-Friedrichs-Lewy (CFL) condition as a special case. Numerical sensitivity experiments are also carried out by varying the model parameters.