The dynamical stability of the cable-driven lower-limb rehabilitation training robot (CLLRTR) is a crucial question. Based on the established dynamics model of CLLRTR, the solution to the wrench closure of the under-constrained system is presented. Secondly, the stability index of CLLRTR is proposed by the Krasovski method. Finally, in order to analyze the stability distribution of CLLRTR in the workspace, the stability evaluation index in the workspace is calculated using the eigenvalue decomposition method. The stability distribution laws of CLLRTR are further verified by the experimental study. The results provide references for studying trajectory planning and anti-pendulum control of CLLRTR.

Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem as our model. Highly eccentric orbits are out of the Hill stability regions. However, mean motion resonances can provide phase protection and orbits with long-term stability exist. We construct maps of dynamical stability based on the computation of chaotic indicators and we figure out regions in phase space, where the long-term stability is guaranteed. We focus on regions where at least one planet is highly eccentric and attempt to associate them with the existence of stable periodic orbits. The values of the orbital elements, which are derived from observational data, are often given with very large deviations. Generally, phase space regions of high eccentricities are narrow and thus, our dynamical analysis may restrict considerably the valid domain of the system's location.