An Analytical Study of the Effects of Kinematic Parameters on the Motion Stability of a 3-RPR Parallel Manipulator in Singular Configurations

Abstract

Due to the Jacobian matrix rank reduction near singularities, applying numerical methods to study PMs’ motion stability at singularities is quite difficult. As a result, there is a scarcity of literature on the investigation of PMs’ dynamic behaviors near singularities and the influence of kinematic parameters on the motion stability of PMs. To address the research gap related to the above issues, based on the Gerschgorin perturbation method, Hurwitz exact approach, and the Lyapunov dynamic stability theory, the influence of kinematic parameters and external loads on a PM’s motion stability at singularities is studied for the first time. The theoretical analysis results reported in this paper reveal many previously undiscovered features beyond those derived from previous numerical methods, and indicate the limitations of some widely accepted statements. For example, increasing the angular speed of the movable platform can expand the range of the external loads that meet the motion stability at singular configurations. The prevailing notion in prior research that PMs are unable to support external loads in the direction of the gained DoF at singular configurations is only partially accurate. This pioneering research establishes a theoretical foundation for exploring a new real-time approach to avoid dynamic singularities by fully exploiting the influence mechanisms of kinematic parameters on PMs’ dynamic stability at singularities.