Traversing Type-II singularities by leveraging PM’s inherent dynamic characteristics

Abstract

This paper presents a precise path-tracking method for a parallel manipulator (PM) to navigate Type-II singularities by leveraging its dynamic characteristics, thereby eliminating the need for offline recalibration, redundancy, or added mass. The approach is based on new insights into the singularity-free kinematic parameter region (SFKPR), an interconnected, high-dimensional hypersurface revealed through analytical investigations of how kinematic parameters influence the dynamical stability of the PM at singularities. By maintaining the kinematic parameters within the SFKPR, the manipulator can achieve stable motion at singularities. Furthermore, adjusting these kinematic parameters enables efficient changes to the SFKPR’s dimensions. The feasibility of this method is validated by applying three carefully designed paths to a 3-RPR PM to transfer the singular point. It was observed that all eigenvalues of the PM dynamic system at singularities have negative real parts, confirming that the PM successfully follows the paths with stable motion. This outcome indicates that the proposed method is effective and meets the Lyapunov stability criterion. While the kinematic parameters required for stable motion at the singular point vary along these paths, the PM cannot traverse singularities in a static state. Notably, when input kinematic parameters exceed certain thresholds, a singularity-free design can be achieved throughout the workspace during path planning. Overall, the proposed approach allows the PM to navigate Type-II singularities with both precision and flexibility. It is particularly advantageous in aerospace engineering, where minimizing weight and complexity is essential while ensuring safety and control accuracy.