Kinematic Solving and Stable Workspace Analysis of a Spatial Under-Constrained Cable-Driven Parallel Mechanism

This study systematically investigates the kinematic characteristics and static stability of a spatial under-constrained four-cable-driven parallel mechanism, specifically designed for supporting aircraft models in wind tunnel tests. Addressing the inherent strong coupling between kinematics and statics in such systems, an integrated solution framework is proposed. Firstly, a hybrid intelligent algorithm integrating genetic algorithm, chaos optimization, and particle swarm optimization is introduced to efficiently solve the direct and inverse geometric-statics problems, ensuring the identification of physically feasible equilibrium configurations under constraints such as cable tension limits and mechanical interference. Subsequently, a stability evaluation method based on the eigenvalue analysis of the system’s total stiffness matrix is employed, establishing a criterion (minimum eigenvalue λmin > 0) to identify statically stable equilibrium points. Finally, the static feasible workspace and the static stable workspace are systematically analyzed and quantified, providing practical operational limits for mechanism design and trajectory planning. The effectiveness of the proposed solution framework is validated through numerical computations, simulations, and experimental tests, demonstrating its superiority over benchmark methods. This study provides theoretical support for the design, analysis, and control of under-constrained four-cable-driven parallel mechanisms.