Optimal Design of a 2T2R Parallel Mechanism with Inner-Limbs Closed Loops
摘要
Parallel mechanisms used in machining processing are mainly 3-degree of freedom (DOF) and 5-DOF systems. However, the comprehensive precision machining of large, complex parts requires more flexible 4-DOF parallel mechanisms combined with large-travel moving bolster. Symmetrical 4-DOF parallel mechanisms, prone to issues such as singularities, are still in the theoretical research stage with few mature products applied in practice. Therefore, this paper proposes a 2T2R 4-DOF parallel mechanism with inner-limbs closed loops. Initially, a kinematic model of the 2T2R parallel mechanism with inter-limbs closed loops is established based on the loop closure equations method. Then, a static stiffness model of the mechanism is developed using a semi-analytical method and compares with the finite element analysis to verify the effectiveness of the static stiffness model and provide a theoretical basis for global multi-objective optimization. Finally, the average values of the global condition number of linear stiffness matrix and torsional stiffness matrix, and the ratio of maximum and minimum torsional stiffness in orientation space are used as the stiffness performance evaluation indices, the ratio of the mechanism’s workspace to its volume and isotropy of static stiffness are used as the optimization goals, and multi-objective optimization algorithm is conducted using the Pareto front, obtaining the optimal parameters based on the principle of minimum distance target matching. After optimization, the isotropy of static stiffness increased by 33.1%. The optimization and analysis results indicate that the proposed optimization method for the 2T2R 4-DOF parallel mechanism is feasible and effective, providing a theoretical foundation for the subsequent development of engineering prototypes.