Performance Comparison of Multi-Objective Optimizers for Dynamic Balancing of Six-Bar Watt Linkages Using a Fully Cartesian Model

Balancing mechanisms require the minimization of both the Shaking Moment (ShM) and Shaking Force (ShF), a complex multi-criteria challenge often tackled using single-objective algorithms. However, these methods face difficulties in navigating competing objectives. In contrast, multi-objective algorithms provide a more efficient and adaptable framework, while Fully Cartesian Coordinates (FCC) simplify the balancing equations compared to conventional Cartesian formulations. This study focuses on optimizing the dynamic balance of a six-bar Watt linkage using FCC. A wide set of optimization methods is analyzed and compared, and among them, the S-Metric Selection Evolutionary Multi-objective Optimization Algorithm (SMS-EMOA) demonstrates superior performance. This algorithm achieves the most significant hypervolume value in only 10.44 min of execution. The results indicate that multi-objective algorithms outperform single-objective approaches, offering faster and more diverse optimization solutions. Additionally, this study introduces an analytical method that enables the straightforward identification of removable counterweights, achieving an equally effective balance while minimizing the number of counterweights required.