Global-Local Search for Topology Optimization of Linkage Mechanisms Using Spring-Connected Link Model

Abstract This study presents a novel optimization-based synthesis framework for linkage mechanisms with a single degree-of-freedom. Current topology optimization-based mechanism synthesis methods often result in infeasible solutions due to the highly nonlinear and multi-modal nature of the objective function. To address this, we propose a new optimization framework that uses binary links as design components, defining candidate mechanisms through node adjacency matrices that specify topologies, end effector positions, and ground-anchoring nodes. These candidates are screened for invalid motions and topologies by considering reducibility and isomorphism. Our approach conducts global-local optimization exclusively on candidates with valid degrees-of-freedom, ensuring a higher chance of identifying feasible solutions by avoiding the exploration of invalid mechanisms. The first optimization step involves a global search that simultaneously optimizes the topology and shape of a linkage to best follow the target path. The second step fine-tunes the linkage shape by optimizing the nodal coordinates. The effectiveness of the proposed method is validated through case studies, demonstrating its capability to solve mechanisms with up to seven-node linkages.