Topology optimization of underactuated spring-linkage mechanisms

Linkage mechanisms are widely used to transform simple input motions into desired end-effector motions. For applications requiring adaptation to obstacles or uncertain environments, a fully actuated one-degree-of-freedom linkage can be converted into an underactuated mechanism by incorporating elastic springs. However, designing such spring-linkage mechanisms remains challenging because the topologies and dimensions of rigid links and springs must be determined simultaneously. In this study, we propose a topology optimization method for synthesizing 1-DOF underactuated spring-linkage mechanisms without any predefined baseline linkage and spring configuration. The method unifies a linkage design space, represented by a spring-connected rigid block model with artificial zero-length springs, and a spring design space, represented by finite-length real elastic springs. An energy-based formulation with gradient-based optimization enables efficient computation. Case studies, including adaptive grippers interacting with obstacles of various shapes, demonstrate the method’s ability to automatically generate effective spring-linkage mechanisms.