Automated synthesis of planar 1-DOF mechanisms for prescribed trajectories

This paper presents an automated two-stage synthesis framework for planar single-degree-of-freedom mechanisms that generate prescribed end-effector trajectories. Candidate designs are represented by a symbolic hierarchical encoding that unifies revolute–prismatic topology decisions with discretized joint-location and link-size choices, enabling a one-to-one mapping from integer codes to mechanism instances. Using this encoding, Monte Carlo Tree Search, MCTS, performs budgeted exploration of a large combinatorial configuration–size space and identifies high-potential candidates under simulation-driven evaluation. To recover geometric resolution lost in discretization and address the strong parameter sensitivity of path generation, the selected mechanisms are subsequently refined via genetic algorithm, GA, based continuous optimization. The refinement tunes a bounded continuous parameter vector comprising joint offsets, link dimensions, and end-effector attachment offsets to maximize the same trajectory-similarity reward used in discrete search. Trajectory agreement is quantified by a phase- and symmetry-invariant metric that combines frequency-domain alignment with Procrustes-based shape matching under planar similarity transforms. The approach is validated on three task-relevant reference trajectories with distinct geometric characteristics, including 8-shaped, dolphin-shaped, and wedge-shaped paths, and is further examined using an additional non-smooth triangular trajectory. The refined mechanisms consistently reach trajectory similarity values near 90% and exhibit clear improvements over the discretized seeds. An automated SOLIDWORKS API workflow further generates fully constrained assemblies and fabrication-ready part files, and prototype builds together with SOLIDWORKS Motion studies demonstrate practical realizability of the synthesized designs.