One degree of freedom (1DOF) linkages are persistent in mechanical systems. However, designing linkages to follow a desired path, known as path synthesis, is challenging due to non-linearities, combinatorial nature, and strict geometric constraints. Current state-of-the-art algorithms cannot scale well to linkages with higher-order linkage graphs. One reason for this is that state-of-the-art algorithms spend the majority of the time exploring constraint-violating designs. This work uses an Assur group 0DOF linkage as a graph grammar rule to modify both linkage graph and spatial parameters, ensuring all designs are valid 1DOF linkages. Using this graph grammar, this paper formulates linkage path synthesis as a tree search and uses a Deep Reinforcement Learning (DRL) agent to search the space of kinematically feasible planar 1DOF linkages. This paper introduces a method using a Graph Convolution Policy for High-Order Linkage Graph Optimization called GCP-HOLO. An any-time algorithm, GCP-HOLO outputs linkages with 1-8 loops (4-16 bars) efficiently. When comparing the GCP-HOLO formulation to a recent state-of-the-art paper that solves a Mixed Integer Conic Program, GCP-HOLO generates sets of solutions of varying linkage complexities to 8 test trajectories in a quarter of the time. Extending GCP-HOLO with a global node optimization, such as Covariance Matrix Adaptation Evolutionary Strategy, the results quickly converge to finding better solutions for 4/8 tests, with the whole pipeline capable of a 13X speed increase.

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