The synthesis of functional molecular linkages is constrained by difficulties in fabricating nano-links of arbitrary shapes and sizes. However, the classical mechanism synthesis methods, which assume the ability to manufacture any designed links, do not provide a systematic synthesis process for molecular linkages.

We propose a new approach to build functional mechanisms with prescribed mobility by only using elements from a predefined link soup. First, we enumerate an exhaustive set of topologies, while employing divide-and-conquer algorithms to control the generation and elimination of redundant topologies. Then, we construct the linkage arrangements for each valid topology. Finally, we output a set of feasible geometries through a positional analysis step that minimizes the error associated with closure of the loops in the linkage while avoiding geometric interference. The proposed systematic approach outputs the ATLAS of candidate mechanisms, which can be further processed for downstream applications. The resulting synthesis procedure is the first of its kind that is capable of synthesizing functional linkages with prescribed mobility constructed from a soup of primitive entities.

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