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Is there a name for the field of computer science that classifies these linkages by their topological proporties other than just general CAD stuff? It would be awesome to say I have linkage A and linkage C, what kind of linkage B can I put in the middle?

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Yes, there is: "kinematic synthesis." It is not typically considered a "computer science" topic; it is instead taught in various forms in mechanical engineering curriculums.

Can you recommend any good books on kinematic synthesis?

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