Automated sketching of non-fractionated kinematic chains

The sketching problem arises frequently in the conceptual design of mechanisms, especially in the enumeration process where a large number of topological solutions automatically generated must be analyzed. This paper presents a new graph layout algorithm to sketch non-fractionated kinematic chains. A combinatorial algorithm based on the independent loops of the graph representation of the kinematic chain, is used to find an adequate initial position of graph vertices with minimal edge crossings; its execution is followed by a force-directed algorithm based on spring repulsion and electrical attraction, including a new concept of edge-to-vertex repulsion to improve esthetics and preserve edge crossings. Both algorithms are used in sequence to generate a representative layout of the graph which optimizes a given quality measure. Finally, standard rules are followed to convert the graph into the sketch, using new heuristic correction rules to avoid newly generated edge crossings. Atlases of complex non-fractionated kinematic chains are used to validate the results. A qualitative comparison with a set of sketches found in the literature is included, showing the advantages of the proposed algorithm.