Automated sketching of non-fractionated kinematic chains

• We propose a new algorithm to draw kinematic chains using loops and pseudophysics.
• We propose a new edge-crossing preserving algorithm to improve the esthetics.
• New rules to convert the graph into the sketch of the kinematic chain are proposed.
• The algorithm was tested to layout kinematic chains with up to 6 independent loops.
• A comparison with tests of the literature shows the advantages of the algorithm.

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.

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