Automated Sketching of Non-Fractionated Kinematic Chains

Abstract

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 nonfractionated kinematic chains. A combinatorial algorithm based on the 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 aesthetics 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 nonfractionated 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.