This paper introduces the spanning tree theory to the topological synthesis of compliant mechanisms, in which spanning trees connect all the vertices together using a minimum number of edges. A valid topology is regarded as a network connecting input, output, support, and intermediate nodes, which contains at least one spanning tree among the introduced nodes. Invalid disconnected topologies can be weeded out if no spanning tree is included. No further deformation analysis and performance evaluation is needed to invalidate disconnected topologies. Problem-dependent objectives are optimized for topological synthesis of compliant mechanisms. Constraints about maximum input displacement and force, maximum stress and overlapping connections are directly imposed during optimization process. The discrete optimization problem is solved by genetic algorithm with penalty function handling constraints. Two examples are given to verify the effectiveness of the proposed synthesis procedure.
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