Structural optimization of compliant mechanisms is a systematic and automated approach for synthesizing the topology (layout) of mechanisms given the motion requirements. Here, two optimization approaches are presented: one employing a traditional full ground structure and one utilizing a modular ground structure whose nodes are allowed to wander within specified ranges. For problems discretized by many elements, the modular ground structure effectively reduces the number of design variables and speeds design convergence. In addition, relocation of node coordinates allows for geometric variation within the topology (layout) design stage. Linear finite element analysis using truss elements is utilized along with a sequential quadratic programming algorithm to optimize the mechanisms. Derivation of an efficiency based objective formulation is presented to determine the optimal mechanism design which satisfies motion requirements while maximizing the transfer of energy through the mechanism. Calculation of design derivatives with respect to element cross-section area and node position is performed using the adjoint variable method which provides faster and more stable convergence over finite difference approaches. Design examples are presented which directly compare the performance of topology optimized designs for the fixed node full ground structure to the floating node modular ground structure.

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