Flexure-based compliant mechanisms are the preferred motion guiding systems for small range, nano-precision positioning applications because of excellent characteristics like friction-free continuous motion. These mechanisms are commonly used in nano fabrication equipment and ultra precision instruments. However, machining imperfections induced geometric errors in the mechanisms are known to cause undesirable parasitic motion and significant loss of precision. A systematic design approach to minimize the sensitivity of the flexure mechanisms to geometric errors induced by machining tolerances is presented here. Central to the design approach is the screw systems based analytical model to study the spatial motion characteristics of flexure mechanisms. Using this model, the parasitic motion is classified into those errors which can be corrected by calibration (extrinsic) and those which are coupled with the mechanism motion and cannot be corrected by apriori calibration (intrinsic). Metric to quantify the intrinsic parasitic motion results naturally from the screw systems analysis, and is used to represent the precision capability of the flexure mechanism. The analytical model enables the selection of geometric parameters of flexure joints of the mechanism via an optimization scheme with the aim of minimizing the parasitic motion metric. The statistical nature of the machining tolerances is accounted for by sampling the random variables at every iteration step of the optimization, leading to a stochastic formulation. The robust design approach is illustrated using a one DOF rotational flexure mechanism that is used in nano-imprint lithography equipment. Numerical results of the optimization indicate up to 40% improvement in the precision capability of the mechanism without any change in the manufacturing tolerance limits. Further, it is shown via eigenscrew analysis of mechanism compliance that the robustness resulting from the optimal flexure joint design can be attributed to the improved compliance distribution.

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