Robust design of selectively compliant flexure-based precision mechanisms
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Nano-scale positioning and metrology are at the cutting edge of motion control technology, driven by ever-increasing number of applications, including semiconductor fabrication, data storage, nano-fabrication, biotechnology among others. In this ‘very small range (few µm) and very high precision (few nm) domain’, flexure-based mechanisms are the preferred means for the motion guiding systems, because of several exceptional properties like selective compliance, monolithic design, absence of friction, hysteresis, and wear. However, despite their numerous advantages, their motion characteristics are extremely sensitive to thermal variations, material property variations, machining tolerances among others. The geometric errors induced by machining process variations interact with the mechanism geometry, and lead to parasitic motion in directions other than the mechanism degrees of freedom. These errors cannot be completely eliminated by calibration, as they are coupled with the desired mechanism motion. This thesis focuses on the problem of parasitic motion in flexure based precision compliant mechanisms in the presence of geometric errors induced by machining tolerances. A spatial kinematics approach based on screw systems is used to model the compliance of the flexure mechanisms. The geometric errors induced by machining tolerances are systematically included in the modeling. The model not only determines the complete spatial motion of flexure mechanisms, but also provides geometric insight into the parasitic motion problem, which leads to decoupling of error motions into intrinsic and extrinsic parasitic motion. The intrinsic error motion is shown to be tied to the mechanism motion, and cannot be corrected by calibration. A metric to quantify the intrinsic error motion is obtained for both rotational and translational degree of freedom systems, and is used to define the precision capability of the flexure mechanisms. The model is used to formulate an optimization problem that aims to minimize the intrinsic parasitic motion metric by optimal joint compliance design. The stochastic optimization problem is solved numerically for both rotational and translational flexure mechanisms with one degree of freedom. A test setup is developed to characterize the pitch of screw motion of a one degree of freedom rotational flexure mechanism. The experimental results validate the existence of intrinsic parasitic motion. The setup demonstrates the metrology capability required for parasitic motion characterization, and forms a preliminary prototype for a quality control station for evaluating precision capability of flexure mechanisms. Significant contributions from the proposed work include, (1) complete mathematical and geometric interpretation of parasitic motion of flexure mechanisms due to machining tolerances, (2) formulation and solution of the flexure mechanism joint compliance robust design problem applied to rotational and translational one degree of freedom mechanisms, (3) development of an experimental setup to characterize the spatial parasitic motion of one DOF rotational flexure mechanism, that forms the basis of a modular quality control station in a ‘test-and-select’ approach for precision flexure-based compliant mechanisms.