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Design methodology for multi-degrees-of-freedom compliant mechanisms with optimal stiffness and dynamic properties

Compliant mechanisms are flexible structures that utilize elastic deformation to achieve their desired motions. Using their unique mode of actuation, compliant mechanisms can achieve highly repeatable motions that are essential for high precision micro/nano-positioning applications. As a result, they have been utilized for a wide range of applications like positioning mechanisms for high resolution imaging systems, industrial nano-imprint and nano-alignment applications, and numerous other micro/nano-manipulation tasks. The performance of the compliant mechanisms is highly dependent on their stiffness and dynamic properties because these properties dictate their workspace, transient responses and capabilities to reject disturbances. However, despite the importance of compliant mechanisms, it is still an open challenge to optimize such properties when these structures have multi-degrees-of-freedom. This thesis addresses these limitations by developing an integrated design methodology that can create multi-degrees-of-freedom compliant mechanisms with optimal dynamic and stiffness properties. This methodology first employs a kinematic approach to select suitable parallel-kinematic configurations for the compliant mechanisms. Subsequently, a structural optimization approach is used to automatically synthesize and optimize the sub-chains’ structural topology, shape and size. In order to integrate the kinematic and structural optimization approaches, a new topological optimization algorithm termed the mechanismbased approach has been created. In comparison with existing algorithms, a notable benefit for the mechanism-based approach is that it can eliminate infeasible solutions that have no physical meanings while having a flexible way to change its topology during the optimization process. This algorithm has been shown to be able to develop various devices such as a μ-gripper, a compliant prismatic joint, and a compliant prismatic-revolute joint. A generic semi-analytical dynamic model that can accurately predict the fundamental natural frequency for compliant mechanisms with parallel-kinematic configurations has also been developed for the proposed integrated design methodology. The effectiveness of the proposed methodology is demonstrated by synthesizing a X− Y− θz flexure-based parallel mechanism (FPM). This FPM has a large workspace of 1.2 mm×1.2 mm×6◦, bandwidth of 117 Hz, and translational and rotational stiffness ratios of 130 and 108, respectively. The achieved stiffness and dynamic properties show significant improvement over existing 3-degreesof-freedom, centimeter-scale compliant mechanisms that can deflect more than 0.5 mm and 0.5◦. These compliant mechanisms typically only have stiffness ratios and bandwidth that are less than 50 and 45 Hz, respectively. The stiffness and dynamic properties of the optimal FPM were validated experimentally and they deviated less than 9% from the simulation results. Based on the inspirational performance of the X− Y− θz FPM, we envision that the proposed methodology can inspire a variety of high precision machines that have optimal performances.