A Multi-Layer Parallelogram Flexure Architecture for Higher Out-of-Plane Load Bearing Stiffness

Parallelogram flexure mechanism (PFM) is a common flexure module that is widely used as a building block in the design and manufacturing of flexure-based XY motion stages that provide in-plane degrees-of-freedom (DoFs). In such motion stages, low in-plane stiffness along the DoF helps increase the DoF range of motion and reduce the actuation effort. At the same time, high out-of-plane stiffness is paramount to suppress out-of-plane parasitic motions, support heavy payloads, and mitigate the negative impacts of out-of-plane resonant modes. Achieving both of these design objectives simultaneously is extremely challenging in PFMs and flexure mechanisms comprising PFMs due to the inherent tradeoff between the in-plane and out-of-plane stiffnesses. This paper resolves this tradeoff by proposing a novel multi-layer PFM architecture, referred to as the sandwich PFM, that achieves significant improvements in the out-of-plane translational and rotational stiffnesses compared to conventional single-layer PFMs without impacting the in-plane DoF stiffness. Analytical models will be derived for the in-plane and out-of-plane stiffnesses of the sandwich PFM, which closely match the Finite Element Analysis (FEA) results. Several design insights into the performance of the sandwich PFM are discussed using the analytical stiffness models, and a general procedure is proposed to design a sandwich PFM.