Modeling Stiffness and Stress in Serpentine Flexures for Use in a Compliant Bone Plate

Abstract Serpentine flexures offer several advantages for use in linear motion mechanisms, including distributed compliance to reduce stress and increase range of motion. In this work, we develop an analytical model for predicting the moment, vertical deflection, and maximum stress experienced in serpentine flexures in response to an input vertical force. Two classes of serpentines are introduced and modeled with linear motion boundary conditions enforced. Finite element analysis demonstrates a mean model error of 0.86% for these metrics across many flexure topologies. Experimental testing is performed to validate the force-deflection response of three steel serpentine compliant mechanisms. The model is able to predict the experimental stiffness data with a mean error at yield of 5.3%, compared to 6.5% with finite element analysis. Large displacement simulations show the model could remain below 10% error for deflections 3-7 times beyond the mechanisms' deflection at yield. Finally, the model's utility is demonstrated in the design of a novel single-piece compliant fracture fixation plate that leverages serpentine flexures to deliver controlled axial motion for long bone secondary healing. Model-derived stress-equivalent flexures are compared in their transverse and torsional rigidity. The proposed model and specific findings can be leveraged to design linear motion mechanisms that incorporate serpentine flexures across a wide range of applications.