Comparative study on three matrix-based kinetostatic and dynamic modeling approaches for cartwheel flexure hinge

Flexure hinges are crucial in compliant mechanisms that transfer force and energy through elastic deformation. Research on flexure hinges with serial-parallel features and their simultaneous kinetostatic and dynamic modeling approaches remains limited. Therefore, it is crucial to develop a cohesive and concise theoretical framework for performance prediction. In this study, the cartwheel flexure hinge was chosen as the practical example that is widely used in many scientific and engineering applications. To address significant modeling errors caused by complex irregular connections of spatial flexures, a novel transfer matrix formulation for spatial flexure beam elements with non-collinear end nodes has been developed. This formulation is based on Taylor series expansions of both Bernoulli-Euler and Timoshenko beam theories. Then, a comparative study was conducted using three matrix-based modeling approaches, including the graphic transfer matrix method, the transfer matrix method, and the dynamic stiffness matrix method. These approaches were applied to simultaneously analyze both the kinetostatic and dynamic performances through a stylized analysis process. In detail, the closed-form equations of compliance, rotational precision, natural frequencies and dynamic compliance matrix were obtained. Lastly, detailed finite element simulations and experimental tests were conducted to verify the three matrix-based modeling approaches. The study focused on cartwheel flexure hinges connected with two types of right adjacent square beams of different sizes. An Insight into the dynamic compliance of flexure hinges, not limited to the cartwheel flexure hinge, is provided. This result, previously less studied, can help researchers better capture their dynamic characteristics.