Extended Dynamic Stiffness Model for Analyzing Flexure-Hinge Mechanisms With Lumped Compliance

This paper introduces an extended dynamic stiffness modeling approach for concurrent kinetostatic and dynamic analyses of planar flexure-hinge mechanisms with lumped compliance. First, two novel dynamic stiffness matrices are derived for two types of flexure hinge connected to rigid bodies by shifting the end node to the mass center of rigid bodies considering the geometric effect of rigid motion. A straightforward modeling procedure is then proposed for the whole compliant mechanism based on d'Alembert's principle by selecting the displacements at both the mass center of rigid bodies and the rest end nodes of flexure hinges as the hybrid state variables. With the presented method, the statics and dynamics of flexure-hinge mechanisms with irregular-shaped rigid bodies in complex serial-parallel configurations can be analyzed in a concise form. The presented method is compared with other theoretical models, finite element simulation, and experiments for three case studies of a bridge-type compliant mechanism, a leveraged XY precision positioning stage, and a Scott–Russell-mechanism-based XYθ flexure manipulator. The results reveal the easy operation and well prediction accuracy of the presented method.