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. Firstly, two novel dynamic stiffness matrices are derived for a flexure hinge connected to rigid bodies by shifting its end node to the mass centre of rigid bodies considering the geometric effect of rigid motion. A straightforward modeling procedure is then proposed for the whole compliant mechanism by selecting the displacements at both the mass centre of rigid bodies and the rest end nodes of flexure hinges as the hybrid state variables, differing from the traditional finite element method. With the presented approach, the statics and dynamics of flexure-hinge mechanisms with irregular-shaped rigid body in complex serial-parallel configurations can be analyzed in a concise form. At last, 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 XY𝑣 flexure manipulator. The results reveal the easy operation and satisfying prediction accuracy of the presented method.