Kinetostatic and dynamic analyses of planar compliant mechanisms via a two-port dynamic stiffness model

Serial-parallel configurations are widely designed in compliant mechanisms. In this paper, the transfer matrix method is combined with D'Alembert's principle to develop a two-port dynamic stiffness model for analyzing the kinetostatics and dynamics of complex compliant mechanisms with serial-parallel configurations. In detail, two kinds of improved transfer matrices for parallel sub-chains are derived in a unified form by summarizing the common serial-parallel substructures in compliant mechanisms. Then, a two-port dynamic stiffness model describing the frequency-dependent input and output force-displacement relationship of compliant mechanisms is established. Based on the two-port dynamic stiffness model, procedures for solving the static and dynamic performances of compliant mechanisms are presented. The proposed approach is demonstrated by calculating the displacement amplification ratio, input/output stiffness, natural frequencies and forced dynamic response of two typical precision flexure manipulators. The advantage of the proposed approach lies in its capability to describe the simultaneous kinetostatics and dynamics for a large class of serial-parallel configurations with very few degrees of freedom (DOFs), differing from the previous Lagrange-based dynamic modeling methods in the context of compliant mechanisms and should be of interest to designers.