Graphic Transfer Matrix Method for Kinetostatic and Dynamic Analyses of Compliant Mechanisms

Kinetostatic and dynamic analyses of compliant mechanisms with complex configurations continue to be an attractive issue for obtaining a process-concise and result-accurate solution. In this paper, the transfer matrix method (TMM) is improved for a unified linear kinetostatics and dynamic modeling of compliant mechanisms with complex serial-parallel configurations in an oriented graphic way. In detail, the transfer matrices of typical building blocks commonly used in compliant mechanisms are summarized and derived. Then, a graphic transfer matrix modeling procedure capturing both the kinetostatics and dynamics of general compliant mechanisms is introduced. The displacement amplification ratio, input/output stiffness, parasitic error, natural frequencies, and frequency response of a typical compliant microgripper and a planar parallel three-degrees-of-freedom (3DOF) nanopositioner are calculated with such a graphic transfer matrix method. The advantages of the proposed modeling method lie in its convenience and uniformity in formulating both the kinetostatic and dynamic behaviors of a class of compliant mechanisms with distributed and lumped compliances in a transfer matrix manner, which has minimal DOF and is easily programmed.