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

Abstract

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 dynamics 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 3-DOF 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 degrees of freedom and is easily programmed.

A pseudo-rigid-body approach for determination of parasitic displacements of lumped compliant parallel-guiding mechanisms

“…In this way, the unwanted effects of friction, bucklash, and wear, which always appear during the exploitation of mechanisms with classic joints, were avoided. In the literature, various procedures have been developed for kinetostatic and dynamic analyses of compliant mechanisms such as the transfer matrix method [6][7][8][9][10], the dynamic stifness method [11,12], the beam theory based method [13][14][15], the pseudo-rigid-body model [16][17][18][19][20], the finite element method [21][22][23], the multi-compliant-body matrix method [24], the compliance matrix method [25][26][27], the Castigliano's second theorem based method [28], the unit-load method [29] etc. A survey of results, methods, and ongoing problems in compliant mechanisms research field was given in [30].…”