A semi-analytical modeling method for the static and dynamic analysis of complex compliant mechanism

Dynamic Analysis of a 5‐DOF Flexure‐Based Nanopositioning Stage

“…It can be found from Table 3 that FEA results are well in agreement with experimental test results, but the analytical modal results have larger difference. The reason is that the proposed multibody dynamic model only takes into account the flexibilities of flexure hinges [26]. Although the analytical modal results are mostly well in agreement with FEA and experimental test results, the errors of lower order modal frequencies are less than the higher order modal frequencies, up to about 20%.…”

“…In PRBM, a flexure hinge is considered as a single DOF rotation joint; the cross-axis coupling is naturally neglected, which may cause noticeable errors of modal frequencies between the analytical and experimental results [20][21][22][23][24][25]. Ling [26] presented three criteria to perform dynamic modeling with high accuracy and efficiency and proposed a semianalytical modeling method considering the compliances of the flexure hinges as well as the flexible beams. Considering the 5-DOF nanopositioning stage as an assembly of rigid bodies interconnected by elastic flexure hinges, multibody system approach is suitable to model such system [6,16,27].…”

Kinetostatic and Dynamic Modeling of Flexure-Based Compliant Mechanisms: A Survey

“…The finite element method can deal with complex geometric shapes by discretizing the structure into small elements. Kinetostatic and dynamic modeling of small-deflection compliant mechanisms based on the finite element method is easy to be implemented [92,125]. However, formulizing the global stiffness matrix will become complicated with time-consuming iterative computations for nonlinear large-deflection analysis.…”

“…The theoretical compliance matrix of circular flexure hinges was converted into the elemental stiffness matrix in the framework of the finite element method in 2008 [90]. With similar conversion formulas, the kinetostatic and dynamic modeling of all kinds of flexure-hingebased compliant mechanisms were carried out based on the finite element method without dealing with the complicated issue of variable cross section in flexure hinges [91,92]. [2,5,51,52] (Reprinted with permission from Wang and Xu [2].…”

“…The third category is termed the distributed-parameter model with finite number of DOFs [124][125][126][127][128][129][130][131][132], in which compliant mechanisms are usually discretized into several submembers and the dynamic model is established by calculating total elastic and kinetic energies. For example, a method similar to the rigid-multibody dynamics [19,126] was used to design flexure manipulators by several groups [127][128][129][130]; moreover, various finite element dynamic models have been developed in the last decades [92,124,125].…”