Design, modeling and testing of a novel flexure-based displacement amplification mechanism

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

“…6.1 Lagrange-Based Methods. Over the past three decades, Lagrange-based dynamic modeling approaches have been developed for compliant mechanisms [113][114][115][116][117][118][119][120][121][122][123][124][125][126][127][128][129][130]. Generally speaking, the reported approaches can be roughly classified into three categories, as shown in Fig.…”

“…Dynamic Model. In the distributed-parameter model, the detailed DOFs of each flexure member or rigid-body member are taken as the variables, in which compliant mechanisms are usually discretized into several subelements and the dynamic model is established by formulating the total elastic and kinetic energies and combining them with Lagrange's equation [124][125][126][127][128][129][130]. In the literature, two different approaches can be found for the distributed-parameter dynamic formulation of compliant mechanisms, namely, the finite element method and a rigidmultibody-similar dynamic model introduced by Ryu et al [126].…”

“…On the other hand, the use of rigid-multibody-similar dynamic approach proposed by Ryu et al [126] seems to be a useful way because of its concise modeling procedure. This method was applied to the dynamic modeling of lumped compliant mechanisms or their composed flexure manipulators by several research groups [127][128][129][130][277][278][279]. As shown in Fig.…”

“…Two books in the field of compliant mechanisms [1,97] mainly involve the kinetostatic issue. To sum up, the previous dynamic modeling of compliant mechanisms was mainly based on Lagrange's method [113][114][115][116][117][118][119][120][121][122][123][124][125][126][127][128][129][130]. In recent years, some newly dynamic modeling approaches, such as the pseudorigid-body model with mass factors [108] and the dynamic stiffness modeling method based on d'Alembert's principle [18,131,132], were developed for the dynamic analysis of compliant mechanisms.…”

“…In the second category, the equivalent input/output stiffness of compliant mechanisms is first modeled by using a variety of kinetostatic methods, the dynamic model can be then formulated by calculating elastic and kinetic energies based on Lagrange's equation with motion degrees-offreedom (DOFs) as the variables, all these solutions can be classified as a lumped-parameter dynamic model [119][120][121][122][123]. 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].…”