Modeling Large Spatial Deflections of Slender Bisymmetric Beams in Compliant Mechanisms Using Chained Spatial-Beam Constraint Model

Abstract

Modeling large spatial deflections of flexible beams has been one of the most challenging problems in the research community of compliant mechanisms. This work presents a method called chained spatial-beam constraint model (CSBCM) for modeling large spatial deflections of flexible bisymmetric beams in compliant mechanisms. CSBCM is based on the spatial-beam constraint model (SBCM), which was developed for the purpose of accurately predicting the nonlinear constraint characteristics of bisymmetric spatial beams in their intermediate deflection range. CSBCM deals with large spatial deflections by dividing a spatial beam into several elements, modeling each element with SBCM, and then assembling the deflected elements using the transformation defined by Tait–Bryan angles to form the whole deflection. It is demonstrated that CSBCM is capable of solving various large spatial deflection problems either the tip loads are known or the tip deflections are known. The examples show that CSBCM can accurately predict large spatial deflections of flexible beams, as compared to the available nonlinear finite element analysis (FEA) results obtained by ansys. The results also demonstrated the unique capabilities of CSBCM to solve large spatial deflection problems that are outside the range of ansys.

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

“…Zhao et al [246] developed the analytical static model for the Cartwheel flexure hinge while Malaeke and Moeenfard [245] investigated the mixed flexure-rigid-link mechanisms with the beam constraint model. Recently, Chen et al included the shear effect [98] and developed the beam constraint model for large-deflection analysis of planar and spatial flexure beams, namely, the chained beam constraint model [99,100], in which a flexible beam was divided into a few elements and each element was modeled by the beam constraint model. The secondorder Taylor series in the beam constraint model was expanded to the third order [247].…”

“…The beam constraint model was classified as an intermediate-range kinetostatic method of compliant mechanisms in "Handbook of Compliant Mechanisms" [97]. Afterward, this method was further enhanced by including shear effects [98] and extended for large-deflection analysis of flexure beams [99,100], namely, the chained beam constraint model.…”

Design and analysis of symmetric and compact 2R1T (in-plane 3-DOC) flexure parallel mechanisms

“…2). The stiffness matrix of each wire beam with regard to the local coordinate system is expressed as with d = 12/t 2 and δ = GJ /(EI ) = 1.69G/E in which J = 2.25T 4 /16 is the torsional constant considering warping (ignoring warping constraint) of square cross sections, and G is the shear modulus (Chen and Bai, 2016).…”

Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

“…In our previous work [17], general compliance equations that are symmetric with respect to the two dimensions were obtained to facilitate the design of torsional beams in compliant mechanisms. These equations had been used in characterizing parasitic motions of compliant mechanisms [18,19] and spatial deflections modeling [20][21][22]. However, there still lacks an equation for predicting the maximum stress in torsional beams that is symmetric with respect to the two dimensions.…”