Chained Beam-Constraint-Model (CBCM): A Powerful Tool for Modeling Large and Complicated Deflections of Flexible Beams in Compliant Mechanisms

2014 ◽  
Author(s):  
Fulei Ma ◽  
Guimin Chen
Keyword(s):  
Large Deflection ◽  
Compliant Mechanisms ◽  
Research Community ◽  
The Other ◽  
New Method ◽  
Flexible Beam ◽  
Large Deflections ◽  
Flexible Beams ◽  
Constraint Model

Modeling large deflections has been one of the most fundamental problems in the research community of compliant mechanisms. Although many methods are available, there still exists a need for a method that is simple, accurate, and can be applied to a vast variety of large deflection problems. Based on the beam constraint model (BCM), we propose a new method for modeling large deflections called chained BCM (CBCM), which divides a flexible beam into a few elements and models each element by BCM. It is demonstrated that CBCM is capable of modeling various large and complicated deflections of flexible beams in compliant mechanisms. In general, CBCM obtains accurate results with no more than 6 BCM elements, thus is more efficient than most of the other discretization-based methods.

Modeling Large Planar Deflections of Flexible Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Fulei Ma ◽  
Guimin Chen
Keyword(s):  
Strain Energy ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Research Community ◽  
New Method ◽  
Flexible Beam ◽  
Large Deflections ◽  
Flexible Beams ◽  
Versatile Tool ◽  
Constraint Model

Modeling large deflections has been one of the most fundamental problems in the research community of compliant mechanisms. Although many methods are available, there still exists a need for a method that is simple, accurate, and can be applied to a vast variety of large deflection problems. Based on the beam-constraint model (BCM), we propose a new method for modeling large deflections called chained BCM (CBCM), which divides a flexible beam into a few elements and models each element by BCM. The approaches for determining the strain energy stored in a deflected beam and the stress distributed on it are also presented within the framework of CBCM. Several typical examples were analyzed and the results show CBCMs capabilities of modeling various large deflections of flexible beams in compliant mechanisms. Generally, CBCM can serve as an efficient and versatile tool for solving large deflection problems in a variety of compliant mechanisms.

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

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Guimin Chen ◽  
Ruiyu Bai
Keyword(s):  
Finite Element Analysis ◽  
Compliant Mechanisms ◽  
Research Community ◽  
Nonlinear Finite Element ◽  
Nonlinear Constraint ◽  
Element Analysis ◽  
Flexible Beams ◽  
Spatial Beams ◽  
Spatial Beam ◽  
Constraint Model

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.

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

2015 ◽  
Author(s):  
Guimin Chen ◽  
Ruiyu Bai
Keyword(s):  
Compliant Mechanisms ◽  
Research Community ◽  
Nonlinear Constraint ◽  
Flexible Beams ◽  
Spatial Beams ◽  
Spatial Beam ◽  
Constraint Model

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 whether the tip loads are known or the tip deflections are known. The examples show that CSBCM can accurately predict the large spatial deflections of flexible beams, as compared to the available nonlinear 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.

scholarly journals A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
N. Tolou ◽  
J. L. Herder
Keyword(s):  
Cantilever Beam ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Geometrical Nonlinearity ◽  
Adomian Decomposition Method ◽  
Analytical Form ◽  
Point Load ◽  
Large Deflections ◽  
Adomian Decomposition

The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

Kinematic Synthesis of Planar, Shape-Changing Compliant Mechanisms Using Pseudo-Rigid-Body Models

2012 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Flexible Beam ◽  
Beam Model ◽  
Flexible Beams ◽  
Multi Objective Genetic Algorithm ◽  
Optimization Loop

This paper presents a procedure using Pseudo-Rigid-Body Models (PRBMs) to synthesize partially compliant mechanisms capable of approximating a shape change defined by a set of morphing curves in different positions. To generate a single-piece compliant mechanism, flexural pivots and flexible beams are both utilized in the mechanism. New topologies defined by compliant mechanism matrices are enumerated by modifying the components that make up a single degree-of-freedom (DOF) rigid-body mechanism. Because of the introduction of the PRBM for flexural pivots and the simplified PRBM for flexible beams, torsional springs are attached at the characteristic pivots of the 1-DOF rigid-body mechanism in order to generate a corresponding pseudo-rigid-body mechanism. A multi-objective genetic algorithm is employed to find a group of viable compliant mechanisms in the form of candidate pseudo-rigid-body mechanisms that tradeoff minimizing shape matching error with minimizing actuator energy. Since the simplified beam model is not accurate, an optimization loop is established to find the position and shape of the flexible beam using a finite link beam model. The optimal flexible beams together with the pseudo-rigid-body mechanism define the solution mechanism. The procedure is demonstrated with an example in which a partially compliant mechanism approximating two closed-curve profiles is synthesized.

A Load Independent Pseudo-Rigid-Body 3R Model for Determining Large Deflection of Beams in Compliant Mechanisms

2008 ◽  
Author(s):  
Hai-Jun Su
Keyword(s):  
Rigid Body ◽  
Numerical Integration ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Three Dimensional ◽  
Flexible Beams ◽  
Fea Model ◽  
Revolute Joints ◽  
Characteristic Radius ◽  
Key Steps

Modeling flexible beams that undergo large deflection is one of the key steps in analyzing and synthesizing compliant mechanisms. Geometric nonlinearities introduced by large deflections often complicate the analysis of mechanism systems comprising such members. Several pseudo-rigid-body (PRB) or multi segment models in the literature have been proposed to approximate the tip deflection and slope. However these models are either dependent on external loads or too complicated to analyze. They are neither appropriate for analyzing mechanisms in which loads change significantly as they move, nor for synthesizing mechanisms where a parametric model is preferred. In this paper, a load independent PRB 3R model which comprises of four rigid links joined by three revolute joints and three torsion springs is proposed. The traditional PRB 1R models are first studied for both small deflection beams and large deflection beams. These studies provide fundamental insights to the geometric nonlinearity of large deflection beams. Numerical integration is applied to compute tip deflections for various loads. A three-dimensional search routine has been developed to find the optimal set of characteristic radius factors for the proposed PRB 3R model. Detailed error analysis and comparison against the result by the numerical integration and the PRB 1R model are accomplished for different load modes. The benefits of the PRB 3R model include (a) high accuracy for large deflection beams, (b) load independence which is critical for applications where loads vary significantly and (c) explicit kinematic and static constraint equations derived from the model. To demonstrate the use of the PRB 3R model, a compliant 4-bar linkage is studied and verified by a numerical example. The result shows a maximum tip deflection error of 1.2% compared with the FEA model.

Mathematical Model for Large Deflection Dynamics of a Compliant Beam Device

1999 ◽  
Vol 123 (2) ◽  
pp. 283-288 ◽  
Author(s):  
Michael J. Panza
Keyword(s):  
Mathematical Model ◽  
Large Deflection ◽  
The Other ◽  
Flexible Beam ◽  
Static Deflection ◽  
System Behavior ◽  
Mass System ◽  
Curved Space ◽  
Compliant Motion ◽  
Rotating Hinge

A mathematical model for the large deflection dynamics of a compliant beam device is presented. The device simulates the motion of a slider-crank device. The system contains a highly flexible beam that provides the compliant motion from a sliding mass at one end to a rotating hinge point at the other end. Basic models for friction and beam dissipation effects are included. A nonlinear integro-partial differential equation is derived for the complete beam/mass system in the curved space of the deformed beam. The resulting equation is cast into a generalized nondimensional form suitable for studying system behavior for a broad range of system sizes. The dynamic equation is solved in curved space by applying a spatial solution that closely represents the large static deflection measured for the beam. The nonlinear system dynamics are simulated for an initial large deflection of the system and compared to experimental results for an actual physical system.

Bi-BCM: A Closed-Form Solution for Fixed-Guided Beams in Compliant Mechanisms

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Fulei Ma ◽  
Guimin Chen
Keyword(s):  
Closed Form ◽  
Compliant Mechanisms ◽  
Closed Form Solution ◽  
Form Solution ◽  
The Other ◽  
Boundary Line ◽  
Final Solution ◽  
Second Mode ◽  
Design Calculations ◽  
Constraint Model

A fixed-guided beam, with one end is fixed while the other is guided in that the angle of that end does not change, is one of the most commonly used flexible segments in compliant mechanisms such as bistable mechanisms, compliant parallelogram mechanisms, compound compliant parallelogram mechanisms, and thermomechanical in-plane microactuators. In this paper, we split a fixed-guided beam into two elements, formulate each element using the beam constraint model (BCM) equations, and then assemble the two elements' equations to obtain the final solution for the load–deflection relations. Interestingly, the resulting load–deflection solution (referred to as Bi-BCM) is closed-form, in which the tip loads are expressed as functions of the tip deflections. The maximum allowable axial force of Bi-BCM is the quadruple of that of BCM. Bi-BCM also extends the capability of BCM for predicting the second mode bending of fixed-guided beams. Besides, the boundary line between the first and the second modes bending of fixed-guided beams can be easily obtained using a closed-form equation. Bi-BCM can be immediately used for quick design calculations of compliant mechanisms utilizing fixed-guided beams as their flexible segments (generally no iteration is required). Different examples are analyzed to illustrate the usage of Bi-BCM, and the results show the effectiveness of the closed-form solution.

An Elliptic Integral Solution to the Multiple Inflections Large Deflection Beams in Compliant Mechanisms

2014 ◽  
Vol 971-973 ◽  
pp. 349-352 ◽  
Author(s):  
Jiang Yong Song
Keyword(s):  
Euler Equations ◽  
Inflection Point ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Accurate Method ◽  
Integral Solution ◽  
Large Deflections ◽  
Cantilever Beams ◽  
Inflection Points

In this paper, a solution based on the elliptic integrals is proposed for solving multiples inflection points large deflection. Application of the Bernoulli Euler equations of compliant mechanisms with large deflection equation of beam is obtained ,there is no inflection point and inflection points in two cases respectively. The elliptic integral solution which is the most accurate method at present for analyzing large deflections of cantilever beams in compliant mechanisms.

Kinetostatic Modeling of Planar Compliant Mechanisms with Flexible Beams, Linear Sliders, Multinary Rigid Links and Multiple Loops

2021 ◽  
pp. 1-18
Author(s):  
I-Ting Chi ◽  
Pei-Lun Chang ◽  
Ngoc Dang Khoa Tran ◽  
Dung-An Wang
Keyword(s):  
Finite Element ◽  
Compliant Mechanisms ◽  
Building Blocks ◽  
Static Equilibrium ◽  
Finite Element Analyses ◽  
Equilibrium Conditions ◽  
Flexible Beams ◽  
Beam Type ◽  
Constraint Model

Abstract This paper presents kinetostatic models of planar compliant mechanisms with multinary rigid links, multinary joints, sliders and multiple loops based on the chained beam constraint model. The focus is on modelling of several building blocks of the beam type compliant mechanisms to aid in their design. The modelling approaches are based on the loop closure equations and the static equilibrium conditions. Models of the multinary rigid links, multinary joints, sliders are presented. As a result, the kinetostatic models of the compliant mechanisms can be systematically formulated by using these building blocks. Several mechanisms constructed by the building blocks are modelled and verified by finite element analyses. A case study is provided to demonstrate the application of the developed models. These models pave the way for versatile applications of the chained beam constraint model for the design and analysis of beam type planar compliant mechanisms.

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