Modeling and Analysis of Beam Flexure Based Double Parallel Guiding Mechanisms: A Modified Pseudo-Rigid-Body Approach

2016 ◽  
Author(s):  
Pengbo Liu ◽  
Peng Yan
Keyword(s):  
Rigid Body ◽  
Axial Force ◽  
Compliant Mechanisms ◽  
Parametric Method ◽  
Nonlinear Effects ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
Design And Optimization ◽  
Accurate Model ◽  
Characteristic Radius

In the present paper, we take the complaint double parallel guiding mechanism as a particular case study to investigate a modified pseudo-rigid-body (MPRB) modeling approach for beam flexure based mechanisms by considering the nonlinear effects of the center-shift and the load-stiffening. In particular, through incorporating the elastic stretch of the beam flexure into the linear Bernoulli-Euler equation, a more accurate model of the beam flexure is derived. Accordingly an MPRB model for a beam flexure is established, which consists of two rigid links joined at a revolute joint and a torsional spring along the beam. Different from traditional PRB model, the location of the torsion spring is not only determined by the characteristic radius factor, but also a purely elastic stretch under the action of the axial force. Meanwhile, both the characteristic radius factor and the equivalent stiffness of the beam flexure are no longer constant values, but affected by the applied general tip load, especially the axial force. Based on the analysis results of a beam flexure, we obtain a more accurate model of the double parallel guiding mechanisms, which is further verified by the finite element analysis (FEA) results. The proposed MPRB model provides a more parametric method to predict the performance characteristics such as deformation capability, stiffness variation, as well as error motions of the beam flexure based complaint mechanisms, and offers a new look into the design and optimization of beam-based compliant mechanisms.

scholarly journals A modified pseudo-rigid-body modeling approach for compliant mechanisms with fixed-guided beam flexures

2017 ◽  
Vol 8 (2) ◽  
pp. 359-368 ◽  
Author(s):  
Pengbo Liu ◽  
Peng Yan
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Nonlinear Effects ◽  
Accurate Method ◽  
Element Analysis ◽  
Design And Optimization ◽  
Modeling Approach ◽  
The Finite Element Analysis ◽  
Constraint Model ◽  
Translational Mechanisms

Abstract. In the present paper, we investigate a modified pseudo-rigid-body (MPRB) modeling approach for compliant mechanisms with fixed-guided beam flexures by considering the nonlinear effects of center-shifting and load-stiffening. In particular, a fixed-guided compliant beam is modeled as a pair of fixed-free compliant beams jointed at the inflection point, where each fixed-free beam flexure is further modeled by a rigid link connected with an extension spring by a torsion spring, based on the beam constraint model (BCM). Meanwhile, the characteristic parameters of the proposed MPRB model are no longer constant values, but affected by the applied general tip load, especially the axial force. The developed MPRB modeling method is then applied to the analysis of three common compliant mechanisms (i.e. compound parallelogram mechanisms, bistable mechanisms and 1-DOF translational mechanisms), which is further verified by the finite element analysis (FEA) results. The proposed MPRB model provides a more accurate method to predict the performance characteristics such as deformation capability, stiffness variation, as well as error motions of complaint mechanisms with fixed-guided beam flexures, and offers a new look into the design and optimization of beam-based compliant mechanisms.

Modeling and Analysis of Leaf Spring Based Double Parallel-Guiding Mechanism Considering Thermal Effect

2019 ◽  
Author(s):  
Shuaishuai Lu ◽  
Peng Yan
Keyword(s):  
Thermal Effect ◽  
Temperature Variation ◽  
Compliant Mechanisms ◽  
Parametric Method ◽  
Leaf Spring ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
Constraint Model ◽  
And Control

Abstract In the present paper, we take the leaf spring based double parallel-guiding mechanism (DPGM) as a particular case study to investigate a parametric model by considering the stress stiffening effect of the temperature variation based on the beam constraint model (BCM). In particular, a model with the temperature variation term of the DPGM is derived by incorporating the elastic stretch induced by the thermal effect of the leaf spring flexure into the BCM. Different from the traditional BCM, the compliance calculated by the established model is no longer only affected by the external loads, but the thermal deformation generated by the temperature variation. Therefore the derived model can describe both the load-nonlinearity and the thermal-nonlinearity. Based on the analysis results of a basic parallelogram module (BPM), we obtain a model of the DPGM, and the finite element analysis (FEA) method is adopted to verify the proposed model. The proposed model is a general parametric method to characterize the mechanical property of the DPGM, which can be further explored to support the optimization and control of motion systems composed of leaf spring based compliant mechanisms.

Pseudo-rigid-body dynamic modeling and analysis of compliant mechanisms

2017 ◽  
Vol 232 (9) ◽  
pp. 1665-1678 ◽  
Author(s):  
Yue-Qing Yu ◽  
Qian Li ◽  
Qi-Ping Xu
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Dynamic Models ◽  
Compliant Mechanisms ◽  
Lagrange Equation ◽  
Dynamic Responses ◽  
Modeling And Analysis ◽  
Rigid Body Dynamic ◽  
Body Dynamic

An intensive study on the dynamic modeling and analysis of compliant mechanisms is presented in this paper based on the pseudo-rigid-body model. The pseudo-rigid-body dynamic model with single degree-of-freedom is proposed at first and the dynamic equation of the 1R pseudo-rigid-body dynamic model for a flexural beam is presented briefly. The pseudo-rigid-body dynamic models with multi-degrees-of-freedom are then derived in detail. The dynamic equations of the 2R pseudo-rigid-body dynamic model and 3R pseudo-rigid-body dynamic model for the flexural beams are obtained using Lagrange equation. Numerical investigations on the natural frequencies and dynamic responses of the three pseudo-rigid-body dynamic models are made. The effectiveness and superiority of the pseudo-rigid-body dynamic model has been shown by comparing with the finite element analysis method. An example of a compliant parallel-guiding mechanism is presented to investigate the dynamic behavior of the mechanism using the 2R pseudo-rigid-body dynamic model.

Application of Rigid-Body-Linkage Static Balancing Techniques to Reduce Actuation Effort in Compliant Mechanisms

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Sangamesh R. Deepak ◽  
Amrith N. Hansoge ◽  
G. K. Ananthasuresh
Keyword(s):  
Rigid Body ◽  
General Framework ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Small Length ◽  
Element Analysis ◽  
Static Balancing ◽  
Free Length ◽  
First Order ◽  
Taylor’S Series

There are analytical methods in the literature where a zero-free-length spring-loaded linkage is perfectly statically balanced by addition of more zero-free-length springs. This paper provides a general framework to extend these methods to flexure-based compliant mechanisms through (i) the well know small-length flexure model and (ii) approximation between torsional springs and zero-free-length springs. We use first-order truncated Taylor's series for the approximation between the torsional springs and zero-free-length springs so that the entire framework remains analytical, albeit approximate. Three examples are presented and the effectiveness of the framework is studied by means of finite-element analysis and a prototype. As much as 70% reduction in actuation effort is demonstrated. We also present another application of static balancing of a rigid-body linkage by treating a compliant mechanism as the spring load to a rigid-body linkage.

Using Rigid-Body Mechanism Topologies to Design Shape-Changing Compliant Mechanisms

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Shape Matching ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Shape Change ◽  
Mesh Network ◽  
Adaptive Antenna ◽  
Optimal Size ◽  
Dimensional Synthesis ◽  
Element Analysis

This paper uses rigid-body mechanism topologies to synthesize fully distributed compliant mechanisms that approximate a shape change defined by a set of morphing curves in different positions. For a shape-change problem, a rigid-body mechanism solution is generated first to provide the base topology. This base topology defines a preselected design space for the structural optimization in one of two ways so as to obtain a compliant mechanism solution that is typically superior to the local minimum solutions obtained from searching more expansive design spaces. In the first strategy, the dimensional synthesis directly determines the optimal size and shape of the distributed compliant mechanism having exactly the base topology. In the second strategy, an initial mesh network established from the base topology is used to generate different topologies (in addition to the base), and an improved design domain parameterization scheme ensures that only topologies with well-connected structures are evaluated. The deformation of each generated compliant mechanism is evaluated using geometrically nonlinear finite element analysis (FEA). A two-objective genetic algorithm (GA) is employed to find a group of viable designs that trade off minimizing shape matching error with minimizing maximum stress. The procedure's utility is demonstrated with three practical examples—the first two approximating open-curve profiles of an adaptive antenna and the third approximating closed-curve profiles of a morphing wing.

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.

Design of a Compliant Endoscopic Suturing Instrument

2008 ◽  
Vol 2 (2) ◽  
Author(s):  
James A. Cronin ◽  
Mary I. Frecker ◽  
Abraham Mathew
Keyword(s):  
Finite Element Analysis ◽  
Minimally Invasive Surgery ◽  
Compliant Mechanisms ◽  
Stress Relief ◽  
Natural Orifice ◽  
Endoscopic Suturing ◽  
Element Analysis ◽  
Design And Optimization ◽  
Puncture Force ◽  
Nonlinear Deformations

This paper describes the initial design and optimization of a compliant endoscopic suturing instrument. The emerging field of Natural Orifice Transluminal Endoscopic Surgery (NOTES) requires innovative instruments to meet the size limitations inherent in this type of minimally invasive surgery; using compliant mechanisms is proposed as one method of meeting this requirement. The compliant design was modeled and optimized to maximize the distal opening and provide a puncture force of at least 4.6N, while being small enough to fit within a 3.3mm working channel. The design utilizes contact for stress relief and intertwining parts for added deflection. ANSYS® was used for finite element analysis including contact and nonlinear deformations. A prototype was fabricated from the optimized geometry and experimentally tested. The best geometry is predicted to have a distal opening of 14.6mm at the tips and supply a puncturing force of 4.83N. The force supplied at the tip was measured and was found to exceed the required 4.6N. The prototype successfully passed two complete sutures and qualitative results are provided. The results of the study will lead to further refinements and improvements in future designs.

The Analysis of a Simplified 2R Pseudo-Rigid-Body Model with Moment Load

2012 ◽  
Vol 224 ◽  
pp. 18-23
Author(s):  
Yun Jiao Zhang ◽  
Guo Wu Wei ◽  
Jian Sheng Dai
Keyword(s):  
Rigid Body ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Three Dimensional ◽  
Body Model ◽  
Design Variables ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Moment Load

Pseudo-rigid-body model (PRBM) method, which simplifies the geometrical nonlinear analysis, has become an important tool for the analysis and synthesis of compliant mechanisms. In this paper, a simplified 2R PRBM with two rigid links and two torsion springs is proposed. The characteristic radius factor and stiffness coefficients are selected as the design variables; in order to be better to simulate the tip point and tip slope, a three-dimensional objective function is formulated to optimize the new pseudo-rigid-body model. It is revealed in this paper that the precision of the tip point simulation can be improved when the coefficient of the tip slope error in the objective function is reduced.

Design of a Continuum Mechanism that Matches the Movement of an Eight-bar Linkage

2020 ◽  
pp. 1-11
Author(s):  
Xueao Liu ◽  
J. Michael McCarthy
Keyword(s):  
Finite Element Analysis ◽  
Rigid Body ◽  
Design Methodology ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Initial Structure ◽  
Element Analysis ◽  
Kinematic Synthesis ◽  
Generic Structure ◽  
Straight Line

Abstract This paper presents a design methodology for mechanisms consisting of a single continuous structure, continuum mechanisms, that blends the kinematic synthesis of rigid-body mechanisms with topology optimization for compliant mechanisms. Rather than start with a generic structure that is shaped to achieve a required force deflection task for a compliant mechanism, our approach shapes the initial structure based on kinematic synthesis of a rigid body mechanism for the required movement, then the structure is shaped using Finite Element Analysis to achieve the required force deflection relationship. The result of this approach is a continuum mechanism with the same workpiece movement as the rigid link mechanism when actuated. An example illustrates the design process to obtain an eight-bar linkage that guides its workpiece in straight-line rectilinear movement. We show that the resulting continuum mechanism provides the desired rectilinear movement. A 210 mm physical model machined from Nylon-6 is shown to achieve 21.5mm rectilinear movement with no perceived deviation from a straight-line.

The Stiffness Model of Leaf-Type Isosceles-Trapezoidal Flexural Pivots

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Pei Xu ◽  
Yu Jingjun ◽  
Zong Guanghua ◽  
Bi Shusheng
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Rigid Body ◽  
Compliant Mechanisms ◽  
Nonlinear Finite Element Analysis ◽  
Nonlinear Finite Element ◽  
Leaf Segment ◽  
Element Analysis ◽  
Leaf Type ◽  
Stiffness Model

A leaf-type isosceles-trapezoidal flexural pivot can be of great practical use for designing compliant mechanisms. The analysis of load-deflection behavior for such a pivot is essential to the study of the mechanisms that are comprised of them. Based on the analysis of a single special loaded leaf segment, a pseudo-rigid-body four-bar model is proposed. The four-bar model is further simplified to a pin-joint model for some simple applications. The accuracy of both models is demonstrated by comparing results to those of nonlinear finite element analysis. At last, the two models are applied to analyze the cartwheel hinge as an example.

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