Analytical Modeling and Analysis of an Annulus-Shaped Flexural Pivot

2012 ◽  
Author(s):  
Yanbin Yao ◽  
Shusheng Bi ◽  
Hongzhe Zhao
Keyword(s):  
Analytical Modeling ◽  
Compliant Mechanisms ◽  
Bending Moment ◽  
Vertical Force ◽  
Rotational Stiffness ◽  
Element Analysis ◽  
Rotational Angle ◽  
Modeling And Analysis ◽  
The Finite Element Analysis ◽  
Constraint Model

Annulus-shaped flexural pivots (ASFP), composed of three or more identical leaves that are symmetrically arrayed in an annulus, can be used widely in compliant mechanisms for their excellent performances. This paper proposes the accurate load-rotation models of ASFP with three straight leaves, which include the load cases of bending moment combined with horizontal force and vertical force. Firstly, the load-rotation models of ASFP are derived based on the Beam Constraint Model (BCM). Then, the rotational stiffness and buckling characteristics are analyzed based on the derived models. Finally, the accuracy of the models is validated by the finite element analysis (FEA). The relative error of the load-rotation models is within 7% for various load cases even if the rotational angle reaches 0.07 (4°). The results show that the models are accurate enough to be used for initial parametric designing of ASFP.

Deterministic Design for a Compliant Parallel Universal Joint With Constant Rotational Stiffness

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Yan Xie ◽  
Jingjun Yu ◽  
Hongzhe Zhao
Keyword(s):  
Compliant Mechanisms ◽  
Experimental Testing ◽  
Rotational Stiffness ◽  
Universal Joint ◽  
Element Analysis ◽  
Rotational Angle ◽  
Constant Stiffness ◽  
Stiffness Model ◽  
Stiffness Characteristics ◽  
Constraint Model

Compliant universal joints have been widely employed in high-precision fields due to plenty of good performance. However, the stiffness characteristics, as the most important consideration for compliant mechanisms, are rarely involved. In this paper, a deterministic design for a constraint-based compliant parallel universal joint with constant rotational stiffness is presented. First, a constant stiffness realization principle is proposed by combination of the freedom and constraint topology (FACT) method and beam constraint model (BCM) to establish a mapping relationship between stiffness characteristics and topology configurations. A parallel universal joint topology is generated by the constant stiffness realization principle. Then, the analytical stiffness model of the universal joint with some permissible approximations is formulated based on the BCM, and geometrical prerequisites are derived to achieve the desired constant rotational stiffness. After that, finite element analysis (FEA), experimental testing, and detailed stiffness analysis are carried out. It turns out that the rotational stiffness of the universal joint can keep constant with arbitrary azimuth angles even if the rotational angle reaches up to ±5 deg. Meanwhile, the acceptable relative errors of rotational stiffness are within 0.53% compared with the FEA results and 2.6% compared with the experimental results, which indicates the accuracy of the theoretical stiffness model and further implies the feasibility of constant stiffness realization principle on guiding the universal joint design.

The Accurate Modeling and Performance Analysis of Cross-Spring Pivot as a Flexure Module

2008 ◽  
Author(s):  
Hongzhe Zhao ◽  
Shusheng Bi ◽  
Jingjun Yu ◽  
Guanghua Zong
Keyword(s):  
Compliant Mechanisms ◽  
Bending Moment ◽  
Element Analysis ◽  
Rotational Angle ◽  
Rotational Displacement ◽  
Center Shift ◽  
Rotational Element ◽  
Displacement Behavior ◽  
And Performance ◽  
Relative Errors

The load-displacement behavior of a cross-spring pivot as a kind of rotational element or module in compliant mechanisms is a subject of keen interest for many researchers. The model allowing not only quick design but also characteristics capture is pursued. This paper addresses some accurate closed-form results via approximations. These expressions are simple for a designer to understand the parameters without resorting to a tedious iterative procedure. The rotational displacement and center shift of the pivot are analyzed both qualitatively and quantitatively, with a general-purposed load applied including bending moment, horizontal and vertical forces. Meanwhile, a concise expression for center shift without approximations is proposed. The validity of the model is verified by finite element analysis (FEA). The relative error of the rotational displacement is less than 1.8% even if the rotational angle reaches ±20° the relative errors for the two components of center shift are less than 6% and 4% respectively, in the case of typical but general configurations and loads.

Modeling of a Cartwheel Flexural Pivot

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Bi Shusheng ◽  
Zhao Hongzhe ◽  
Yu Jingjun
Keyword(s):  
Parametric Design ◽  
Bending Moment ◽  
Equivalent Model ◽  
Vertical Force ◽  
Element Analysis ◽  
Rotational Angle ◽  
Single Beam ◽  
Primary Motion ◽  
Center Shift ◽  
Parasitic Motion

A cartwheel flexural pivot has a small center shift as a function of loading and ease of manufacturing. This paper addresses an accurate model that includes the loading cases of a bending moment combined with both a horizontal force and a vertical force. First, a triangle flexural pivot is modeled as a single beam. Then, the model of cartwheel flexural pivot based on an equivalent model is developed by utilizing the results of the triangle pivot. The expressions for rotational displacement and center shift are derived to evaluate the primary motion and the parasitic motion; the maximum rotational angle is simply formulated to predicate the range of motion. Finally, the model is verified by finite element analysis. The relative error of the primary motion is less than 1.1% for various loading cases even if the rotational angle reaches ±20 deg, and the predicted errors for the two center shift components are less than 15.4% and 7.1%. The result shows that the model is accurate enough for designers to use for initial parametric design studies, such as for conceptual design.

A decoupled flexure-based rotary micropositioning stage with compact size

2017 ◽  
Vol 232 (22) ◽  
pp. 4167-4179 ◽  
Author(s):  
Xiaobo Zhu ◽  
Zhijie Wen ◽  
Guozhen Chen ◽  
Jiaxin Liang ◽  
Pinkuan Liu
Keyword(s):  
Piezoelectric Actuator ◽  
Analytical Modeling ◽  
Rotational Stiffness ◽  
Element Analysis ◽  
Rotational Angle ◽  
Rotation Center ◽  
Working Space ◽  
Symmetric Configuration ◽  
Compact Size ◽  
Rotary Mechanism

This paper presents the design and analysis of a novel compact flexure-based rotary micropositioning stage driven by piezoelectric actuator. The developed stage possesses a double four-bar rotary mechanism with rotational symmetric configuration and totally kinematic decoupling, which can convert the linear motion of the piezoelectric actuator into the pure rotational motion, significantly minimizing the parasitic error at the rotation center. Based on the configuration, a single piezoelectric actuator is employed to drive the stage, avoiding actuator redundancy and large configuration size. Meanwhile, we introduce a compliant rotational guiding mechanism to enhance the rotational stiffness and dynamics of the stage. Analytical modeling and finite element analysis are adopted to facilitate the design of dimension. Finally, a prototype of the stage is manufactured and tested, which is capable of a rotational angle of [Formula: see text] with the first natural frequency of 430 Hz, whilst the well-constrained maximum center shift along the X- and Y-axis are 0.29 µm and 0.12 µm, respectively, indicating good decoupling capability. Furthermore, the compact size of [Formula: see text] is beneficial for limited working space.

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.

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.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

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.

scholarly journals A Review on Numerical Analysis of RC Flat Slabs Exposed to Fire

2020 ◽  
Vol 27 (1) ◽  
pp. 1-5
Author(s):  
Hanadi Naji ◽  
Nibras Khalid ◽  
Mutaz Medhlom
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Analysis ◽  
Bending Moment ◽  
Mechanical And Thermal Properties ◽  
Vertical Deflection ◽  
Element Analysis ◽  
Flat Slabs ◽  
Numerical Studies ◽  
The Finite Element Analysis

This paper aims at presenting and discussing the numerical studies performed to estimate the mechanical and thermal behavior of RC flat slabs at elevated temperature and fire. The numerical analysis is carried out using finite element programs by developing models to simulate the performance of the buildings subjected to fire. The mechanical and thermal properties of the materials obtained from the experimental work are involved in the modeling that the outcomes will be more realistic. Many parameters related to fire resistance of the flat slabs have been studied and the finite element analysis results reveal that the width and thickness of the slab, the temperature gradient, the fire direction, the exposure duration and the thermal restraint are important factors that influence the vertical deflection, bending moment and force membrane of the flat slabs exposed to fire. However, the validation of the models is verified by comparing their results to the available experimental date. The finite element modeling contributes in saving cost and time consumed by experiments.

scholarly journals Finite Element Analysis and Parametric Study of Spudcan Footing Geometries Penetrating Clay Near Existing Footprints

2019 ◽  
Vol 7 (6) ◽  
pp. 175 ◽  
Author(s):  
Long Yu ◽  
Heyue Zhang ◽  
Jing Li ◽  
Xian Wang
Keyword(s):  
Bending Moment ◽  
Vertical Force ◽  
Leg Length ◽  
Element Analysis ◽  
Centrifuge Tests ◽  
Flat Base ◽  
Key Factor ◽  
The Stability ◽  
Resultant Forces ◽  
Theoretical Analyses

Most existing research on the stability of spudcans during reinstallation nearing footprints is based on centrifuge tests and theoretical analyses. In this study, the reinstallation of the flat base footing, fusimform spudcan footing and skirted footing near existing footprints are simulated using the coupled Eulerian–Lagrangian (CEL) method. The effects of footprints’ geometry, reinstallation eccentricity (0.25D–2.0D) and the roughness between spudcan and soil on the profiles of the vertical force, horizontal force and bending moment are discussed. The results show that the friction condition of the soil–footing interface has a significant effect on H profile but much less effect on M profile. The eccentricity ratio is a key factor to evaluate the H and M. The results show that the geometry shape of the footing also has certain effects on the V, H, and M profiles. The flat base footing gives the lowest peak value in H but largest in M, and the performances of the fusiform spudcan footing and the skirted footing are similar. From the view of the resultant forces, the skirted footing shows a certain potential in resisting the damage during reinstallation near existing footprints by comparing with commonly used fusiform spudcan footings. The bending moments on the leg–hull connection section of different leg length at certain offset distances are discussed.

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