A Linear Scheme for the Displacement Analysis of Micropositioning Stages with Flexure Hinges

1994 ◽  
Vol 116 (3) ◽  
pp. 770-776 ◽  
Author(s):  
I. Her ◽  
J. C. Chang
Keyword(s):  
Stage Structure ◽  
Flexure Hinge ◽  
Element Analysis ◽  
Displacement Analysis ◽  
Constraint Equations ◽  
Flexure Hinges ◽  
Analytical Scheme ◽  
The Finite Element Analysis ◽  
Linear Scheme ◽  
Micropositioning Stages

In this paper we present an analytical scheme for the displacement analysis of micropositioning stages with flexure hinges. The proposed scheme is based on linearization of the geometric constraint equations of the stage structure. A design chart for evaluating the stiffness of the flexure hinge is also presented in this paper. This chart provides more accurate estimations than the design formula presently in use. The proposed linear scheme is general, easy to use, yet capable of obtaining results close to those obtained from the finite element analysis.

A Linear Scheme for the Displacement Analysis of Micropositioning Stages With Flexure Hinges

1994 ◽  
Author(s):  
I. Her ◽  
J. C. Chang
Keyword(s):  
Stage Structure ◽  
Flexure Hinge ◽  
Element Analysis ◽  
Displacement Analysis ◽  
Constraint Equations ◽  
Flexure Hinges ◽  
Analytical Scheme ◽  
The Finite Element Analysis ◽  
Linear Scheme ◽  
Micropositioning Stages

Abstract In this paper we present an analytical scheme for the displacement analysis of micropositioning stages with flexure hinges. The proposed scheme is based on linearization of the geometric constraint equations of the stage structure. A design chart for evaluating the stiffness of the flexure hinge is also presented in this paper. This chart provides more accurate estimations than the design formula presently in use. The proposed linear scheme is general, easy to use, yet capable of obtaining results close to those obtained from the finite element analysis.

An Empirically Determined Design Guideline for Rectangular Cross Section Nitinol Flexure Hinges With the Focus on Flexibility-Strength Trade-Off

2018 ◽  
Author(s):  
S. Coemert ◽  
M. Olmeda ◽  
J. Fuckner ◽  
C. Rehekampff ◽  
S. V. Brecht ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Cross Section ◽  
Electrical Discharge Machining ◽  
Rectangular Cross Section ◽  
Flexure Hinge ◽  
Element Analysis ◽  
Design Guideline ◽  
Trade Off ◽  
Flexure Hinges ◽  
Compliance Modeling

In our group, we are developing flexure hinge based manipulators made of nitinol for minimally invasive surgery. On the one hand, sufficient flexibility is required from flexure hinges to be able to cover the surgical workspace. On the other hand, the bending amount of the flexure hinges has to be limited below the yielding point to ensure a safe operation. As a result of these considerations, it has to be questioned how much bending angle a nitinol flexure hinge with given geometric dimensions can provide without being subject to plastic deformation. Due to the nonlinearities resulting from large deflections and the material itself, the applicability of the suggested approaches in the literature regarding compliance modeling of flexure hinges is doubtful. Therefore, a series of experiments was conducted in order to characterize the rectangular cross section nitinol flexure hinges regarding the flexibility-strength trade-off. The nitinol flexure hinge samples were fabricated by wire electrical discharge machining in varying thicknesses while keeping the length constant and in varying lengths while keeping the thickness constant. The samples were loaded and unloaded incrementally until deflections beyond visible plastic deformation occured. Each pose in loaded and unloaded states was recorded by means of a digital microscope. The deflection angles yielding to permanent set values corresponding to 0.1% strain were measured and considered as elastic limit. A quasilinear correlation between maximum elastic deflection angle and length-to-thickness ratio was identified. Based on this correlation, a minimal model was determined to be a limit for a secure design. The proposed guideline was verified by additional measurements with additional samples of random dimensions and finite element analysis.

scholarly journals Multi-objective optimization of a type of ellipse-parabola shaped superelastic flexure hinge

2016 ◽  
Vol 7 (1) ◽  
pp. 127-134 ◽  
Author(s):  
Zhijiang Du ◽  
Miao Yang ◽  
Wei Dong
Keyword(s):  
Compliant Mechanisms ◽  
Pareto Frontier ◽  
Flexure Hinge ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Element Analysis ◽  
Multi Objective ◽  
Flexure Hinges ◽  
Static Responses ◽  
Motion Range

Abstract. Flexure hinges made of superelastic materials is a promising candidate to enhance the movability of compliant mechanisms. In this paper, we focus on the multi-objective optimization of a type of ellipse-parabola shaped superelastic flexure hinge. The objective is to determine a set of optimal geometric parameters that maximizes the motion range and the relative compliance of the flexure hinge and minimizes the relative rotation error during the deformation as well. Firstly, the paper presents a new type of ellipse-parabola shaped flexure hinge which is constructed by an ellipse arc and a parabola curve. Then, the static responses of superelastic flexure hinges are solved via non-prismatic beam elements derived by the co-rotational approach. Finite element analysis (FEA) and experiment tests are performed to verify the modeling method. Finally, a multi-objective optimization is performed and the Pareto frontier is found via the NSGA-II algorithm.

Design of Contact-aided Compliant Flexure Hinge Mechanism Using Superelastic Nitinol

2021 ◽  
pp. 1-19
Author(s):  
Zhongyuan Ping ◽  
Tianci Zhang ◽  
Chi Zhang ◽  
Jianbin Liu ◽  
Siyang Zuo
Keyword(s):  
Compliant Mechanism ◽  
Nickel Titanium ◽  
Flexure Hinge ◽  
Maximum Strain ◽  
Clinical Value ◽  
Element Analysis ◽  
Flexure Hinges ◽  
Static Models ◽  
Flexible Instruments ◽  
Bending Behaviour

Abstract This paper presents a novel miniature contact-aided compliant mechanism (CCM) that includes flexure hinges and contact-aided structures. This continuum mechanism comprises a nickel–titanium alloy (Nitinol) tube with CCM cut via laser micromachining and actuated using wires bending from −80° to +80° in four directions. The proposed CCM has the following merits: perfect capacity for deflection around the centroid, a self-backbone, and improved torsional as well as tensile strengths. Further, it is pre-assembled. First, kinematic and static models are used to predict the bending behaviour of the mechanism. Thereafter, the maximum strain is evaluated using finite element analysis (FEA) then compared with the static models. Finally, the performances of the mechanism are characterized by experiments. The results validate the proposed models and demonstrate that the torsional and tensile strengths of the proposed CCM increased by more than 100% and 30%, respectively, compared with those of conventional non-CCMs with a similar fatigue life. Moreover, with the integrated forceps and probe, the proposed mechanism can achieve object transfer and square trajectory scanning of the targeted location. These experimental results demonstrate the potential clinical value of the proposed mechanism and provide important insights into the design of long and flexible instruments for endoscopic surgery.

scholarly journals Analysis of Bridge-type Distributed-compliance Mechanism

2018 ◽  
Vol 213 ◽  
pp. 01005
Author(s):  
Lei-Jie Lai ◽  
Xiao-Qia Yin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Analytical Model ◽  
Element Analysis ◽  
Amplification Ratio ◽  
Flexure Hinges ◽  
The Finite Element Analysis ◽  
Practical Design ◽  
Bridge Type ◽  
Compliance Mechanism

This paper analyses a class of bridge-type distributed-compliance mechanism, which has better performances than traditional bridge-type mechanisms using notch flexure hinges. An analytical model for the displacement amplification ratio and input stiffness calculations of the bridge-type mechanism is established based on the stiffness matrix method. The finite element analysis results are then given to validate the correctness of the analytical model. The differences of the analytical results with respect to the finite element analysis results are less than 8%, which demonstrate the high accuracy of the analytical model. The influences of the geometric parameters on the amplification ratio and input stiffness of the mechanism are also investigated using the analytical model to provide theoretical guidelines for the practical design.

Design of a New Compliant Mechanical Amplifier

2005 ◽  
Author(s):  
P. R. Ouyang ◽  
W. J. Zhang ◽  
M. M. Gupta
Keyword(s):  
Natural Frequencies ◽  
Lateral Displacement ◽  
Critical Parameters ◽  
Element Analysis ◽  
Amplification Ratio ◽  
Flexure Hinges ◽  
Compact Size ◽  
Double Beam ◽  
The Finite Element Analysis ◽  
Better Than

In this paper, a new topology that is a symmetric five bar profile for displacement amplification is proposed, and a compliant mechanical amplifier (CMA) based on the new topology is designed to amplify the stroke of a piezoelectric actuator. The new CMA can convert the motion generated by a PZT actuator with a large amplification ratio (24.4) in a very compact size, and it has a high natural frequency (573 Hz) and no lateral displacement. First, three existing topologies of CMA are analyzed and evaluated, which results in the new topology of CMA. After that, the new CMA is designed with different flexure hinges. The finite element analysis for the CMA shows that the double-beam symmetric five bar structure using the corner-filleted hinges can provide the best performance in terms of the displacement amplification and natural frequencies. The designed CMA is clearly better than the CMA based on the topology of a double symmetric four bar profile. Finally, the design is fine-tuned by examining critical parameters for the proposed CMA in light of a large displacement amplification ratio.

scholarly journals Analytical Compliance Equations of Generalized Elliptical-Arc-Beam Spherical Flexure Hinges for 3D Elliptical Vibration-Assisted Cutting Mechanisms

Materials ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 5928
Author(s):  
Han Wang ◽  
Shilei Wu ◽  
Zhongxi Shao
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Flexure Hinge ◽  
Matrix Formulation ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Flexure Hinges ◽  
Elliptical Vibration ◽  
Relative Standard ◽  
Cutting Mechanisms

Elliptical vibration-assisted cutting technology has been widely applied in complicated functional micro-structured surface texturing. Elliptical-arc-beam spherical flexure hinges have promising applications in the design of 3D elliptical vibration-assisted cutting mechanisms due to their high motion accuracy and large motion ranges. Analytical compliance matrix formulation of flexure hinges is the basis for achieving high-precision positioning performance of these mechanisms, but few studies focus on this topic. In this paper, analytical compliance equations of spatial elliptic-arc-beam spherical flexure hinges are derived, offering a convenient tool for analysis at early stages of mechanism design. The mechanical model of a generalized flexure hinge is firstly established based on Castigliano's Second Theorem. By introducing the eccentric angle as the integral variable, the compliance matrix of the elliptical-arc-beam spherical flexure hinge is formulated. Finite element analysis is carried out to verify the accuracy of the derived analytical compliance matrix. The compliance factors calculated by the analytical equations agree well with those solved in the finite element analysis for the maximum error; average relative error and relative standard deviation are 8.25%, 1.83% and 1.78%, respectively. This work lays the foundations for the design and modeling of 3D elliptical vibration-assisted cutting mechanisms based on elliptical-arc-beam spherical flexure hinges.

scholarly journals Compliance and Fatigue Life Analysis of U-shaped Flexure Hinge

Mechanika ◽  
2019 ◽  
Vol 25 (6) ◽  
pp. 501-510
Author(s):  
JingJing Liang ◽  
Rui Qin Li ◽  
Shao Ping Bai ◽  
Qing Li ◽  
Shu Hua Kang
Keyword(s):  
Fatigue Life ◽  
Major Axis ◽  
Flexure Hinge ◽  
Structure Parameters ◽  
Element Analysis ◽  
Flexure Hinges ◽  
Notch Width ◽  
Life Analysis ◽  
Fatigue Life Analysis ◽  
Close Form

This paper establishes four models of U-shaped flexure hinges with different notch shapes and structure parameters, and presents the close-form compliance equations for the four structure types of U-shaped flexure hinges. The compliance of the flexure hinges is developed based on the Castiglione’s second theorem and calculus theory. A relationship between compliances and structure parameters is deduced using the models. The influences of the notch structure parameters on the compliance of the flexure hinges are investigated. Moreover, fatigue life of U-shaped flexure hinges is studied by finite element analysis, the results show that the fatigue life of flexure hinge increases gradually with the increasing of flexure hinge center thickness t and hinge notch width m.  With the increasing of the major axis of the ellipse a and semi minor axis of the ellipse b, the fatigue life of flexure hinge fluctuates locally, the general trend is a gradual decrease. The stress and fatigue life of U-shaped flexure hinges and arc flexure hinge are compared. The results show that the reliability of U-shaped flexure hinge is higher than that of circular arc flexure hinge.

Optimization and Analysis of Z-Type Flexure Hinge Based on Workbench

2014 ◽  
Vol 668-669 ◽  
pp. 226-229
Author(s):  
Hui Xue Bao ◽  
Qiang Liu ◽  
Rong Qi Wang ◽  
Cheng Ming Zuo ◽  
Xiao Qin Zhou
Keyword(s):  
Compliant Mechanisms ◽  
Structural Parameters ◽  
Optimization Method ◽  
Optimal Parameters ◽  
Element Analysis ◽  
Flexure Hinges ◽  
Performance Indexes ◽  
The Finite Element Analysis ◽  
Critical Components ◽  
Significant Factors

Flexure hinges are regarded as the critical components of the compliant mechanisms, its performance is one of the significant factors which could directly determine the merits and demerits of designed compliant mechanisms. So how to optimize the flexure hinges becomes the key step in designing processes of compliant mechanisms. In view of the presented importance of flexure hinges, this paper proposes a sort of multi-objective optimization method which can rapidly analyze the sensitivity and interactional laws between the performance indexes and the structural parameters of flexure hinges with the Workbench software, then to select the optimal parameters by combining with the actual working conditions of flexure hinges. Finally the finite element analysis is employed to analyze the optimization results and verify the effectiveness of proposed optimization method.

scholarly journals New empirical stiffness equations for corner-filleted flexure hinges

2013 ◽  
Vol 4 (2) ◽  
pp. 345-356 ◽  
Author(s):  
Q. Meng ◽  
Y. Li ◽  
J. Xu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Large Deformation ◽  
Flexure Hinge ◽  
Minimum Thickness ◽  
Element Analysis ◽  
Flexure Hinges ◽  
Fillet Radius

Abstract. This paper investigates the existing stiffness equations for corner-filleted flexure hinges. Three empirical stiffness equations for corner-filleted flexure hinges (each fillet radius, r, equals to 0.1 l; l, the length of a corner-filleted flexure hinge) are formulated based on finite element analysis results for the purpose of overcoming these investigated limitations. Three comparisons made with the existing compliance/stiffness equations and finite element analysis (FEA) results indicate that the proposed empirical stiffness equations enlarge the range of rate of thickness (t, the minimum thickness of a corner-filleted flexure hinge) to length (l), t/l (0.02 ≤ t/l ≤ 1) and ensure the accuracy for each empirical stiffness equation under large deformation. The errors are within 6% when compared to FEA results.

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