Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Guimin Chen ◽  
Xiaoyuan Liu ◽  
Yunlei Du
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Single Type ◽  
Flexure Hinge ◽  
Circular Arc ◽  
Generalized Model ◽  
Percent Error ◽  
New Class ◽  
Flexure Hinges ◽  
Hinge Model

Flexure hinges have been used to produce frictionless and backlashless transmissions in a variety of precision mechanisms. Although there are many types of flexure hinges available, designers often chose a single type of flexure hinge (e.g., circular flexure hinges) without considering others in the design of flexure-based mechanisms. This is because the analytical equations are unique to each kind of flexure hinge. This work offers a solution to this problem in the form of a generalized flexure hinge model. We propose a new class of flexure hinges, namely, elliptical-arc-fillet flexure hinges, which brings elliptical arc, circular-arc-fillet, elliptical-fillet, elliptical, circular, circular-fillet, and right-circular flexure hinges together under one set of equations. The closed-form equations for all the elements in the compliance and precision matrices of elliptical-arc-fillet flexure hinges have been derived. The analytical results are within 10 percent error compared to the finite element results and within 8 percent error compared to the experimental results. The equations for evaluating the strain energy and stress level for elliptical-arc-fillet flexure hinges are also provided. This model can be used as a complementary model for the generalized model for conic flexure hinges.

scholarly journals Generalized model for conic-V-shaped flexure hinges

2020 ◽  
Vol 103 (4) ◽  
pp. 003685042098121
Author(s):  
Jianyi Kong ◽  
Zhao Huang ◽  
Xiaodong Xian ◽  
Yingrui Wang ◽  
Puliang Yu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Nonlinear Equations ◽  
Polar Coordinates ◽  
Generalized Equations ◽  
Element Analysis ◽  
Generalized Model ◽  
New Class ◽  
Flexure Hinges ◽  
Dimensional Parameters

This paper presents a new class of flexure hinges, namely, conic-V-shaped flexure hinges (CFHs), which can be used as a generalized model for flexure hinges with profiles such as parabolic-V-shape, elliptical-V-shape, and hyperbolic-V-shape. Compliance and precision equations for the CFHs were derived as a set of nonlinear equations using Castigliano’s second theorem. The parameters of the nonlinear equations inputted to the compliance and precision matrices were based on the generalized equations used for conic curves in polar coordinates. Furthermore, the compliance equations were verified by means of finite element analysis and experiments. The errors in the finite element and experimental results were within 10% and 8% compared to the analytical results, respectively. Finally, the effects of dimensional parameters on the analytical model could be effectively analyzed by numerical simulations and comparisons.

Dynamics of a compliant mechanism based on flexure hinges

2005 ◽  
Vol 219 (2) ◽  
pp. 225-235 ◽  
Author(s):  
K-B Choi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Compliant Mechanism ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
Flexure Hinge ◽  
Flexure Hinges ◽  
Better Than ◽  
Element Method

This paper presents a novel equation of motion for flexure hinge-based mechanisms. The conventional equation of motion presented in previous work does not adequately describe the behaviours of rigid bodies for the following reasons: firstly, rotational directions for a transformed stiffness lack consistency at the two ends of a flexure hinge; secondly, the length of the flexure hinge is not considered in the equation. The equation of motion proposed in this study solves these problems. Modal analyses are carried out using the proposed equation of motion, the conventional equation of motion found in previous work, and a finite element method. The results show that the proposed equation of motion describes the behaviours of the rigid bodies better than the conventional equation of motion does.

Corner-Filleted Flexure Hinges

2000 ◽  
Vol 123 (3) ◽  
pp. 346-352 ◽  
Author(s):  
Nicolae Lobontiu ◽  
Jeffrey S. N. Paine ◽  
Ephrahim Garcia ◽  
Michael Goldfarb
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Finite Element Simulation ◽  
Analytical Approach ◽  
Flexure Hinge ◽  
Closed Form Solutions ◽  
Flexure Hinges ◽  
Element Simulation ◽  
Model Predictions ◽  
The Right

The paper presents an analytical approach to corner-filleted flexure hinges. Closed- form solutions are derived for the in-plane compliance factors. It is demonstrated that the corner-filleted flexure hinge spans a domain delimited by the simple beam and the right circular flexure hinge. A comparison that is made with the right circular flexure hinges indicates that the corner-filleted flexures are more bending-compliant and induce lower stresses but are less precise in rotation. The finite element simulation and experimental results confirmed the model predictions.

Design and Performance Analysis of Double C-Type Flexure Hinges

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Lifang Qiu ◽  
Gang Huang ◽  
Siqi Yin
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Simulation Analysis ◽  
Flexure Hinge ◽  
Equivalent Stiffness ◽  
Bending Performance ◽  
Flexure Hinges ◽  
Element Simulation ◽  
And Performance ◽  
Better Than

This paper proposes a series of double C-type flexure hinges for lamina emergent mechanisms (LEMs), designs the structure, and deduces the formula of the equivalent stiffness of the double C-type flexure hinge. Theoretical calculation and finite element simulation analyses of the design examples are used to verify the correctness of the equivalent stiffness calculation formula. In order to improve the bending performance of the flexure hinges, we propose a method to remove some materials of the semicircle of the flexure hinges according to certain rules. Then, the structure of the double C-type flexure hinge is further improved. Finally, the performance of the improved and unimproved double C-type flexure hinges is compared through the finite element simulation analysis, and the results show that the bending performance of the improved double C-type flexure hinge is better than the unimproved double C-type flexure hinge, while the antitensile properties undergo no significant decline.

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 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.

Design and Optimization of a New Hollow Circular Flexure Hinge for Precision Mechanisms

2019 ◽  
Vol 889 ◽  
pp. 337-345 ◽  
Author(s):  
Van Khien Nguyen ◽  
Duy Luong Tuong ◽  
Huy Tuan Pham ◽  
Huy Hoang Pham
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Optimization Procedure ◽  
Longitudinal Axis ◽  
Maximum Load ◽  
Flexure Hinge ◽  
Element Analysis ◽  
Design And Optimization ◽  
Parasitic Motion ◽  
Flexure Hinges

Flexure hinges have been used in many precision mechanisms where repeatable, friction free motion and high precision are required. Many kinds of flexure profiles have been proposed during the past decade. This paper presents a new type of flexure hinge which combines circular longitudinal axis beams to form hollow joint. This novel design will help to improve the range of motion, reduce stress level and increase the maximum load before yielding. Due to its special design, the cavity inside the hinge can also be filled with an elastomeric filler material to provide vibration damping. In order to synthesis this hinge, shape optimization integrating genetic algorithm and response surface methodology is used. The optimization procedure is programmed in MATLAB whereas finite element analysis in ANSYS is also embedded into the codes to enhance the calculation process. The new flexure hollow hinge is compared to the conventional straight-axis solid hinges (circular, elliptical and corner-filleted flexure hinges) in terms of stiffness, rotational precision and stress levels. It is also supposed that this new design would increase the precision of the mechanism due to reducing the parasitic motion. Finite element analysis in ANSYS is used to verify for the viability of the design before it can be fabricated and tested.

Parametric Study of Circular Micro Flexure Hinge Design

2006 ◽  
Author(s):  
Sarin Shrestha ◽  
Raymond K. Yee
Keyword(s):  
Finite Element ◽  
Parametric Study ◽  
Compliant Mechanism ◽  
Flexure Hinge ◽  
Finite Element Models ◽  
Maximum Output ◽  
Maximum Displacement ◽  
Output Displacement ◽  
Design Guide ◽  
Hinge Model

Compliant mechanism is a monolithic device that utilizes flexible elements, instead of pins, to transform the input to a useful output position, and flexure hinge is an integral part of a compliant mechanism. Flexure hinge design is important because it provides a means for motion actuation in a mechanism. An ideal design of a flexure hinge for a displacement output mechanism is that it provides maximum displacement output with minimum input. The objective of this study is to establish a design guide based on stiffness, displacement, and stresses for a generalized circular micro flexure hinge model using finite element method. Parametric study of a circular flexure hinge was performed using ABAQUS finite element code. The finite element results were compared with relevant analytical model from literature. Micro flexure hinge finite element models with selected range of dimensions for study were evaluated, and the optimal dimensions for flexure hinge design for maximum output displacement and minimum stresses were identified. From this study, the following parameters were established as design guide for a circular micro flexure hinge. With the width (w) of a circular flexure from 300 to 500μm range, our recommended flexure hinge height (h) is twice of the width, and the flexure hinge thickness ratio (b/t) is about 10.

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

1977 ◽  
Vol 5 (2) ◽  
pp. 102-118 ◽  
Author(s):  
H. Kaga ◽  
K. Okamoto ◽  
Y. Tozawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Temperature Rise ◽  
Strain Energy ◽  
Internal Stresses ◽  
Vertical Load ◽  
The Finite Element Method ◽  
Internal Temperature ◽  
Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

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