Torsional stiffness of several variable rectangular cross-section flexure hinges for macro-scale and MEMS applications

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.

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Thrust Force Modeling of the Flagella-Like Swimming Micro-Robot

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.461.930 ◽

2013 ◽

Vol 461 ◽

pp. 930-941

Author(s):

Ling Wang ◽

Bai Chen ◽

Peng Wang ◽

Sun Chen ◽

Qian Yun Zhu ◽

...

Keyword(s):

Mechanical Properties ◽

Cross Section ◽

Thrust Force ◽

Rectangular Cross Section ◽

Helix Angle ◽

Simulation Data ◽

Force Modeling ◽

Macro Scale ◽

Micro Robot ◽

Resistive Force Theory

In this paper, helix tails with rectangular cross-section were designed for propelling a kind of flagella-like swimming robot. CFD (Computational Fluid Dynamics) software was applied to analyze the major influencing factors of the robots mechanical properties. It is revealed that the thrust reaches the maximum when the helix tails cross-section width is 0.36 times the diameter. Meanwhile, the helix tails should be designed according to the requirements with the largest diameter, close to but less than 45° helix angle and multi-turns under the limitation of the workspace. Combining these simulation data with the derivation process of Resistive Force Theory, the models for the mechanical properties simulation of the swimming robot were revised, and the explicit empirical formula of propulsive force is obtained. This model lays a good foundation for the robots motion control as well as unified mathematical description for macro-scale and micro-scale robots.

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The test bench for testing torsional stiffness of active anti-roll bar made of extended profiles with rectangular cross-section

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/148/1/012018 ◽

2016 ◽

Vol 148 ◽

pp. 012018

Author(s):

K R Macikowski ◽

S Kaszuba

Keyword(s):

Cross Section ◽

Test Bench ◽

Rectangular Cross Section ◽

Torsional Stiffness

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Why Is (111) Silicon a Better Mechanical Material for MEMS: Torsion Case

Microelectromechanical Systems ◽

10.1115/imece2003-41869 ◽

2003 ◽

Cited By ~ 3

Author(s):

Donghun Kwak ◽

Jongpal Kim ◽

Sangjun Park ◽

Hyoungho Ko ◽

Dong-Il Cho

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Cross Section ◽

Rectangular Cross Section ◽

Silicon Wafers ◽

Torsional Stiffness ◽

Rotational Inertia ◽

The Finite Element Method ◽

Element Type ◽

Simulation Results

This paper shows that using the Finite Element Method (FEM), the torsional stiffness of silicon varies by the least amount on silicon (111) with respect to crystallographic directions, when compared to silicon (100) and (110). The used simulator is ANSYS 5.7 with the element type of Solid 64. As a simulation model, we use a simple torsion system, in which a rotational inertia is attached to the center of clamped-clamped beam with a rectangular cross-section. From the results of the modal analysis, the torsional stiffness is derived using the formula between the natural frequency and the torsional stiffness. Simulation results show that the maximum variations of the torsional stiffness on silicon (111), (100) and (110) are 2.3%, 26.5%, and 31.2%, respectively. This implies that on <100> and <110> silicon wafers, substantially different physical dimensions are necessary for devices with the same torsional characteristics, but with different orientations. Therefore, <111> silicon wafers represent a more suitable substrate to design and fabricate torsional micro and nano systems.

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Empirical Compliance Equations for Constant Rectangular Cross Section Flexure Hinges and Their Applications

Mathematical Problems in Engineering ◽

10.1155/2016/5602142 ◽

2016 ◽

Vol 2016 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Tiemin Li ◽

Yunsong Du ◽

Yao Jiang ◽

Jinglei Zhang

Keyword(s):

Finite Element ◽

Stress Concentration ◽

Cross Section ◽

Rectangular Cross Section ◽

Great Influence ◽

Exponential Model ◽

Geometrical Parameters ◽

Element Analysis ◽

Flexure Hinges ◽

Wide Range

This paper presents the derivation of empirical compliance equations of the constant rectangular cross section flexure hinge. The stress concentration caused by changes in cross section is analyzed based on finite element analysis results for the purpose of overcoming compliance calculation errors. It shows that the stress concentration has great influence on axial compliance calculation, while it has little influence on shear and bending compliance calculation. Then empirical compliance equations with a relative wide range ofh/Landt/Lare derived based on the exponential model in conjunction with consideration of all geometrical parameters of flexure hinges and the influence of the stress concentration on axial compliance calculation. Finally, in order to verify the validity of the empirical equations, the input/output compliance and displacement amplification ratios of bridge-type microdisplacement amplification mechanisms are analyzed. Meanwhile, an experimental platform of displacement amplification mechanisms is set up. The experimental results and finite element method (FEM) values are in good agreement with the theoretical arithmetic, which demonstrates the accuracy of the empirical compliance equations. It provides a reference point for further studies on the design and optimization of flexure hinges and compliant mechanisms.

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