Stiffness analysis of corrugated flexure beam using stiffness matrix method

2018 ◽  
Vol 233 (5) ◽  
pp. 1818-1827 ◽  
Author(s):  
Nianfeng Wang ◽  
Zhiyuan Zhang ◽  
Xianmin Zhang
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Beam Theory ◽  
Analytical Models ◽  
The Finite Element Method ◽  
Compliance Matrix ◽  
Stiffness Analysis ◽  
Compliance Matrix Method ◽  
Euler Bernoulli Beam ◽  
The Relationship

Precision positioning techniques present a significant opportunity to support the instrumentation development for state-of-the-art micro-positioning research. The requirement of large stroke and high resolution of the mechanism without a need for amplifier mechanisms is universally recognized. Corrugated flexure beam can have some potential if designed right because of its large flexibility obtained from longer overall length on the same span. This paper presents stiffness analysis of corrugated flexure beam using stiffness or compliance matrix method. Based on Euler–Bernoulli beam theory and Mohr’s integral method, the deformation analyses of straight segment and semi-circle segment are presented. And the stiffness matrix of corrugated flexure unit is then obtained via transformation matrix. By combining the stiffness matrix of every single corrugated flexure unit, the stiffness matrix of corrugated flexure beam is delivered, which reflects the relationship between the load and displacement. The analytical models are verified by taking advantage of the finite element method, which shows that all the results can be of considerable use in the design of corrugated flexure beam.

Matrix Method for Buckling Analysis of Frames Based on Hencky Bar-Chain Model

2019 ◽  
Vol 19 (08) ◽  
pp. 1950093 ◽  
Author(s):  
W. H. Pan ◽  
C. M. Wang ◽  
H. Zhang
Keyword(s):  
Matrix Method ◽  
Structural Changes ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Chain Model ◽  
Bernoulli Beam ◽  
Various Boundary Conditions ◽  
End Restraint ◽  
Euler Bernoulli Beam ◽  
General Frames

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems.

The design and kinetostatic modeling of 3PPR planar compliant parallel mechanism based on compliance matrix method

2019 ◽  
Vol 90 (4) ◽  
pp. 045102 ◽  
Author(s):  
Hongtao Yu ◽  
Chi Zhang ◽  
Bao Yang ◽  
Si-Lu Chen ◽  
Zaojun Fang ◽  
...  
Keyword(s):  
Matrix Method ◽  
Parallel Mechanism ◽  
Compliance Matrix ◽  
Compliant Parallel Mechanism ◽  
Compliance Matrix Method

Optimal plane beams modelling elastic linear objects

Robotica ◽  
2009 ◽  
Vol 28 (1) ◽  
pp. 135-148 ◽  
Author(s):  
Sung K. Koh ◽  
Guangjun Liu
Keyword(s):  
Motion Planning ◽  
Analytical Model ◽  
Cantilever Beam ◽  
Inverse Kinematics ◽  
Beam Theory ◽  
Analytical Models ◽  
Bernoulli Beam ◽  
Deterministic Models ◽  
Bernoulli Beam Theory ◽  
Euler Bernoulli Beam

SUMMARYThis paper discusses analytical and deterministic models for a plane curve with minimum deformation that may be utilized in planning the motion of elastic linear objects and investigating the inverse kinematics of a hyper-redundant robot. It usually requires intensive computation to determine the configuration of elastic linear objects. In addition, conventional optimization-based numerical techniques that identify the shape of elastic linear objects in equilibrium involve non-deterministic aspects. Several analytical models that produce the configuration of elastic linear objects in an efficient and deterministic manner are presented in this paper. To develop the analytical expressions for elastic linear objects, we consider a cantilever beam where the deflections are determined according to the Euler–Bernoulli beam theory. The deflections of the cantilever beam are determined for prescribed constraints imposed on the deflections at the free end to replicate various elastic linear objects. Deflections of a cantilever beam with roller supports are explored to replicate elastic linear objects in contact with rigid objects. We verify the analytical models by comparing them with exact beam deflections. The analytical model is precisely accurate for beams with small deflections as it is developed on the basis of the Euler–Bernoulli beam theory. Although it is applied to beams undergoing large deflections, it is still reasonably accurate and at least as precise as the conventional pseudo-rigid-body model. The computational demand involved in using the analytical models is negligible. Therefore, efficient motion planning for elastic linear objects can be realized when the proposed analytical models are combined with conventional motion planning algorithms. We also demonstrate that the analytical model solves the inverse kinematics problem in an efficient and robust manner through numerical simulations.

Three-dimensional flexural-joint stiffness analysis of flexible manipulator arms

Robotica ◽  
1988 ◽  
Vol 6 (3) ◽  
pp. 203-212 ◽  
Author(s):  
A. Meghdari ◽  
M. Shahinpoor
Keyword(s):  
Stiffness Matrix ◽  
Three Dimensional ◽  
Joint Stiffness ◽  
Beam Theory ◽  
Flexible Manipulator ◽  
Robotic Arm ◽  
Flexible Robot ◽  
Stiffness Analysis ◽  
Stiffness Matrices ◽  
Stiffness Properties

SUMMARYThis paper presents a complete derivation of the combined flexural-joint stiffness matrix and the elastic deformation field of flexible manipulator arms treated in a three-dimensional fashion. The stiffness properties are derived directly from the differential equations used in the engineering beam theory. The expressions developed here can readily be used in the modeling, control and design of light weight flexible robot manipulators. A two-link arm is used to formulate these expressions and the results can be generalized to n–link manipulators. The stiffness matrix for a robotic link element in 3-D is of the order of 12 X 12, and for an n–link robotic arm the total elemental and system stiffness matrices will be of the order of the (12n X 12n) and 6(n + 1) X 6(n + 1), respectively.

Free Vibration Analysis of Frames Using the Transfer Dynamic Stiffness Matrix Method

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Tsung-Hsien Tu ◽  
Jen-Fang Yu ◽  
Hsin-Chung Lien ◽  
Go-Long Tsai ◽  
B. P. Wang
Keyword(s):  
Free Vibration ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
System Matrix ◽  
Dynamic Stiffness Matrix ◽  
3D Space ◽  
Euler Bernoulli Beam ◽  
Good Agreement

A method for free vibration of 3D space frame structures employing transfer dynamic stiffness matrix (TDSM) method based on Euler–Bernoulli beam theory is developed in this paper. The exact TDSM of each member is assembled to obtain the system matrix that is frequency dependent. All free vibration eigensolutions including coincident roots for the characteristic equation can be obtained to any desired accuracy using the algorithm developed by Wittrick and Williams (1971, “A General Algorithm for Computing Natural Frequencies of Elastic Structures,” Q. J. Mech. Appl. Math., 24, pp. 263–284). Exact eigenfunction of structures can then be computed using the dynamic shape function and the corresponding eigenvector. The results showed good agreement with those computed by finite element method.

Vibration Analysis of Linear Beam With Moving Loads Based on Riccati Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Lu Sun ◽  
Xue Rui ◽  
Dieter Bestle ◽  
Guoping Wang ◽  
Jianshu Zhang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Mode Shapes ◽  
Moving Loads ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

The paper presents the dynamic response of an Euler-Bernoulli beam supported by an elastic foundation and subjected to a moving step load. The Riccati transfer matrix method for linear multibody systems (Riccati MSTMM) is employed to find eigenfrequencies and mode shapes of the supported beam. A comparison of results obtained with the finite element method (FEM) indicates that the Riccati MSTMM is more accurate when using the same number segments. Based on these results, the dynamic response of the beam with moving step load is investigated for different propagation velocities by mode superposition, and the effect of loads is discussed.

Stiffness Analysis for a Novel Parallel-Robot Based High-Precision Flexible Assembly Fixture

2007 ◽  
Vol 364-366 ◽  
pp. 327-332 ◽  
Author(s):  
Hong Jian Yu ◽  
Bing Li ◽  
Xiao Jun Yang ◽  
Ying Hu ◽  
Hong Hu
Keyword(s):  
Stiffness Matrix ◽  
Screw Theory ◽  
System Modeling ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Stiffness Analysis ◽  
Flexible Assembly ◽  
Global Stiffness Matrix ◽  
The Relationship ◽  
Assembly Fixture

In this paper, a novel parallel mechanism (3-RRRS/UPR) used in flexible fixture with configuration composed of two parallel robots (2-RR and 3-RRRS/ UPR) is presented. First, system modeling including the mobility study is conducted. Then a novel methodology is proposed that makes use of screw theory to analyze the deformation and stiffness of the mechanism: firstly we identified the existence of the deformation of the subchain, in terms of the relationship between the effective screw and deformation screw; then we took the deformation as an infinitesimal motion of the mechanism, and the stiffness matrix corresponding to the deformation can be deduced. Finally the global stiffness matrix of the whole mechanism is modeled by assembling different stiffness characters based on the presented methodology.

Static characteristics of thermohydrodynamic journal bearing operating under lubricants containing nanoparticles

2015 ◽  
Vol 67 (1) ◽  
pp. 38-46 ◽  
Author(s):  
Sreedhar Babu Kalakada ◽  
Prabhakaran Nair Nair Kumarapillai ◽  
Rajendra Kumar P K
Keyword(s):  
Temperature Distribution ◽  
Journal Bearing ◽  
Performance Characteristics ◽  
Analytical Models ◽  
The Finite Element Method ◽  
Content Type ◽  
Weight Concentration ◽  
Static Performance ◽  
Energy Equations ◽  
The Relationship

Purpose – The purpose of this work is to investigate the static performance characteristics of thermohydrodynamic journal bearing operating under nanolubricants (lubricants containing per cent weight concentration of nanoparticles). Design/methodology/approach – Addition of nanoparticles in the lubricant increases lubricant viscosity. To study the effect of this variation on journal bearing, analytical models are developed for the relationship between viscosity, 0-0.5 per cent weight concentration of nanoparticles and temperature range of 300-900°C. To obtain pressure and temperature distribution, modified Reynolds and energy equations are solved by using the finite element method. The viscosity field (varies with temperature and per cent weight concentration of nanoparticles) is updated in these two equations by using the developed analytical model. The steady-state performance characteristics are computed for various values of eccentricity ratios for non-thermoviscous (viscosity of lubricant varies with per cent weight concentration of nanoparticles) and thermoviscous (viscosity of lubricant varies with per cent weight concentration of nanoparticles and temperature) cases. The lubricant and the nanoparticles used for the present work are SAE15W40, copper oxide (CuO), cerium oxide (CeO2) and aluminum oxide (Al2O3). Findings – The pressure and temperature distribution across the lubricant film in the clearance space of journal bearing and static performance characteristics are calculated. Originality/value – The computed results show that addition of nanoparticles in the lubricant influences the performance characteristics considerable in thermoviscous case than non-thermoviscous case.

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