Analytical Compliance Analysis and Synthesis of Flexure Mechanisms

2011 ◽  
Author(s):  
Hai-Jun Su ◽  
Hongliang Shi ◽  
JingJun Yu
Keyword(s):  
Design Method ◽  
External Loading ◽  
Motion Direction ◽  
Compliance Matrix ◽  
Flexure Mechanism ◽  
Physical Experiments ◽  
Stiffness Matrices ◽  
Analysis And Synthesis ◽  
Flexure Joints ◽  
Robust Design Method

This paper presents a symbolic formulation for analytical compliance analysis and synthesis of flexure mechanisms with arbitrary topologies. Compliance analysis or mapping is to determine the relationship between the deformation of a mechanism and the external loading applied. It is a crucial step for the control and design of flexure mechanisms. Most of the current work relies on physical experiments or numerical simulations for studying the compliance or stiffness of flexure mechanisms. There is a lack of formal tools for the compliance synthesis whose goal is to determine the geometry of flexures or assembly of multiple flexures for a prescribed compliance in the motion direction of interest. In this work, we first derive a symbolic formulation of the compliance and stiffness matrices for commonly-used flexure elements, flexure joints and simple chains. Elements of these matrices are all explicit functions of flexure parameters. To analyze a complex flexure mechanism, we subdivide the mechanism into multiple structural modules which we identify as serial, parallel or hybrid chains. We then analyze each module with the known flexure structures in the library. At last we use a bottom-up approach to obtain the compliance matrix for the overall mechanism. Our symbolic formulation enables subsequent compliance synthesis or sensitivity analysis which is to determine how each flexure parameter affects the overall compliance of the mechanism. Four practical examples are provided to demonstrate the approach. The result is a robust design method for the compliance analysis and synthesis of flexure mechanisms.

scholarly journals A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Hai-Jun Su ◽  
Hongliang Shi ◽  
JingJun Yu
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Screw Theory ◽  
Element Model ◽  
Fe Model ◽  
Flexure Mechanism ◽  
Stiffness Matrices ◽  
Analysis And Synthesis ◽  
Flexure Joints

This paper presents a symbolic formulation for analytical compliance analysis and synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. Our approach is based on the screw theory that characterizes flexure deformations with motion twists and loadings with force wrenches. In this work, we first derive a symbolic formulation of the compliance and stiffness matrices for commonly used flexure elements, flexure joints, and simple chains. Elements of these matrices are all explicit functions of flexure parameters. To analyze a general flexure mechanism, we subdivide it into multiple structural modules, which we identify as serial, parallel, or hybrid chains. We then analyze each module with the known flexure structures in the library. At last, we use a bottom-up approach to obtain the compliance/stiffness matrix for the overall mechanism. This is done by taking appropriate coordinate transformation of twists and wrenches in space. Four practical examples are provided to demonstrate the approach. A numerical example is employed to compare analytical compliance models against a finite element model. The results show that the errors are sufficiently small (2%, compared with finite element (FE) model), if the range of motion is limited to linear deformations. This work provides a systematical approach for compliance analysis and synthesis of general flexure mechanisms. The symbolic formulation enables subsequent design tasks, such as compliance synthesis or sensitivity analysis.

A Compliance-Based Compensation Approach for Designing High-Precision Flexure Mechanism

2012 ◽  
Author(s):  
S. Z. Li ◽  
J. J. Yu ◽  
G. H. Zong ◽  
Hai-jun Su
Keyword(s):  
High Precision ◽  
Motion Compensation ◽  
Design Method ◽  
Flexure Mechanism ◽  
Parasitic Motion ◽  
Translation Error ◽  
Fea Simulation ◽  
Compensation Approach ◽  
Robust Design Method

This paper presents an approach of utilizing parasitic motion compensation for designing high-precision flexure mechanism. This approach is expected to improve the accuracy of flexure mechanism without changing its degree of freedom (DOF) characteristic. Different from the method which mainly concentrates on how to compensate the parasitic translation error of a parallelogram-type flexure mechanism existing in most of the literatures, the proposed approach can compensate the parasitic motion produced by rotation in company with translation. Besides, the parasitic motion of a flexure mechanism is formulated and evaluated by utilizing its compliance. To specify it, the compliance of a general flexure mechanism is calculated firstly. Then the parasitic motions introduced by both rotation and translation are analyzed by utilizing the resultant compliance. Subsequently, a compliance-based compensation approach is addressed as the most important part of this paper. The design principles and procedure are further proposed in detail to help with improving the accuracy of the flexure mechanism. Finally, a case study of a 2R1T flexure mechanism is provided to illustrate this approach, and FEA simulation is implemented to demonstrate its validity. The result shows that it is a robust design method for the design of high-precision flexure mechanism.

Design Optimization for a Parallel MEMS Mechanism With Flexure Joints

2004 ◽  
Author(s):  
Byoung Hun Kang ◽  
John T. Wen ◽  
Nicholas G. Dagalakis ◽  
Jason J. Gorman
Keyword(s):  
Performance Metrics ◽  
Design Method ◽  
Design Tool ◽  
Analysis Tool ◽  
Parallel Mechanisms ◽  
Analysis And Design ◽  
Design Variables ◽  
Stiffness Matrices ◽  
Flexure Joints ◽  
Task Specification

This paper presents an analysis tool and design method for MEMS parallel mechanisms. Due to processing constraints in MEMS fabrication, flexure joints are frequently used in MEMS mechanisms. Flexure joints offer advantages over other joint designs due to their monolithic characteristics. They can be used to reduce the size of manipulators or to increase the precision of motion. Their inherent flexibility, however, also results in task space compliance which needs to be carefully designed to match the task specification. This paper presents an analysis and design tool for such mechanisms by using the differential kinematics. Performance metrics are chosen based on manipulability and task stiffness matrices, which in turn are used in a multi-objective optimization. As an illustrative example, a 1-DOF MEMS parallel mechanism based on the macro- and meso-scale models designed by NIST is considered with several choices of performance metrics and design variables. The resulting designs are successfully fabricated using DRIE process.

ANALYSIS AND SYNTHESIS OF RADIATION PATTERNS FROM CIRCULAR APERTURES

1960 ◽  
Vol 38 (1) ◽  
pp. 78-99 ◽  
Author(s):  
A. Ishimaru ◽  
G. Held
Keyword(s):  
Radiation Pattern ◽  
Traveling Wave ◽  
Design Method ◽  
Source Distribution ◽  
Circular Aperture ◽  
Narrow Beam ◽  
Wave Type ◽  
Numerical Examples ◽  
Analysis And Synthesis ◽  
Improved Design

Part I considers the problem of determining the source distribution over a circular aperture required to produce a prescribed radiation pattern. In particular, the problem of optimizing the narrow broadside pattern from a circular aperture is discussed in detail and an improved design method over Taylor's for line source is devised. Numerical examples are given.Part II deals with the analysis of the radiation pattern from a circular aperture from γ1 to γ2 with the traveling wave type source functions. Expressions suitable to the analysis and the synthesis are obtained and the narrow-beam and shaped-beam synthesis are discussed.

An XYZ Parallel Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

2011 ◽  
Author(s):  
Shorya Awtar ◽  
John Ustick ◽  
Shiladitya Sen
Keyword(s):  
Degrees Of Freedom ◽  
Element Analysis ◽  
Motion Direction ◽  
Form Analysis ◽  
Flexure Mechanism ◽  
Non Linear ◽  
Decoupled Motion ◽  
Motion Range ◽  
Parallel Kinematic ◽  
Cross Axis

We present the constraint-based design of a novel parallel kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz). The geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via non-linear finite element analysis. A proof-of-concept prototype of the flexure mechanism is fabricated to validate its large range and decoupled motion capability. The analyses as well as the hardware demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the non-linear FEA predicts a cross-axis error of less than 3%, parasitic rotations less than 2 mrad, less than 4% lost motion, actuator isolation less than 1.5%, and no perceptible motion direction stiffness variation. Ongoing work includes non-linear closed-form analysis and experimental measurement of these error motion and stiffness characteristics.

scholarly journals Novel Robust Design Method of Multilayer Optical Coatings

ISRN Optics ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Suyong Wu ◽  
Xingwu Long ◽  
Kaiyong Yang
Keyword(s):  
Robust Design ◽  
Optimization Design ◽  
Design Method ◽  
Analytical Calculation ◽  
Design Procedure ◽  
Deposition Process ◽  
Practical Significance ◽  
Optical Coatings ◽  
Optical Films ◽  
Robust Design Method

We present a novel fast robust design method of multilayer optical coatings. The sensitivity of optical films to production errors is controlled in the whole optimization design procedure. We derive an analytical calculation model for fast robust design of multilayer optical coatings. We demonstrate its effectiveness by successful application of the robust design method to a neutral beam splitter. It is showed that the novel robust design method owns an inherent fast computation characteristic and the designed film is insensitive to the monitoring thickness errors in deposition process. This method is especially of practical significance to improve the mass production yields and repetitive production of high-quality optical coatings.

An XYZ Parallel-Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Shorya Awtar ◽  
John Ustick ◽  
Shiladitya Sen
Keyword(s):  
Degrees Of Freedom ◽  
Finite Elements Analysis ◽  
Motion Direction ◽  
Flexure Mechanism ◽  
Nonlinear Finite Elements ◽  
Decoupled Motion ◽  
Motion Range ◽  
Stiffness Variation ◽  
Parallel Kinematic ◽  
Cross Axis

A novel parallel-kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz) is presented. Geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via nonlinear finite elements analysis (FEA). A proof-of-concept prototype is fabricated to validate the predicted large range and decoupled motion capabilities. The analysis and the hardware prototype demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the nonlinear FEA predicts cross-axis errors of less than 7.8%, parasitic rotations less than 10.8 mrad, less than 14.4% lost motion, actuator isolation better than 1.5%, and no perceptible motion direction stiffness variation.

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

scholarly journals Strategic company management in the digital business environment

2018 ◽  
Vol 26 (3-4) ◽  
pp. 82-91
Author(s):  
Mykola Gennadiyovych Nikolaev
Keyword(s):  
Strategic Management ◽  
Industrial Revolution ◽  
Design Method ◽  
Business Environment ◽  
Future Research ◽  
Digital Environment ◽  
Doing Business ◽  
Analysis And Synthesis ◽  
Modern Business ◽  
The Impact

Purpose – to analyze strategic company management in the digital business environment. Design/Method/Approach. General scientific methods are applied: systematization, comparison, generalization, analysis, and synthesis. Findings. The essence of strategic management and its significance to a company has been analyzed. The relationship between strategic company management and digital business environment has been elucidated. Basic trends for doing business in the digital environment have been defined. Theoretical implications. Theoretical significance of the research is in the advancement of opinion on the strategic company management in digital business environment. Practical implications. The practical value of the research is in the possibility of applying the results obtained by both international and domestic companies for strategic management in the digital business environment that emerged as a result of the Fourth industrial revolution. Originality/Value. The main trends of modern business in the digital environment have been identified. The choice of strategies of multinational companies has been identified, as well as the areas of their application in digital business environment. Research limitations/Future research. The prospects for further research are to study the strategic management of international companies and analyze the impact of digital business environment on their development. Paper type – theoretical.

Robust Layout Synthesis of a MEM Crab-Leg Resonator Using a Constrained Genetic Algorithm

2007 ◽  
Author(s):  
Zhun Fan ◽  
Sofiane Achiche
Keyword(s):  
Genetic Algorithm ◽  
Robust Design ◽  
Optimization Problem ◽  
Design Method ◽  
Research Work ◽  
Constrained Optimization Problem ◽  
Geometric Uncertainties ◽  
Layout Synthesis ◽  
Target Performance ◽  
Robust Design Method

The research work carried out in this paper introduces a robust design method for layout synthesis of MEM resonator subject to inherent geometric uncertainties such as the fabrication error on the sidewall of the structure. The robust design problem is formulated as a multi-objective constrained optimization problem with certain assumptions and treated by a special constrained genetic algorithm. The MEM design used for validation is a crab-leg resonator taken from the literature. The results show that the approach proposed in this research can lead to design results that meet the target performance and are less sensitive to geometric uncertainties than typical designs.

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