A Generalized Constraint Model for Two-Dimensional Beam Flexures

2009 ◽  
Author(s):  
Shorya Awtar ◽  
Shiladitya Sen
Keyword(s):  
Two Dimensional ◽  
Finite Elements Analysis ◽  
Beam Shape ◽  
Qualitative And Quantitative ◽  
Flexure Mechanism ◽  
Elastic Load ◽  
Quantitative Understanding ◽  
Constraint Model ◽  
Generalized Constraint ◽  
Displacement Model

To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop a qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates any general loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified extensively by non-linear Finite Elements Analysis.

A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Shorya Awtar ◽  
Shiladitya Sen
Keyword(s):  
Two Dimensional ◽  
Finite Elements Analysis ◽  
Nonlinear Load ◽  
Beam Shape ◽  
Flexure Mechanism ◽  
Elastic Load ◽  
Nonlinear Finite Elements ◽  
Wide Range ◽  
Load Displacement ◽  
Constraint Model

To utilize beam flexures in constraint-based flexure mechanism design, it is important to develop qualitative and quantitative understanding of their constraint characteristics in terms of stiffness and error motions. This paper provides a highly generalized yet accurate closed-form parametric load-displacement model for two-dimensional beam flexures, taking into account the nonlinearities arising from load equilibrium applied in the deformed configuration. In particular, stiffness and error motions are parametrically quantified in terms of elastic, load-stiffening, kinematic, and elastokinematic effects. The proposed beam constraint model incorporates a wide range of loading conditions, boundary conditions, initial curvature, and beam shape. The accuracy and effectiveness of the proposed beam constraint model is verified by nonlinear finite elements analysis.

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.

Nonlinear Constraint Model for Symmetric Three-Dimensional Beams

2010 ◽  
Author(s):  
Shiladitya Sen ◽  
Shorya Awtar
Keyword(s):  
Three Dimensional ◽  
Practical Interest ◽  
Nonlinear Constraint ◽  
Element Analysis ◽  
Flexure Mechanism ◽  
Spatial Beam ◽  
Non Linear ◽  
Simplifying Assumptions ◽  
Non Linear Load ◽  
Constraint Model

The constraint-based design of flexure mechanisms requires a qualitative and quantitative understanding of the constraint characteristics of flexure elements that serve as constraints. This paper presents the constraint characterization of a slender, uniform and symmetric cross-section, spatial beam, which is one of the most basic flexure elements used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the non-linear load-displacement relations of the beam. Appropriate simplifying assumptions are made in deriving these relations so that relevant non-linear effects (load-stiffening, kinematic, and elastokinematic) are captured in a compact, closed-form, and parametric manner. The resulting spatial beam constraint model is shown to be accurate, using non-linear finite element analysis, within a load and displacement range of practical interest. The utility of this model lies in the physical and analytical insight that it offers into the constraint behavior of a spatial beam flexure, its use in 3D flexure mechanism geometries, and fundamental performance tradeoffs in flexure mechanism design.

scholarly journals Use of the transpiration method to study polonium evaporation from liquid lead-bismuth eutectic at high temperature

2014 ◽  
Vol 102 (12) ◽  
Author(s):  
Borja Gonzalez Prieto ◽  
Alessandro Marino ◽  
Jun Lim ◽  
Kris Rosseel ◽  
Johan Martens ◽  
...  
Keyword(s):  
Liquid Lead ◽  
Driven Systems ◽  
Qualitative And Quantitative ◽  
Transpiration Method ◽  
Equilibrium And Kinetics ◽  
Quantitative Understanding ◽  
Safety Assessments ◽  
Lead Bismuth Eutectic ◽  
Accelerator Driven Systems ◽  
Kinetics Of

AbstractQualitative and quantitative understanding of Po volatilization under different conditions is of key importance for safety assessments of lead-bismuth eutectic (LBE) based nuclear reactors, spallation targets and accelerator driven systems. In this work we explore the possibilities of the transpiration method in combination with simple models to study the equilibrium and kinetics of Po evaporation from highly diluted solutions in lead-bismuth eutectic between 600 and 1000 ℃ in Ar/5% H

Fixed-wing approach techniques for complex environments

2015 ◽  
Vol 119 (1218) ◽  
pp. 999-1016
Author(s):  
P. R. Thomas ◽  
S. Bullock ◽  
U. Bhandari ◽  
T. S. Richardson
Keyword(s):  
Complex Environments ◽  
Flight Tests ◽  
Qualitative And Quantitative ◽  
Alternative Approach ◽  
Potential Benefits ◽  
Quantitative Understanding ◽  
Control Authority ◽  
The Stability ◽  
Glide Slope ◽  
Space Requirements

AbstractThe landing approach for fixed-wing small unmanned air vehicles (SUAVs) in complex environments such as urban canyons, wooded areas, or any other obscured terrain is challenging due to the limited distance available for conventional glide slope descents. Alternative approach methods, such as deep stall and spin techniques, are beneficial for such environments but are less conventional and would benefit from further qualitative and quantitative understanding to improve their implementation. Flight tests of such techniques, with a representative remotely piloted vehicle, have been carried out for this purpose and the results are presented in this paper. Trajectories and flight data for a range of approach techniques are presented and conclusions are drawn as to the potential benefits and issues of using such techniques for SUAV landings. In particular, the stability of the vehicle on entry to a deep stall was noticeably improved through the use of symmetric inboard flaps (crow brakes). Spiral descent profiles investigated, including spin descents, produced faster descent rates and further reduced landing space requirements. However, sufficient control authority was maintainable in a spiral stall descent, whereas it was compromised in a full spin.

Elastic Averaging in Flexure Mechanisms: A Three-Beam Parallelogram Flexure Case Study

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Shorya Awtar ◽  
Kevin Shimotsu ◽  
Shiladitya Sen
Keyword(s):  
Improve Performance ◽  
Mathematical Basis ◽  
Element Analysis ◽  
Redundant Constraints ◽  
Flexure Mechanism ◽  
Design Paradigm ◽  
Constraint Model ◽  
Effective Use ◽  
Exact Constraint

Redundant constraints are generally avoided in mechanism design because they can lead to binding or loss in expected mobility. However, in certain distributed-compliance flexure mechanism geometries, this problem is mitigated by the phenomenon of elastic averaging. Elastic averaging is a design paradigm that, in contrast with exact constraint design principles, makes deliberate and effective use of redundant constraints to improve performance and robustness. The principle of elastic averaging and its advantages are illustrated in this paper by means of a three-beam parallelogram flexure mechanism, which represents an overconstrained geometry. In a lumped-compliance configuration, this mechanism is prone to binding in the presence of nominal manufacturing and assembly errors. However, with an increasing degree of distributed-compliance, the mechanism is shown to become more tolerant to such geometric imperfections. The nonlinear elastokinematic effect in the constituent beams is shown to play an important role in analytically predicting the consequences of overconstraint and provides a mathematical basis for elastic averaging. A generalized beam constraint model is used for these predictions so that varying degrees of distributed compliance are captured using a single geometric parameter. The closed-form analytical results are validated against finite element analysis, as well as experimental measurements.

Sign in / Sign up

Export Citation Format

Share Document