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.

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.

A Closed-Form Nonlinear Model for the Constraint Characteristics of Symmetric Spatial Beams

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Shiladitya Sen ◽  
Shorya Awtar
Keyword(s):  
Closed Form ◽  
Virtual Work ◽  
Practical Interest ◽  
Element Analysis ◽  
Nonlinear Load ◽  
Flexure Mechanism ◽  
Spatial Beams ◽  
Spatial Beam ◽  
Load Displacement ◽  
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 uniform and symmetric cross-section, slender, spatial beam—a basic flexure element commonly used in three-dimensional flexure mechanisms. The constraint characteristics of interest, namely stiffness and error motions, are determined from the nonlinear load–displacement relations at the beam end. Appropriate assumptions are made while formulating the strain and strain energy expressions for the spatial beam to retain relevant geometric nonlinearities. Using the principle of virtual work, nonlinear beam governing equations are derived and subsequently solved for general end loads. The resulting nonlinear load–displacement relations capture the constraint characteristics of the spatial beam in a compact, closed-form, and parametric manner. This constraint model is shown to be accurate using nonlinear 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 design and optimization of 3D flexure mechanism geometries, and its elucidation of fundamental performance tradeoffs in flexure mechanism design.

scholarly journals An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

2015 ◽  
Author(s):  
Marijn Nijenhuis ◽  
J. P. Meijaard ◽  
Just L. Herder ◽  
Shorya Awtar ◽  
Dannis M. Brouwer
Keyword(s):  
Three Dimensional ◽  
Beam Element ◽  
Element Analysis ◽  
Cross Sectional ◽  
Flexure Mechanism ◽  
Stiffness Properties ◽  
Spatial Beam ◽  
Discrete Nature ◽  
Stiffness Characteristics

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

Comparison of Rheumatological Diagnoses by a Bayesian Program and by Physicians

1991 ◽  
Vol 30 (03) ◽  
pp. 187-193 ◽  
Author(s):  
H. J. Moens ◽  
J. K. van der Korst
Keyword(s):  
Receiver Operating Characteristics ◽  
Bayesian Decision ◽  
Operating Characteristics ◽  
Likelihood Ratios ◽  
Improve Performance ◽  
Mathematical Basis ◽  
Human Expert ◽  
Test Population ◽  
Sensitivity Specificity ◽  
Diagnostic Outcome

AbstractA Bayesian decision support system was developed for the diagnosis of rheumatic disorders. Knowledge in this system is represented as evidential weights of findings. Simple weights were calculated as the logarithm of likelihood ratios on the basis of 1,000 consecutive patients from a rheumatological clinic. The effect of various methods to improve performance of the system by modification of the weights was studied. Three methods had a mathematical basis; a fourth consisted of weights adapted by a human expert, which allowed inclusion of diagnostic rules such as defined in widely accepted criteria sets. The system’s performance was measured in a test population of 570 different cases from the same clinic and compared with predictions of diagnostic outcome made by rheumatologists. The weights from a human expert gave optimal results (sensitivity 65% and specificity 96%), that were close to the physicians’ predictions (sensitivity 64% and specificity 98%). The methods to measure the performance of the various models used in this study emphasize sensitivity, specificity and the use of receiver operating characteristics.

scholarly journals Ketamine-Assisted Psychotherapy for PTSD Related to Racial Discrimination

2021 ◽  
pp. 153465012199089
Author(s):  
Mailae Halstead ◽  
Sara Reed ◽  
Robert Krause ◽  
Monnica T. Williams
Keyword(s):  
Therapeutic Interventions ◽  
Traumatic Experiences ◽  
Social Avoidance ◽  
Functional Analytic Psychotherapy ◽  
Treatment Resistant ◽  
Psychotherapeutic Treatment ◽  
Presenting Symptoms ◽  
Self Talk ◽  
Effective Use

Current research suggests that ketamine-assisted psychotherapy has benefit for the treatment of mental disorders. We report on the results of ketamine-assisted intensive outpatient psychotherapeutic treatment of a client with treatment-resistant, posttraumatic stress disorder (PTSD) as a result of experiences of racism and childhood sexual abuse. The client’s presenting symptoms included hypervigilance, social avoidance, feelings of hopelessness, and intense recollections. These symptoms impacted all areas of daily functioning. Psychoeducation was provided on how untreated intergenerational trauma, compounded by additional traumatic experiences, potentiated the client’s experience of PTSD and subsequent maladaptive coping mechanisms. Ketamine was administered four times over a 13-day span as an off-label, adjunct to psychotherapy. Therapeutic interventions and orientations utilized were mindfulness-based cognitive therapy (MBCT) and functional analytic psychotherapy (FAP). New skills were obtained in helping the client respond effectively to negative self-talk, catastrophic thinking, and feelings of helplessness. Treatment led to a significant reduction in symptoms after completion of the program, with gains maintained 4 months post-treatment. This case study demonstrates the effective use of ketamine as an adjunct to psychotherapy in treatment-resistant PTSD.

The socio-spatial politics of royalties and their distribution: A case study of the Surat Basin, Queensland

2021 ◽  
pp. 0308518X2110266
Author(s):  
Neil Argent ◽  
Sean Markey ◽  
Greg Halseth ◽  
Laura Ryser ◽  
Fiona Haslam-McKenzie
Keyword(s):  
Cost Effective ◽  
Indigenous Communities ◽  
Energy Extraction ◽  
Grant Application ◽  
Coal Seam Gas ◽  
Spatial Politics ◽  
Developmental Needs ◽  
Development Fund ◽  
Effective Use

This paper is concerned with the socio-spatial and ethical politics of redistribution, specifically the allocation of natural resources rents from political and economic cores to the economic and geographical peripheries whence the resource originated. Based on a case study of the coal seam gas sector in Queensland's Surat Basin, this paper focuses on the operation of the Queensland State Government's regional development fund for mining and energy extraction-affected regions. Employing an environmental justice framework, we critically explore the operation of these funds in ostensibly helping constituent communities in becoming resilient to the worst effects of the ‘staples trap’. Drawing on secondary demographic and housing data for the region, as well as primary information collected from key respondents from mid-2018 to early 2019, we show that funds were distributed across all of the local government areas, and allocated to projects and places primarily on a perceived economic needs basis. However, concerns were raised with the probity of the funds’ administration. In terms of recognition justice, the participation of smaller and more remote towns and local Indigenous communities was hampered by their structural marginalisation. Procedurally, the funds were criticised for the lack of local consultation taken in the development and approval of projects. While spatially concentrated expenditure may be the most cost-effective use of public monies, we argue that grant application processes should be open, transparent and inclusive, and the outcomes cognisant of the developmental needs of smaller communities, together with the need to foster regional solidarity and coherence.

scholarly journals Behavior of Offshore Pile in Calcareous Sand—Case Study

2021 ◽  
Vol 9 (8) ◽  
pp. 839
Author(s):  
Tarek N. Salem ◽  
Nadia M. Elkhawas ◽  
Ahmed M. Elnady
Keyword(s):  
Load Capacity ◽  
High Stress ◽  
Embedment Depth ◽  
Shear Stresses ◽  
Northern Coast ◽  
Compression Tests ◽  
Calcareous Sand ◽  
Element Analysis ◽  
Mixing Ratios

The erosion of limestone and calcarenite ridges that existed parallel to the Mediterranean shoreline forms the calcareous sand (CS) formation at the surface layer of Egypt's northern coast. The CS is often combined with broken shells which are considered geotechnically problematic due to their possible crushability and relatively high compressibility. In this research, CS samples collected from a site along the northern coast of Egypt are studied to better understand its behavior under normal and shear stresses. Reconstituted CS specimens with different ratios of broken shells (BS) are also investigated to study the effect of BS ratios on the soil mixture strength behavior. The strength is evaluated using laboratory direct-shear and one-dimensional compression tests (oedometer test). The CS specimens are not exposed to significant crushability even under relatively high-stress levels. In addition, a 3D finite element analysis (FEA) is presented in this paper to study the degradation offshore pile capacity in CS having different percentages of BS. The stress–strain results using oedometer tests are compared with a numerical model, and it gave identical matching for most cases. The effects of pile diameter and embedment depth parameters are then studied for the case study on the northern coast. Three different mixing ratios of CS and BS have been used, CS + 10% BS, CS + 30% BS, and CS + 50% BS, which resulted in a decrease of the ultimate vertical compression pile load capacity by 8.8%, 15%, and 16%, respectively.

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

2006 ◽  
Author(s):  
Shorya Awtar ◽  
Edip Sevincer
Keyword(s):  
Mechanism Design ◽  
Parametric Model ◽  
Nonlinear Load ◽  
Geometric Imperfections ◽  
Geometric Imperfection ◽  
Flexure Mechanism ◽  
Important Concern ◽  
Proposed Model ◽  
Geometric Arrangements

Over-constraint is an important concern in mechanism design because it can lead to a loss in desired mobility. In distributed-compliance flexure mechanisms, this problem is alleviated due to the phenomenon of elastic averaging, thus enabling performance-enhancing geometric arrangements that are otherwise unrealizable. The principle of elastic averaging is illustrated in this paper by means of a multi-beam parallelogram flexure mechanism. In a lumped-compliance configuration, this mechanism is prone to over-constraint 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 load-stiffening and elasto-kinematic effects in the constituent beams have an important role to play in the over-constraint and elastic averaging characteristics of this mechanism. Therefore, a parametric model that incorporates these nonlinearities is utilized in predicting the influence of a representative geometric imperfection on the primary motion stiffness of the mechanism. The proposed model utilizes a beam generalization so that varying degrees of distributed compliance are captured using a single geometric parameter.

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