Closed-Form Nonlinear Analysis of Beam-Based Flexure Modules

2005 ◽  
Author(s):  
Shorya Awtar ◽  
Alexander H. Slocum
Keyword(s):  
Closed Form ◽  
Element Analysis ◽  
Beam Shape ◽  
Form Analysis ◽  
Motion Range ◽  
Stiffness Variation ◽  
Module Geometry ◽  
Moderate Complexity ◽  
Analytical Tools ◽  
Force Displacement

The simple beam acts as a constraint element when used in flexure mechanisms. Non-linearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms typically suffer from performance tradeoffs in terms of motion range, accuracy and stiffness. This paper presents simple yet accurate approximations that capture this non-linearity and allow for the closed-form analysis of flexure mechanisms of moderate complexity. These general analytical tools enable a designer to parametrically predict key performance parameters of a conceived mechanism such as mobility, over-constraint, stiffness variation, and error motions, without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations are used in deriving the closed-form force-displacement characteristics of several important beam-based flexure modules, and the results are validated using Finite Element Analysis. Variations in the beam shape and flexure module geometry are also considered analytically.

Characteristics of Beam-Based Flexure Modules

2006 ◽  
Vol 129 (6) ◽  
pp. 625-639 ◽  
Author(s):  
Shorya Awtar ◽  
Alexander H. Slocum ◽  
Edip Sevincer
Keyword(s):  
Finite Element Analysis ◽  
Analytical Framework ◽  
Equilibrium Conditions ◽  
Element Analysis ◽  
Flexure Mechanism ◽  
Important Constraint ◽  
Motion Range ◽  
Stiffness Variation ◽  
Force Displacement ◽  
Force Equilibrium

The beam flexure is an important constraint element in flexure mechanism design. Nonlinearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms suffer from performance tradeoffs in terms of motion range, accuracy and stiffness, while benefiting from elastic averaging. This paper presents simple yet accurate approximations that capture the effects of load-stiffening and elastokinematic nonlinearities in beams. A general analytical framework is developed that enables a designer to parametrically predict the performance characteristics such as mobility, over-constraint, stiffness variation, and error motions, of beam-based flexure mechanisms without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations and analysis approach are used in deriving the force–displacement relationships of several important beam-based flexure constraint modules, and the results are validated using finite element analysis. Effects of variations in shape and geometry are also analytically quantified.

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 Linear Closed-form Solution and Finite-element Analysis of an Active Tensegrity Unit

2012 ◽  
Vol 7 (2) ◽  
pp. 71-78
Author(s):  
Stanislav Kmeť ◽  
Peter Platko
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Cable System ◽  
Element Analysis ◽  
Form Analysis ◽  
Tensile Forces

Abstract Results of the linear closed form solution of an active or adaptive tensegrity unit, as well as its numerical analysis using finite element method are presented in the paper. The shape of the unit is an octahedral cell with a square base and it is formed by thirteen members (four bottom and four top cables, four edge struts and one central strut). The central strut is designed as an actuator that allows for an adjustment of the shape of the unit which leads to changes of tensile forces in the cables. Due to the diagonal symmetry of the 3D tensegrity unit the closed-form analysis is based on the 2D solution of the equivalent planar biconvex cable system with one central strut under a vertical point load.

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 Analysis for Wrinkling Behavior of Girth-Welded Line Pipe

1996 ◽  
Author(s):  
Luiz T. Souza ◽  
David W. Murray
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Element Model ◽  
Internal Pressure ◽  
Experimental Test ◽  
Element Model ◽  
Element Analysis ◽  
Line Pipe ◽  
New Era ◽  
Analytical Tools

The paper presents results for finite element analysis of full-sized girth-welded specimens of line pipe and compares these results with the behavior exhibited by test specimens subjected to constant axial force, internal pressure and monotonically increasing curvatures. Recommendations for the ‘best’ type of analytical finite element model are given. Comparisons between the behavior predicted analytically and the observed behavior of the experimental test specimens are made. The mechanism of wrinkling is explained and the evolution of the deformed configurations for different wrinkling modes is examined. It is concluded that the analytical tools now available are sufficiently reliable to predict the behavior of pipe in a manner that was not previously possible and that this should create a new era for the design and assessment of pipelines if the technology is properly exploited by industry.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

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