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Related Concept Videos

Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...
Bending of Curved Members - Strain Analysis01:14

Bending of Curved Members - Strain Analysis

The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member is the...
Bending of Curved Members - Neutral Surface01:16

Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...
Flexural Stress01:16

Flexural Stress

When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
Hooke's Law states that within the material's elastic limits, stress is directly proportional to strain. In a member experiencing a bending moment, the strain at any point is relative to its distance...
Unsymmetric Bending01:18

Unsymmetric Bending

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The orientation of the...

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Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
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Published on: February 4, 2013

Tractable model for concave flexure hinges.

Yakov Tseytlin1

  • 1International Society of Automation, Providence, Rhode Island 02904, USA. yakovtseyt@aol.com

The Review of Scientific Instruments
|February 2, 2011
PubMed
Summary
This summary is machine-generated.

Approximate solutions for flexure notch hinges demonstrate high accuracy, comparable to complex methods. Simple computer-aided evaluations provide reliable hinge rotation analysis within 10% uncertainty.

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Area of Science:

  • Mechanical Engineering
  • Solid Mechanics
  • Compliance Analysis

Background:

  • Flexure notch hinges are critical components in precision mechanisms.
  • Accurate modeling of their rotational compliance is essential for reliable performance.
  • Existing precision solutions often involve complex mathematical and computational approaches.

Purpose of the Study:

  • To validate the accuracy of previously developed approximate solutions for concave flexure notch hinges.
  • To introduce a simplified computer-aided method for evaluating hinge rotational compliance.
  • To compare the accuracy of approximate solutions against complex precision methods.

Main Methods:

  • Application of inverse conformal mapping for approximate solution development.
  • Development of a computer-aided evaluation for approximating circles and their positional shifts.
  • Estimation of the instantaneous center of rotation for the hinge.
  • Comparison with solutions derived from differential equations, finite element models, and experimental data.

Main Results:

  • Approximate solutions achieve accuracy within 10% uncertainty compared to precision solutions.
  • The simplified computer-aided evaluation provides reliable results without requiring analytical expressions.
  • The method accurately estimates the hinge rotation instantaneous center position.

Conclusions:

  • The validated approximate solutions offer a practical and accurate alternative for analyzing flexure notch hinge compliance.
  • The developed computer-aided method simplifies the analysis process while maintaining high accuracy.
  • These findings facilitate more efficient design and analysis of compliant mechanisms.