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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...
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of 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...
Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress...
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...

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Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires
08:46

Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires

Published on: July 24, 2018

A new generalized model for elliptical arc flexure hinges.

Guimin Chen1, Xiaodong Shao, Xinbo Huang

  • 1School of Mechatronics, Xidian University, Xi'an, Shaanxi 710071, People's Republic of China. gmchen@mail.xidian.edu.cn

The Review of Scientific Instruments
|December 3, 2008
PubMed
Summary
This summary is machine-generated.

Engineers can now use a new generalized model for elliptical arc flexure hinges. This model simplifies the design of precision hinges by unifying various profiles into a single, adaptable solution.

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Area of Science:

  • Mechanical Engineering
  • Materials Science
  • Precision Engineering

Background:

  • Flexure hinges are crucial for high-precision and sensitive engineering applications.
  • Existing flexure hinge designs often use specific profiles, limiting adaptability.
  • A unified design approach is needed to streamline the selection and parameterization of flexure hinges.

Purpose of the Study:

  • To develop a generalized closed-form solution for flexure hinge design.
  • To unify circular, right-circular, and elliptical flexure hinge profiles.
  • To provide a versatile model for hinge profile selection and parameter design.

Main Methods:

  • Proposed a generalized elliptical arc flexure hinge model (0 <= phi(m) <= pi/2).
  • Derived compliance matrix elements using mechanics of materials and an eccentric angle integral variable.
  • Reduced compliance calculations to four fundamental integrals.

Main Results:

  • Developed generalized compliance equations applicable to elliptical arc, elliptical, circular, and right-circular hinges.
  • The derived equations simplify compliance calculations significantly.
  • Validated the generalized equations against finite element analysis, existing equations, and experimental data.

Conclusions:

  • The proposed generalized elliptical arc flexure hinge model offers a concise and adequate solution for diverse engineering designs.
  • This unified approach benefits hinge design by simplifying profile selection and parameterization.
  • The model's accuracy and versatility are confirmed through rigorous validation.